nanoelectronics - Institut d'Études Scientifiques de Cargèse (IESC)
nanoelectronics - Institut d'Études Scientifiques de Cargèse (IESC)
nanoelectronics - Institut d'Études Scientifiques de Cargèse (IESC)
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
2012<br />
22 Octobre<br />
27 Octobre<br />
WORKSHOP<br />
« NANOELECTRONICS:<br />
CONCEPTS,<br />
THERORY AND MODELLING »<br />
Jean‐Louis PICHARD<br />
IRAMIS / SPEC<br />
CEA ‐ Saclay<br />
91191 Gif sur Yvette<br />
0169087236<br />
jean‐louis.pichard@cea.frz<br />
Direction scientifique :<br />
Giovanna Chimini<br />
Contact :<br />
Dominique Donzella<br />
tél : 04 95 26 80 40<br />
www.iesc.univ-corse.fr
Nanoelectronics:<br />
Concepts, Theory and Mo<strong>de</strong>ling<br />
Network meeting<br />
and<br />
workshop on<br />
thermoelectric transport<br />
Program and Abstracts<br />
21-27 October 2012<br />
<strong>Cargèse</strong>, Corsica
Afternoon<br />
Morning<br />
Timetable<br />
Monday Tuesday Wednesday Thursday Friday<br />
09:00 Pichard<br />
09:15 Benenti<br />
09:55 Imry<br />
11:00 Coffee<br />
11:30 Saito<br />
09:00 Beenakker<br />
09:45 Molenkamp<br />
10:50 Coffee<br />
11:20 Narayan<br />
12:05 Fleury<br />
08:45 Georges<br />
09:50 Benenti<br />
10:30 Coffee<br />
11:00 Volz<br />
11:40 Round<br />
Table<br />
09:00 Heiblum<br />
10:05 Dolcetto<br />
10:25 Coffee<br />
10:55 Kotetes<br />
11:25 Diez<br />
11:55 Pikulin<br />
09:00 Edge<br />
09:30 Tworzydlo<br />
10:00 Chakraborty<br />
10:15 Coffee<br />
10:45 Raimondi<br />
11:15 Ochoa<br />
11:30 Weick<br />
12:00 Peterfalvi<br />
14:30 Pekola<br />
15:35 Schön<br />
16:15 Coffee<br />
16:40 Bourgeois<br />
17:20 Moskalets<br />
14:30 R Sánchez<br />
15:10 D Sánchez<br />
15:50 Coffee<br />
16:20 Sothmann<br />
16:50 Sols<br />
17:20 Lambert<br />
Excursion<br />
14:30 Rakyta<br />
15:00 Ferrer<br />
15:30 Coffee<br />
16:00 Poster<br />
presentations<br />
16:30 Posters<br />
14:30 Gorini<br />
15:00 Kleshchonok<br />
15:30 Ferradas<br />
15:45 Coffee<br />
16:15 Gómez León<br />
16:30 García Suárez<br />
16:45 Evangelou
Program<br />
Monday October 22<br />
09h00 – 09h15 Jean-Louis Pichard: Welcome, Program of the week, Miscellaneous<br />
09h15 – 09h55 Giuliano Benenti: Introduction to a few basic concepts in thermoelectric transport<br />
09h55 – 11h 00 Yoseph Imry: Thermal Transport and Thermoelectric Coefficients Near the<br />
An<strong>de</strong>rson Transition and in 3-Terminal Molecular-Type Junctions<br />
11h00 – 11h 30 Coffee break<br />
11h30 – 12h25 Keiji Saito: Exact solution of a Levy walk mo<strong>de</strong>l for anomalous heat transport<br />
12h30 Lunch<br />
14h30 – 15h35 Jukka Pekola: Experiments on the distribution of dissipation in electron tunneling<br />
15h35 – 16h15 Gerd Schön: Single-Electron Tunneling and the Fluctuation Theorem<br />
16h15 – 16h40 Coffee break<br />
16h40 – 17h20 Olivier Bourgeois: Impact of nanophononics on thermoelectricity: measurements and<br />
methods<br />
17h20 – 18h00 Michael Moskalets: Scattering approach to heat transport. Application to a singleelectron<br />
emitter for chiral wave-gui<strong>de</strong>s<br />
__________________________________________________________________________<br />
Tuesday October 23<br />
09h00 – 09h45 Carlo Beenakker: Random-matrix theory of thermoelectricity<br />
09h45 – 10h50 Laurens Molenkamp: Thermoelectric Properties of Semiconductor Nanostructures<br />
10h50 – 11h 20 Coffee break<br />
11h20 – 12h05 Vijay Narayan: Anomalous Thermopower in a Low-Density Two-Dimensional Electron<br />
System: Metallic Depen<strong>de</strong>nce, Giant Magnitu<strong>de</strong> and Oscillatory <strong>de</strong>nsity-<strong>de</strong>pen<strong>de</strong>nce<br />
12h05 – 12h25 Geneviève Fleury: Delay Time and Thermopower Distributions at the spectrum edges<br />
of a chaotic scatterer<br />
12h30 Lunch<br />
14h30 – 15h10 Rafael Sánchez: Harvesting fluctuations at electrical hot spots<br />
15h10 – 15h50 David Sánchez: Scattering theory of nonlinear thermoelectric transport
15h50 – 16h20 Coffee Break<br />
16h20 – 16h50 Björn Sothmann: Magnon-driven quantum-dot heat engine<br />
16h50 – 17h20 Fernando Sols: Electron refrigeration by nonadiabatic pumping and related questions<br />
on quantum cooling<br />
17h20 – 17h50 Colin Lambert: Giant Thermopower and Figure of Merit in Single-Molecule Junctions<br />
__________________________________________________________________________<br />
Wednesday October 24<br />
08h45 – 09h50 Antoine Georges: Thermoelectric properties of strongly correlated quantum systems<br />
09h50 – 10h30 Giuliano Benenti: Thermopower and thermoelectric efficiency in systems with<br />
broken time-reversal symmetry<br />
10h30 – 11h00 Coffee break<br />
11h00 – 11h40 Sebastian Volz: Heat and Nanotechnologies : Focus on Thermoelectricity<br />
11h40 – 12h40 Round Table: Thermoelectric energy conversion, insights, prospects for real<br />
applications?<br />
12h45 Lunch<br />
Excursion and Dinner<br />
__________________________________________________________________________<br />
Thursday October 25<br />
09h00 – 10h05 Moty Heiblum: Observation of neutral mo<strong>de</strong>s in the fractional quantum Hall regime<br />
10h05 – 10h25 Giacomo Dolcetto: Tunneling between helical edge states through exten<strong>de</strong>d contacts<br />
10h25 – 10h55 Coffee break<br />
10h55 – 11h25 Panagiotis Kotetes: Spinful Majorana fermions and magnetoelectricity in junctions of<br />
1D quantum wire-superconductor heterostructures<br />
11h25 – 11h55 Mathias Diez: Andreev reflection from a topological superconductor with chiral<br />
symmetry<br />
11h55 – 12h15 Dmitry Pikulin: Zero-bias conductance peak from weak antilocalization in a Majorana<br />
nanowire<br />
12h30 Lunch<br />
14h30 – 15h00 Peter Rakyta: Electronic standing waves on the surface of the topological insulator<br />
Bi 2 Te 3
15h00 – 15h30 Jaime Ferrer: How does Exact DFT compares with exact solutions in simple mo<strong>de</strong>ls of<br />
strongly correlated electrons?<br />
15h30 – 16h00 Coffee break<br />
16h00 – 16h30 Poster Presentations<br />
16h30 – 18h00 Posters<br />
__________________________________________________________________________<br />
Friday October 26<br />
09h00 – 09h30 Jonathan Edge: Metallic phase of the quantum Hall effect in four-dimensional space<br />
09h30 – 10h00 Jakub Tworzydlo: Thermal metal in topological superconductors.<br />
10h00 – 10h15 Akash Chakraborty : Nanoscale inhomogeneities in diluted magnetic systems : Effects<br />
on Curie temperature and spontaneous magnetization<br />
10h15 – 10h45 Coffee break<br />
10h45 – 11h15 Roberto Raimondi: Onsager relations in a two-dimensional electron gas with spinorbit<br />
coupling<br />
11h15 – 11h30 Héctor Ochoa: Spin-orbit coupling assisted by flexural phonons in graphene<br />
11h30 – 12h00 Guillaume Weick: Massless Dirac bosons in honeycomb plasmonic lattices<br />
12h00 – 12h30 Csaba Peterfalvi: Electron Focussing in Graphene<br />
12h30 Lunch<br />
14h30 – 15h00 Cosimo Gorini: Theory of scanning gate microscopy<br />
15h00 – 15h30 Andrii Kleshchonok: Electron interferometry with a Quantum Point Contact: Effect of<br />
electron-electron interaction and temperature<br />
15h30 – 15h45 Rubén Ferradas: Symmetry-induced interference effects in metalloporphyrins wires<br />
15h45 – 16h15 Coffee break<br />
16h15 – 16h30 Álvaro Gómez León: Ac magnetic fields coupled to spin qubits<br />
16h30 – 16h45 Víctor García Suárez: Nonequilibrium transport response from equilibrium transport<br />
theory<br />
16h45 – 17h15 Spiros Evangelou: Quantum chaos in disor<strong>de</strong>red graphene
Monday<br />
Abstracts<br />
Monday, October 22<br />
Introduction to a few basic concepts in thermoelectricity<br />
Giuliano Benenti<br />
Center for Nonlinear and Complex Systems, Università <strong>de</strong>gli Studi <strong>de</strong>ll'Insubria, Via Valleggio<br />
11, 22100 Como, Italy<br />
I will review fundamental aspects of heat to work conversion, including the phenomenological<br />
coupled charge and heat transport equations of non-equilibrium thermodynamics, the<br />
Onsager reciprocity relations, the figure of merit ZT for thermoelectric efficiency, the<br />
Curzhon-Ahlborn efficiency at maximum power, the Wie<strong>de</strong>mann-Franz law and Mott's<br />
formula.<br />
__________________________________________________________________________<br />
Thermal Transport and Thermoelectric Coefficients Near the An<strong>de</strong>rson Transition and<br />
in 3-Terminal Molecular-Type Junctions (*)<br />
Yoseph Imry<br />
Weizmann <strong>Institut</strong>e of Science<br />
(*) Patent application pending<br />
We start by reviewing thermal and thermoelectric linear transport, including the various<br />
coefficients the symmetry relations among them (Onsager) and what <strong>de</strong>termines their<br />
magnitu<strong>de</strong>s. Applications will be briefly mentioned along with the requirements on the above<br />
coefficients.<br />
Next, the An<strong>de</strong>rson localization transition will be consi<strong>de</strong>red at finite temperatures. This<br />
inclu<strong>de</strong>s the electrical conductivity as well as the electronic thermal conductivity and the<br />
thermoelectric coefficients [1-3]. The latter becomes relatively large at low temperatures near<br />
the transition, its interesting critical behavior is found. A method for characterizing the<br />
conductivity critical exponent, an important signature of the transition, using both the<br />
conductivity and thermopower measurements, is outlined.<br />
Then, the thermoelectric transport through a molecular bridge (or a corresponding quantumdot<br />
arrangement) - a mo<strong>de</strong>l nanosystem - will be discussed, with an emphasis on the effects<br />
of inelastic processes of the transport electrons caused by the coupling to the vibrational<br />
mo<strong>de</strong>s of the molecule. In particular it is found that when the molecule is coupled to a<br />
thermal bath of its own, which may be at a temperature different from those of the electronic<br />
reservoirs, a heat current between the molecule and the reservoir can be generated by the<br />
usual electric current. Expressions for the transport coefficients governing this conversion<br />
and similar ones are <strong>de</strong>rived, and possible scenarios for increasing their magnitu<strong>de</strong>s are<br />
outlined along with related semiconductor junction systems [4].<br />
The latter interesting case of three terminals with two types of carriers presents novel<br />
possibilities. We shall conclu<strong>de</strong> by <strong>de</strong>monstrating its advantage over usual two-terminal<br />
situations, for thermoelectric energy conversion [5].<br />
[1] M. Cutler and N. F. Mott, Phys Rev. 181, 1336 (1969)
Monday<br />
[2] U. Sivan and Y. Imry, Phys Rev B33, 551 (1986)<br />
[3] Y. Imry and A. Amir, The localization transition at finite temperatures: electric and thermal<br />
transport, in 50 years of An<strong>de</strong>rson Localization, edited by E. Abrahams (World Scientific,<br />
Singapore, 2010) in press, arXiv:1004.0966<br />
[4] O. Entin-Wohlman, Y. Imry and A. Aharony, Three-terminal thermoelectric transport<br />
through a molecular junction, Phys. Rev. B 82, 115314 (2010); R.Sanchez and M.Büttiker,<br />
ibid. 83, 085428 (2011); J-H Jiang, O. Entin-Wohlman and Y. Imry, Phys Rev B 85, 075412<br />
(2012), and to be published.<br />
[5] J-H Jiang, O. Entin-Wohlman and Y. Imry, in preparation<br />
__________________________________________________________________________<br />
Exact solution of a Levy walk mo<strong>de</strong>l for anomalous heat transport<br />
Keiji Saito<br />
Physics Department, Keio University<br />
Based on results obtained from a large number of numerical simulations and various<br />
analytical approaches it is now believed that Fourier's law is not valid in one and two<br />
dimensional mechanical systems (in particular mo<strong>de</strong>ls where momentum is conserved) and<br />
heat conduction is anomalous. Anomalous behavior in heat conduction is not only a<br />
theoretical issue but recently of experimental relevance in several low-dimensional material<br />
such as carbon-nanotube, and Graphene. Indicators of the anomaly inclu<strong>de</strong> | (i) in steady<br />
states the <strong>de</strong>pen<strong>de</strong>nce of the heat current J on system size L shows the scaling behavior , (ii)<br />
the temperature profiles across systems in nonequilibrium steady states are found to be<br />
nonlinear even for very small applied temperature diferences and, (iii) the spreading of heat<br />
pulses in anharmonic chains is superdiusive. The Levy-walk mo<strong>de</strong>l is known to provi<strong>de</strong> a<br />
good <strong>de</strong>scription of anomalous heat conduction in one-dimensional systems. In this mo<strong>de</strong>l<br />
the heat carriers execute Levy-walks instead of normal diffusion as expected in systems<br />
where Fourier's law holds. Here we calculate exactly the average heat current, the large<br />
<strong>de</strong>viation function of its fluctuations and the temperature profile of the Levy-walk mo<strong>de</strong>l<br />
maintained in a steady state by contact with two heat baths (the open geometry) [1]. We find<br />
that the current is nonlocally connected to the temperature gradient. As observed in recent<br />
simulations of mechanical mo<strong>de</strong>ls, all the cumulants of the current fluctuations have the<br />
same system-size <strong>de</strong>pen<strong>de</strong>nce in the open geometry. The case of the ring geometry is also<br />
discussed.<br />
[1] Abhishek Dhar, Keiji Saito and Bernard Derrida, arXiv:1207.1184<br />
__________________________________________________________________________<br />
Experiments on the distribution of dissipation in electron tunneling<br />
Jukka Pekola<br />
Aalto University, Helsinki, Finland<br />
I discuss work, heat and fluctuation relations in single-electron tunneling driven by a gate<br />
voltage. Our experiments confirm the validity of the most common fluctuation relations un<strong>de</strong>r<br />
isothermal conditions. I discuss a feed back mechanism by which information can be<br />
converted into energy stored in a capacitor in a single-electron circuit. Finally I propose a<br />
measurement of work in a quantum system using a calorimetric <strong>de</strong>tection.
Monday<br />
Single-Electron Tunneling and the Fluctuation Theorem<br />
Gerd Schön 1 , Y. Utsumi 2 , D. S. Golubev 1 , M. Marthaler 1<br />
1<br />
<strong>Institut</strong> für Theoretische Festkörperphysik, Karlsruhe <strong>Institut</strong>e of Technology, 76128<br />
Karlsruhe, Germany<br />
2<br />
Department of Physics Engineering, Faculty of Engineering, Mie University, Tsu, Mi-e, 514-<br />
8507, Japan<br />
Experiments on the direction-resolved full-counting statistics of single-electron tunneling<br />
allow testing the fundamentally important Fluctuation Theorem (FT). At the same time, the<br />
FT provi<strong>de</strong>s a frame for analyzing such data.<br />
Here we consi<strong>de</strong>r tunneling through a double quantum dot (DQD) system which is coupled<br />
capacitively to a quantum point contact (QPC) <strong>de</strong>tector. Fluctuations of the environment,<br />
including the shot noise of the QPC, lead to an enhancement of the effective temperature in<br />
the FT. We provi<strong>de</strong> a quantitative explanation of this effect [1].<br />
In addition we discuss the influence of the finite <strong>de</strong>tector bandwidth on the measurements.<br />
Furthermore, we <strong>de</strong>rive the full counting statistics for the coupled DQD - QPC system and<br />
obtain the joint probability distribution of the charges transferred through the DQD and the<br />
QPC, which is consistent with the fluctuation theorem (FT) [2]. The system can be <strong>de</strong>scribed<br />
by a master equation with tunneling rates <strong>de</strong>pending of the counting fields and satisfying a<br />
generalized local <strong>de</strong>tailed-balance relation.<br />
[1] Bidirectional Single-Electron Counting and the Fluctuation Theorem, Y. Utsumi, D.S.<br />
Golubev, M. Marthaler, K. Saito, T. Fujisawa, and G. Schön, Phys. Rev. B 81, 125331 (2010)<br />
[2] Fluctuation theorem for a double quantum dot coupled to a point-contact electrometer,<br />
D.S. Golubev, Y. Utsumi, M. Marthaler, G. Schön, Phys. Rev. B 84, 075323 (2011)<br />
__________________________________________________________________________<br />
Impact of nanophononics on thermoelectricity: measurements and methods<br />
Olivier Bourgeois, Christophe Blanc, Hossein Ftouni, Dimitri Taïnoff<br />
<strong>Institut</strong> Néel, Université Joseph Fourier-CNRS, 25 rue <strong>de</strong>s Martyrs, BP 166, 38042 Grenoble<br />
Ce<strong>de</strong>x 9, France<br />
We will review recent progresses ma<strong>de</strong> in nanophononics to get a better approach in energy<br />
harvesting [1,2]. The manipulation of phonons in low dimensional suspen<strong>de</strong>d structures<br />
opens up very important questions especially at low temperature [3,4]. Different concepts<br />
have been proposed to transform single crystalline materials into phonon glasses: phononic<br />
crystals, suspen<strong>de</strong>d structured membranes, nanoengineered materials. The possible<br />
reduction of phonon transport in these structures by opening a gap in the dispersion relation,<br />
by reducing the group velocities or by <strong>de</strong>creasing the phonon mean free path is a possible<br />
path towards better thermoelectrics.<br />
The measurement of very small suspen<strong>de</strong>d systems requires the <strong>de</strong>velopment of highly<br />
sensitive experimental techniques. We will <strong>de</strong>scribe state of the art experimental methods<br />
that have been proposed for the measurement of tiny energy exchange from room<br />
temperature to very low temperature [5] (thermal conductance measurement and heat<br />
exchange in general). We will show recent experiments that play with phonons at the<br />
nanoscale. To conclu<strong>de</strong> we will see that nanophononics at low temperature is still a very<br />
open subject especially with suspen<strong>de</strong>d systems containing electrons like graphene or two<br />
dimensional electron gas.
Monday<br />
[1] Clivia M Sotomayor Torres and Jouni Ahopelto, Position Paper on Nanophotonics and<br />
Nanophononics, E-Nano Newsletter (Issue 24) Publishing Date: 2011-12-31.<br />
[2] J. Tang et al. Holey Silicon as an Efficient Thermoelectric Material, Nano Letters 10, 4279<br />
(2010)<br />
[3] J-S. Heron, C. Bera, T. Fournier, N. Mingo, and O. Bourgeois, Blocking phonons via<br />
nanoscale geometrical <strong>de</strong>sign, Phys. Rev. B 82, 155458 (2010).<br />
[4] Christophe Blanc, Ali Rajabpour, Sebastian Volz, Thierry Fournier, and Olivier Bourgeois<br />
Phonon Glass Behaviour in Corrugated Silicon Nanowires Due to Phonon Backscattering.<br />
(2012)<br />
[5] A. Sikora, H. Ftouni, J. Richard, C. Hébert, D. Eon, F. Omnès, and O. Bourgeois, Highly<br />
sensitive thermal conductivity measurements of suspen<strong>de</strong>d membranes (SiN and diamond)<br />
using a 3ω-Völklein method. Rev. Sci. Instrum. 83, 054902 (2012).<br />
__________________________________________________________________________<br />
Scattering approach to heat transport. Application to a single-electron emitter for<br />
chiral wave-gui<strong>de</strong>s<br />
Michael Moskalets<br />
Department of Metal and Semiconductor Physics, National Technical University “Kharkiv<br />
Polytechnical <strong>Institut</strong>e” 61002 Kharkiv, Ukraine<br />
We present a scattering matrix approach to heat transport in dynamical mesoscopic<br />
structures for non-interacting electrons [1-3]. We show quite generally existence of two<br />
effects, heat generation and heat pumping. In particular we analyze energetics [4] of a<br />
single-particle source emitting on-<strong>de</strong>mand electrons and holes [5]. It turns out that the energy<br />
of emitted particles is not fixed unlike their charge. Therefore, even a regular particle flow<br />
carries a fluctuating heat. These heat fluctuations can be measured as temperature<br />
fluctuations of an attached thermometer, which in turn can be measured as the fourth<br />
cumulant of a potential if a thermometer serves simultaneously as a voltage probe. Notice<br />
the fluctuations of a heat of a regular particle flow are a feature of an essentially dynamical<br />
source and it is absent for a DC source. We analyze a heat production [4] of two subsequent<br />
single-particle sources working as a tunable two-particle source [6]. We show that unlike a<br />
charge current the heat current can be non-additive. In particular, in the adiabatic regime the<br />
heat production can be suppressed if the second source is tuned to emit a hole at the time<br />
when the first source emits an electron or vice versa. We show also that the heat generated<br />
becomes enhanced if two electrons or two holes are emitted simultaneously.<br />
[1] M. Moskalets, M. Büttiker, Floquet scattering theory of quantum pumps, Phys. Rev. B 66,<br />
205320 (2002)<br />
[2] L. Arrachea, M. Moskalets, Energy transport and heat production in quantum engines, in<br />
Handbook of Nanophysics: Nanomedicine and Nanorobotics, ed. by Klaus D. Sattler (CRC<br />
Press, Taylor & Francis Group), 38-1 (2010)<br />
[3] M. Moskalets, Scattering matrix approach to non-stationary quantum transport, (Imperial<br />
College Press, London), 280 p. (2011)<br />
[4] M. Moskalets, M. Büttiker, Heat production and current noise for single- and double-cavity<br />
quantum capacitors, Phys. Rev. B 80 081302 (2009)<br />
[5] G. Fève, A. Mahé, J.-M. Berroir, T. Kontos, B. Plaçais, D. C. Glattli, A. Cavanna, B.<br />
Etienne, Y. Jin, An On-Demand Coherent Single-Electron Source, Science 316, 1169 (2007)<br />
[6] J. Splettstoesser, S. Ol’khovskaya, M. Moskalets, M. Büttiker, Electron counting with a<br />
two-particle emitter, Phys. Rev. B 78, 205110 (2008)
Tuesday<br />
Tuesday, October 23<br />
Random-matrix theory of thermoelectricity<br />
Carlo Beenakker<br />
Instituut-Lorentz, Lei<strong>de</strong>n University, P.O. Box 9506, 2300 RA Lei<strong>de</strong>n, The Netherlands<br />
Since Landauer, Büttiker, and Imry’s work in the 1980’s we know that the study of electrical<br />
conductance in mesocopic systems is related to the study of the statistical properties of<br />
scattering matrices. Random-matrix theory was <strong>de</strong>veloped as a powerful tool to make<br />
universal predictions, in<strong>de</strong>pen<strong>de</strong>nt of microscopic <strong>de</strong>tails of the system. Thermoelectric<br />
transport properties typically involve energy <strong>de</strong>rivatives of the conductance, and one might<br />
won<strong>de</strong>r whether random-matrix theory can play an instructive role as well. The relevant<br />
matrix is the socalled time-<strong>de</strong>lay matrix, which contains dynamical information on the<br />
electron scattering. We review some ol<strong>de</strong>r work on the random-matrix theory of<br />
thermoelectricity, and also some recent work on thermal conduction in topological<br />
superconductors.<br />
General background material: ArXiv:0904.1432<br />
__________________________________________________________________________<br />
Thermoelectric Properties of Semiconductor Nanostructures<br />
Laurens W. Molenkamp<br />
Physikalisches <strong>Institut</strong> (EP3) <strong>de</strong>r Universität Würzburg, Am Hubland, 97074 Würzburg<br />
Thermoelectric experiments on nanostructures are often complicated by the need to apply a<br />
temperature difference of a few K across a <strong>de</strong>vice a few 100 nm in size. In semiconductors,<br />
such large gradients lead to very strong phonon drag effects, that overwhelm the electronic<br />
thermoelectric effects a transport physicist usually is interested in.<br />
Over the years, we have <strong>de</strong>veloped a current heating technique that utilizes the relatively<br />
small electron-acoustic phonon coupling in semiconductors to create a thermal gradient in<br />
the electronic system only. This has allowed us to study in <strong>de</strong>tail the thermoelectric<br />
properties of quantum point contacts and quantum dots. More recently, we have started to<br />
apply the technique to spintronic nanostructures. In this talk, I will present some of our recent<br />
results in this direction, with examples such as the thermoelectric properties of a dot in the<br />
Kondo regime, thermal rectification and the diffusion thermopower of (Ga,Mn)As.
Tuesday<br />
Anomalous Thermopower in a Low-Density Two-Dimensional Electron System:<br />
Metallic Depen<strong>de</strong>nce, Giant Magnitu<strong>de</strong> and Oscillatory <strong>de</strong>nsity-<strong>de</strong>pen<strong>de</strong>nce<br />
Vijay Narayan 1 , M. Pepper 2 , J. Griffiths 1 , H. Beere 1 , F. Sfigakis 1 , G. Jones 1 , D. Ritchie 1 and<br />
A. Ghosh 3<br />
1 Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3<br />
0HE, United Kingdom<br />
2 Department of Electronic and Electrical Engineering, University College London, Torrington<br />
Place, London WC1E 7JE, United Kingdom<br />
3 Department of Physics, Indian <strong>Institut</strong>e of Science, Bangalore 560012, India<br />
We present thermopower S and electrical resistivity ρ 2DES measurements in a low-<strong>de</strong>nsity<br />
(~ 10 14 m -2 ) two-dimensional electron system (2DES). We are interested in the regime where<br />
ρ 2DES >> h/e 2 and consequently the 2DES is expected to be strongly localised. Remarkably,<br />
however, we observe several aspects to the 2DES behaviour that are not consistent with<br />
insulating behaviour. First, the temperature-<strong>de</strong>pen<strong>de</strong>nce of S is manifestly metallic, S<br />
growing linearly as a function of temperature up to ≈ 0.7 K. Second, the magnitu<strong>de</strong> of S<br />
exceeds the Mott value valid for non-interacting metallic 2DESs at similar carrier <strong>de</strong>nsities by<br />
over two or<strong>de</strong>rs of magnitu<strong>de</strong>. And third, we observe a seeming <strong>de</strong>coupling between ρ 2DES<br />
and S in their <strong>de</strong>nsity-<strong>de</strong>pen<strong>de</strong>nce whereby strong oscillations and even sign changes are<br />
observed in the latter which are completely absent in the former. We explore the role of the<br />
many-body Coulomb potential in these observations and the scope offered by this system<br />
towards sub-Kelvin Peltier refrigeration.<br />
[1] Vijay Narayan, M. Pepper, J. Griffiths, H. Beere, F. Sfigakis, G. Jones, D. Ritchie and<br />
A. Ghosh, Unconventional metallicity and giant thermopower in a strongly interacting twodimensional<br />
electron system, Phys. Rev. B 86, 125406 (2012)<br />
[2] Vijay Narayan, M. Pepper, J. Griffiths, H. Beere, F. Sfigakis, G. Jones, D. Ritchie and<br />
A. Ghosh, Evi<strong>de</strong>nce of Novel Quasiparticles in a Strongly Interacting Two-Dimensional<br />
Electron System: Giant Thermopower and Metallic Behaviour, J. Low Temp. Phys<br />
(accepted), DOI 10.1007/s10909-012-0718-0<br />
__________________________________________________________________________<br />
Delay-time and thermopower distributions at the spectrum edges of a chaotic<br />
scatterer<br />
A. Abbout (1,2) , G. Fleury (1) , J.-L. Pichard (1) and K. Muttalib (3)<br />
(1)<br />
Service <strong>de</strong> Physique <strong>de</strong> l'Etat Con<strong>de</strong>nsé CNRS URA 2464, CEA Saclay, 91191 Gif-sur-<br />
Yvette, France<br />
(2)<br />
Laboratoire CRISMAT, CNRS UMR 6508, 6 boulevard Maréchal Juin, F-14050, Caen,<br />
France<br />
(3)<br />
Department of Physics, University of Florida, Gainesville, FL 32611-8440, USA<br />
We study chaotic scattering outsi<strong>de</strong> the wi<strong>de</strong> band limit, as the Fermi energy E F approaches<br />
the band edges E B of a one-dimensional lattice embedding a scattering region of M sites [1].<br />
The Hamiltonian H M of this region is taken from the Cauchy orthogonal ensemble. The<br />
scattering is chaotic at E F if the average level <strong>de</strong>nsity per site of H M at E F <strong>de</strong>scribes a semicircle<br />
as E F varies insi<strong>de</strong> the conduction band. The edges of this semi-circle coinci<strong>de</strong> with the<br />
band edges E B . We show that the <strong>de</strong>lay-time and thermopower distributions differ near the<br />
edges from the universal expressions valid in the bulk [2]. To obtain the asymptotic universal<br />
forms of these edge distributions, one must keep constant the energy distance E F – E B<br />
measured in unit of the same energy scale (proportional to M -1/3 ) which is used for rescaling
Tuesday<br />
the energy level spacings at the spectrum edges of large Gaussian matrices. In particular the<br />
<strong>de</strong>lay-time and the thermopower have the same universal edge distributions for arbitrary M<br />
as those for an M=2 scatterer, which we obtain analytically.<br />
[1] A. Abbout, G. Fleury, J.-L. Pichard and K. Muttalib, in preparation<br />
[2] P. W. Brouwer, K. M. Frahm and C. W. J. Beenakker, Quantum Mechanical Time-Delay<br />
Matrix in Chaotic Scattering, Phys. Rev. Lett. 78, 4737 (1997)<br />
__________________________________________________________________________<br />
Harvesting fluctuations at electrical hot spots<br />
Rafael Sánchez<br />
<strong>Institut</strong>o <strong>de</strong> Ciencia <strong>de</strong> Materiales <strong>de</strong> Madrid (ICMM-CSIC), Madrid, Spain<br />
In electrical circuits hot spots occur naturally at places where energy is dissipated. Here we<br />
propose a controlled experiment which can <strong>de</strong>monstrate the appearance of directed current<br />
as a consequence of a hot spot. We investigate transport generated in Coulomb coupled<br />
electrical conductors from excess electric or thermal fluctuations at the coupling capacitance.<br />
If one of the conductors supports a bias voltage, out of equilibrium charge fluctuations<br />
remove <strong>de</strong>tailed balance in the unbiased system manifested in a drag current. Non linear<br />
fluctuation relations can nevertheless be obtained [1].<br />
Coulomb coupled conductors permit separate directions of the heat and current flux [2]. In<br />
our mo<strong>de</strong>l, one of the conductors is connected via only one lead to a hot reservoir. The other<br />
conductor is connected to two leads. Such a geometry can be used for <strong>de</strong>tection of non<br />
linear heat fluctuations [3]. We investigate the minimal conditions nee<strong>de</strong>d to generate<br />
directed current flow for a system of two quantum dot conductors in which both energy and<br />
charge states are quantized. In quantum dots energy to current conversion can be optimal<br />
with one electron transferred for every heat quantum given up by the hot reservoir. We show<br />
that at the point of maximum power extraction the efficiency approaches one half of the<br />
Carnot efficiency. However, the generated power is small.<br />
Larger currents can be generated in a chaotic mesoscopic cavity coupled to two leads. Non<br />
linearities due to energy <strong>de</strong>pen<strong>de</strong>nt contact transmission to leads are responsible for the<br />
rectification of thermal fluctuations in a coupled hot cavity, leading to an electrical current [4].<br />
The maximum power produced by the system will be discussed.<br />
[1] R. Sánchez, R. López, D. Sánchez, and M. Büttiker, Mesoscopic Coulomb drag, broken<br />
<strong>de</strong>tailed balance and fluctuation relations, Phys. Rev. Lett. 104 076801 (2010)<br />
[2] R. Sánchez, and M. Büttiker, Optimal energy quanta to current conversion, Phys. Rev. B<br />
83 085428 (2011)<br />
[3] R. Sánchez, and M. Büttiker, Detection of single electron heat transfer statistics,<br />
arXiv:1207:2587<br />
[4] B. Sothmann, R. Sánchez, A.N. Jordan, and M. Büttiker, Rectification of termal<br />
fluctuations in a chaotic cavity heat engine, Phys. Rev. B 85 205301 (2012)
Tuesday<br />
Scattering theory of nonlinear thermoelectric transport<br />
David Sánchez<br />
<strong>Institut</strong>e for Cross-Disciplinary Physics and Complex Systems IFISC (UIB-CSIC), E-07122<br />
Palma <strong>de</strong> Mallorca, Spain<br />
We discuss nonlinear transport properties of quantum conductors in response to both<br />
electrical and thermal driving forces. Within scattering approach, we <strong>de</strong>termine the<br />
nonequilibrium screening potential of a generic mesoscopic system and find that its response<br />
is dictated by particle and entropic injectivities which <strong>de</strong>scribe the charge and entropy<br />
transfer during transport. We illustrate our mo<strong>de</strong>l analyzing the voltage and thermal<br />
rectification of a resonant tunneling barrier. Importantly, we investigate interaction induced<br />
contributions to the thermopower in the presence of large temperature differences [1].<br />
[1] D. Sánchez and R. López, arxiv:1209.1264 (preprint, 2012).<br />
__________________________________________________________________________<br />
Magnon-driven quantum-dot heat engine<br />
Björn Sothmann, Markus Büttiker<br />
Département <strong>de</strong> Physique Théorique, Université <strong>de</strong> Genève, CH-1211 Genève 4,<br />
Switzerland<br />
The concept of harvesting energy from the environment to power small <strong>de</strong>vices has become<br />
increasingly popular. Recently, there was a particular interest in quantum dot systems that<br />
generate electrical currents from thermal fluctuations [1,2]. The main focus of the emergent<br />
field of spin caloritronics is the i<strong>de</strong>a to drive and control spin currents by heat.<br />
Here, we discuss a setup consisting of a single-level quantum dot coupled to two<br />
ferromagnetic metals and a ferromagnetic insulator held at different temperatures which<br />
combines the i<strong>de</strong>as of energy harvesting and spin caloritronics. We <strong>de</strong>monstrate that this<br />
nanoengine can act as an optimal heat to spin-polarized charge current converter in an<br />
antiparallel geometry, while it acts as a heat to pure spin current converter in the parallel<br />
case. We discuss the maximal output power of the <strong>de</strong>vice and its efficiency [3].<br />
[1] R. Sánchez, M. Büttiker, Optimal energy quanta to current conversion, PRB 83, 085428<br />
(2011)<br />
[2] B. Sothmann, R. Sánchez, A. N. Jordan, M. Büttiker, Rectification of thermal fluctuations<br />
in a chaotic cavity heat engine, PRB 85, 205301 (2012)<br />
[3] B. Sothmann, M. Büttiker, Magnon-driven quantum-dot heat engine, EPL 99 27001 (2012)
Tuesday<br />
Electron refrigeration by nonadiabatic pumping and related questions on quantum<br />
cooling<br />
Fernando Sols<br />
Universidad Complutense <strong>de</strong> Madrid<br />
Some features of nonadiabatic electron heat pumps are studied and connected to general<br />
questions on quantum cooling [1,2]. Inelastic reflection is shown to contribute to heating if the<br />
external driving signal is time symmetric. Within the tunneling limit, it is shown that electron<br />
cooling still occurs if the coherent ac source is replaced by a sufficiently hot thermal bath. A<br />
comparison with related refrigeration setups is presented [3,4]. The quantum of cooling<br />
power (πk B T) 2 /6h$ is shown to be an upper limit to the cooling rate per transport channel in<br />
the presence of an arbitrary driving signal. The question is addressed of whether there is a<br />
universal limit to the cooling rate of a quantum system.<br />
[1] M. Rey, M. Strass, S. Kohler, P. Hänggi, F. Sols. Nonadiabatic electron heat pump, Phys.<br />
Rev. B 76, 085337 (2007).<br />
[2] F. Sols. Aspects of quantum cooling in electron and atom systems, Physica E 42, 466<br />
(2010), Proc. FQMT’08.<br />
[3] J.P. Pekola, F.W.J. Hekking. Normal-Metal-Superconductor Tunnel Junction as a<br />
Brownian Refrigerator, Phys. Rev. Lett. 98, 210604 (2007).<br />
[4] B. Cleuren, B. Rutten, C. Van <strong>de</strong>n Broeck. Cooling by Heating: Refrigeration Powered by<br />
Photons, Phys. Rev. Lett. 108, 120603 (2012).<br />
__________________________________________________________________________<br />
Giant thermopower and figure of merit in single-molecule junctions<br />
Colin Lambert<br />
Department of Physics, Lancaster University, Lancaster, UK, LA1 4YB<br />
Single molecules connected to nanogap electro<strong>de</strong>s provi<strong>de</strong> an opportunity for tuning<br />
electrical and thermoelectrical properties at the sub-nanometre scale. In this talk I shall<br />
present a study of the electronic contribution to thermopower S and the dimensionless figure<br />
of merit ZT in molecules sandwiched between gold electro<strong>de</strong>s. I shall show that for<br />
molecules with pendant groups, the shape of the transmission coefficient can be modified by<br />
Fano resonances near the Fermi energy, which can be tuned to produce huge increases in S<br />
and ZT. Tuning of transmission resonances can also be achieved by varying the coupling<br />
between molecular-scale structures. As an example, results will be presented for electron<br />
transport through single and double C60s. It will be shown that the thermopower and figure<br />
of merit for the latter is enhanced, compared with the former.<br />
[1] Giant thermopower and figure of merit in single-molecule <strong>de</strong>vices, C. M. Finch, V. M.<br />
García-Suárez, and C. J. Lambert, Phys. Rev. B 79, 033405 (2009)<br />
[2] Control of electron transport through Fano resonances in molecular wires, T.A.<br />
Papadopoulos, I.M. Grace and C.J. Lambert, Phys. Rev. B 74 193306 (2006)
Wednesday<br />
Wednesday, October 24<br />
Thermoelectric properties of strongly correlated quantum systems<br />
Antoine Georges<br />
Collège <strong>de</strong> France, Paris - Ecole Polytechnique, Palaiseau, France - Université <strong>de</strong> Genève,<br />
Suisse<br />
Materials with strong electronic correlations, especially transition-metal oxi<strong>de</strong>s, have received<br />
increasing attention as possible thermoelectrics. An interesting regime is that of intermediate<br />
to high temperatures, where enough entropy is unquenched. I will <strong>de</strong>scribe here the<br />
theoretical un<strong>de</strong>rstanding of the temperature–<strong>de</strong>pen<strong>de</strong>nce of the Seebeck coefficient for<br />
simple mo<strong>de</strong>ls of interacting electrons, as well as selected experimental results. On another<br />
note, I will present a recent proposal for studying fundamental aspects of thermoelectric<br />
effects using ultra-cold atomic gases.<br />
__________________________________________________________________________<br />
Thermopower and thermoelectric efficiency in systems with broken time-reversal<br />
symmetry<br />
Giuliano Benenti<br />
Center for Nonlinear and Complex Systems, Università <strong>de</strong>gli Studi <strong>de</strong>ll'Insubria, Via Valleggio<br />
11, 22100 Como, Italy<br />
We show that in systems with broken time-reversal symmetry the maximum efficiency and<br />
the efficiency at maximum power are both <strong>de</strong>termined by two parameters: a ``figure of merit''<br />
which generalizes the thermoelectric figure of merit ZT, and an asymmetry parameter, which<br />
becomes relevant when the thermopower is not an even function of the magnetic field. In<br />
contrast to the time-symmetric case, the figure of merit is boun<strong>de</strong>d from above; nevertheless<br />
the Carnot efficiency can be reached at lower and lower values of the figure of merit as the<br />
asymmetry parameter increases. Moreover, the Curzon-Ahlborn limit for efficiency at<br />
maximum power can be overcome within linear response. We show that a weak magnetic<br />
field generally improves either the efficiency of thermoelectric power generation or of<br />
refrigeration, the efficiencies of the two processes being no longer equal when a magnetic<br />
field is ad<strong>de</strong>d. Finally, we discuss the thermopower asymmetry and thermoelectric efficiency<br />
for a three-dot ring pierced by an Aharonov-Bohm flux, for random matrix mo<strong>de</strong>ls, and for<br />
more abstract transmission mo<strong>de</strong>ls.<br />
[1] K. Saito, G. Benenti and G. Casati, A microscopic mechanism for increasing<br />
thermoelectric efficiency, Chem. Phys. 375, 508 (2010)<br />
[2] G. Benenti and G. Casati, Increasing thermoelectric efficiency: dynamical mo<strong>de</strong>ls unveil<br />
microscopic mechanisms, Phil. Trans. R. Soc. A 369, 466 (2011)<br />
[3] G. Benenti, K. Saito and G. Casati, Thermodynamic bounds on efficiency for systems with<br />
broken time-reversal symmetry, Phys. Rev. Lett. 106, 230602 (2011)
Wednesday<br />
[4] K. Saito, G. Benenti, G. Casati and T. Prosen, Thermopower with broken time-reversal<br />
symmetry, Phys. Rev. B 84, 201306(R) (2011)<br />
[5] V. Balachandran, R. Bosisio and G. Benenti, Validity of Wie<strong>de</strong>mann Franz law in small<br />
molecular wires, Phys. Rev. B 86, 035433 (2012)<br />
[6] M. Horvat, T. Prosen, G. Benenti and G. Casati, Railway switch transport mo<strong>de</strong>l, preprint<br />
arXiv:1207.6014v1 [cond-mat.mes-hall]<br />
Heat and Nanotechnologies : Focus on Thermoelectricity<br />
Sebastian Volz<br />
Laboratoire d'Energétique Moléculaire et Macroscopique, UPR CNRS 288 ,Ecole Centrale<br />
Paris<br />
Nanotechnologies were supposed to give birth to a new revolution based on the <strong>de</strong>sign of<br />
new molecular nanorobot but finally consisted in the fabrication of new materials including<br />
nanostructures with enhanced properties. Thermoelectric materials are one of the outcomes<br />
and will be addressed in the talk.<br />
An introduction on nanotechnologies at broad and on nanoscale heat transport applications<br />
will be provi<strong>de</strong>d. Then a focus on thermoelectric materials will inclu<strong>de</strong> a presentation of the<br />
electrical physical effects as well as the main thermoelectric applications. Heat conduction<br />
effects at nanoscales will then be presented and <strong>de</strong>tailed for several key nanostructures<br />
(nanowires, superlattices and nanoparticles). The corresponding achievements in terms of<br />
figure of merit will finally be presented.
Thursday<br />
Thursday, October 25<br />
Observation of neutral mo<strong>de</strong>s in the fractional quantum Hall regime<br />
Moty Heiblum<br />
Current propagates in the fractional quantum Hall effect (FQHE) regime along the edges of<br />
the two-dimensional-electron gas (2DEG) via chiral edge mo<strong>de</strong>s with a chirality dictated by<br />
the applied magnetic field. Early predictions suggested the presence of counter propagating<br />
edge mo<strong>de</strong>s for some fractional states, the so called, hole-conjugate states, such as ½
Thursday<br />
[3] B. A. Bernevig, T. L. Hughes, and S. -C. Zhang, Science 314, 1757 (2006).<br />
[4] M. Konig et al., Science 318, 766 (2007).<br />
[5] C.-X. Liu et al., Phys. Rev. B 83, 035407 (2011).<br />
[6] D. Chevallier et al., Phys. Rev. B 82, 155318 (2010).<br />
[7] B. J. Overbosch and C. Chamon, Phys. Rev. B 80, 035319 (2009).<br />
[8] J. C. Y. Teo and C. L. Kane, Phys. Rev. B 79, 235321 (2009).<br />
[9] A. Strom and H. Johannesson, Phys. Rev. Lett. 102, 096806 (2009).<br />
[10] T. L. Schmidt, Phys. Rev. Lett. 107, 096602 (2011).<br />
_________________________________________________________________________<br />
Spinful Majorana fermions and magnetoelectricity in junctions of 1D quantum wiresuperconductor<br />
heterostructures<br />
Panagiotis Kotetes 1 , A. Shnirman 2 , G. Schön 1<br />
1 <strong>Institut</strong> für Theoretische Festkörperphysik, Karlsruhe <strong>Institut</strong>e of Technology, 76128<br />
Karlsruhe<br />
2 <strong>Institut</strong> für Theorie <strong>de</strong>r Kon<strong>de</strong>nsierten Materie, Karlsruhe <strong>Institut</strong>e of Technology, 76128<br />
Karlsruhe<br />
Recently, the interest in topological quantum computing has grown due to the appearance of<br />
promising platforms for realizing the long sought Majorana fermions. Among the proposals<br />
that seem suitable for engineering Majorana fermions, the most prominent involves a 1D<br />
semiconducting quantum wire in proximity to a bulk s-wave superconductor, where in<br />
addition a Zeeman field is applied. Here we investigate the Josephson effect in TNT and<br />
NTN junctions, consisting of topological (T) and normal (N) phases of semiconductorsuperconductor<br />
1D heterostructures in the presence of a Zeeman field [1]. A key feature of<br />
our setup is that, in addition to the variation of the phase of the superconducting or<strong>de</strong>r<br />
parameter, we allow the orientation of the magnetic field to change along the junction. We<br />
find a novel magnetic contribution to the Majorana Josephson coupling that permits the<br />
Josephson current to be tuned by changing the orientation of the magnetic field along the<br />
junction. We also predict that a spin current can be generated by a finite superconducting<br />
phase difference, ren<strong>de</strong>ring these materials potential candidates for spintronic applications.<br />
Finally, this new type of coupling not only constitutes a unique fingerprint for the existence of<br />
Majorana fermions but also provi<strong>de</strong>s an alternative pathway for manipulating and braiding<br />
topological qubits in networks of wires.<br />
[1] P. Kotetes, A. Shnirman, G. Schön, arXiv:1207.2691.
Thursday<br />
Andreev reflection from a topological superconductor with chiral symmetry<br />
M. Diez, J. P. Dahlhaus, M. Wimmer, C. W. J. Beenakker<br />
Instituut-Lorentz, Universiteit Lei<strong>de</strong>n, P.O. Box 9506, 2300 RA Lei<strong>de</strong>n, The Netherlands<br />
Chiral symmetry (H -> -H if e h) of the Hamiltonian of electron-hole (e-h) excitations in an<br />
N-mo<strong>de</strong> superconducting wire is associated with a topological quantum number Q ∈ Z<br />
(symmetry class BDI). In Ref. [1] we show that Q=Tr(r he ) equals the trace of the matrix of<br />
Andreev reflection amplitu<strong>de</strong>s, providing a link with the electrical conductance G. We <strong>de</strong>rive<br />
G=(2e 2 /h)|Q| for |Q|=N,N-1, and more generally provi<strong>de</strong> a Q-<strong>de</strong>pen<strong>de</strong>nt upper and lower<br />
bound on G. We calculate the probability distribution P(G) for chaotic scattering, in the<br />
circular ensemble of random-matrix theory, to obtain the Q-<strong>de</strong>pen<strong>de</strong>nce of weak localization<br />
and mesoscopic conductance fluctuations. We investigate the effects of chiral symmetry<br />
breaking by spin-orbit coupling of the transverse momentum (causing a class BDI-to-D<br />
crossover), in a mo<strong>de</strong>l of a disor<strong>de</strong>red semiconductor nanowire with induced<br />
superconductivity. For wire widths less than the spin-orbit coupling length, the conductance<br />
as a function of chemical potential can show a sequence of 2e 2 /h steps - insensitive to<br />
disor<strong>de</strong>r.<br />
[1] M. Diez, J. P. Dahlhaus, M. Wimmer, C. W. J. Beenakker, Andreev reflection from a<br />
topological superconductor with chiral symmetry, Phys. Rev. B 86 094501 (2012)<br />
__________________________________________________________________________<br />
Zero-bias conductance peak from weak antilocalization in a Majorana nanowire<br />
Dmitry I. Pikulin*, J. P. Dahlhaus*, M. Wimmer*, H. Schomerus', and C. W. J. Beenakker*<br />
*Instituut-Lorentz, Universiteit Lei<strong>de</strong>n, P.O. Box 9506, 2300 RA Lei<strong>de</strong>n, The Netherland,<br />
'Department of Physics, Lancaster University, Lancaster, LA1 4YB, United Kingdom<br />
We show [1] that weak antilocalization by disor<strong>de</strong>r coexists with resonant Andreev reflection<br />
by Majorana zero-mo<strong>de</strong>, both producing zero-voltage conductance peak of or<strong>de</strong>r e 2 /h in a<br />
superconducting nanowire. The peak is wi<strong>de</strong>ly believed to be the smoking gun signature of<br />
the Majorana zero-mo<strong>de</strong> [2], its observation has been reported [3]. We i<strong>de</strong>ntify methods to<br />
distinguish the Majorana resonance from the weak antilocalization effect.<br />
[1] D. I. Pikulin, J. P. Dahlhaus, M. Wimmer, H. Schomerus, and C. W. J. Beenakker, arXiv<br />
1206.6687 (2012)<br />
[2] K. T. Law, P. A. Lee, and T. K. Ng, Phys. Rev. Lett. 103, 237001 (2009)<br />
[3] V. Mourik, K. Zuo, S. M. Frolov, R. Plissard, E. P. A.M. Bakkers, and L. P. Kouwenhoven,<br />
Science 336, 1003 (2012); M. T. Deng, C. L. Yu, G. Y. Huang, M. Larsson, P. Caroff, and H.<br />
Q. Xu, arXiv:1204.4130 (2012); A. Das, Y. Ronen, Y. Most, Y. Oreg, M. Heiblum, and H.<br />
Shtrikman, arXiv:1205.7073 (2012)
Thursday<br />
Electronic standing waves on the surface of the topological insulator Bi 2 Te 3<br />
P.Rakyta 1 , A.Pályi 2 , J.Cserti 1<br />
1 Department of Physics of Complex Systems, Eötvös University, H-1117 Budapest, Pázmány<br />
Péter sétány 1/A, Hungary<br />
2 Department of Materials Physics, Eötvös University, H-1117 Budapest, Pázmány Péter<br />
sétány 1/A, Hungary<br />
A line <strong>de</strong>fect on a metallic surface induces standing waves in the electronic local <strong>de</strong>nsity of<br />
states (LDOS). Asymptotically far from the <strong>de</strong>fect, the wave number of the LDOS oscillations<br />
at the Fermi energy is usually equal to the distance between nesting segments of the Fermi<br />
contour, and the envelope of the LDOS oscillations shows a power-law <strong>de</strong>cay as moving<br />
away from the line <strong>de</strong>fect. Here, we theoretically analyze the LDOS oscillations close to a<br />
line <strong>de</strong>fect on the surface of the topological insulator Bi 2 Te 3 , and i<strong>de</strong>ntify an important<br />
preasymptotic contribution with wave-number and <strong>de</strong>cay characteristics markedly different<br />
from the asymptotic contributions. The calculated energy <strong>de</strong>pen<strong>de</strong>nce of the wave number of<br />
the preasymptotic LDOS oscillations is in quantitative agreement with the result of a recent<br />
scanning tunneling microscopy experiment [1].<br />
[1] Z.Alpichshev, J.G.Analytis, J.-H.Chu, I.R.Fisher, Y.L.Chen, Z.X.Shen, A.Fang and<br />
A.Kapitulnik, Phys. Rev. Lett. 104, 016401 (2010)<br />
__________________________________________________________________________<br />
How does Exact DFT compares with exact solutions in simple mo<strong>de</strong>ls of strongly<br />
correlated electrons ?<br />
Jaime Ferrer, Diego Carrascal<br />
Departamento <strong>de</strong> Física, Universidad <strong>de</strong> Oviedo<br />
We present analytic expressions for the exact <strong>de</strong>nsity functional and Kohn-Sham<br />
Hamiltonian of simple tight-binding mo<strong>de</strong>ls of correlated electrons. These are the single- and<br />
double-site versions of the An<strong>de</strong>rson, Hubbard and spinless fermion mo<strong>de</strong>ls. The exact<br />
exchange and correlation potentials keep the full non-local <strong>de</strong>pen<strong>de</strong>nce on electron<br />
occupations. The analytic expressions allow to compare the Kohn-Sham eigenstates of exact<br />
<strong>de</strong>nsity functional theory with the many-body quasi-particle states of these correlate<strong>de</strong>lectron<br />
systems. The exact Kohn-Sham spectrum <strong>de</strong>scribes correctly many of the non-trivial<br />
features of the many-body quasi-particle spectrum, as for example the precursors of the<br />
Kondo peak. However, we find that some pieces of the quasi-particle spectrum are missing<br />
because the many-body phase-space for electron and hole excitations is richer [1].<br />
[1] D. Carrascal and J. Ferrer, Phys. Rev. B 85 045110 (2012)
Friday<br />
Friday, October 2<br />
Metallic phase of the quantum Hall effect in four-dimensional space<br />
Jonathan M. Edge, J. Tworzydlo, C. W. J. Beenakker<br />
Instituut-Lorentz, Universiteit Lei<strong>de</strong>n, P.O. Box 9506, 2300 RA Lei<strong>de</strong>n, The Netherlands<br />
<strong>Institut</strong>e of Theoretical Physics, Faculty of Physics, University of Warsaw, Hoza 69, 00--681<br />
Warsaw, Poland<br />
We study the phase diagram of the quantum Hall effect in four-dimensional (4D) space [1].<br />
Unlike in 2D, in 4D there exists a metallic as well as an insulating phase, <strong>de</strong>pending on the<br />
disor<strong>de</strong>r strength. The critical exponent ≈ 1.2 of the diverging localization length at the<br />
quantum Hall insulator-to-metal transition differs from the semiclassical value = 1 of 4D<br />
An<strong>de</strong>rson transitions in the presence of time-reversal symmetry. Our numerical analysis is<br />
based on a mapping of the 4D Hamiltonian onto a 1D dynamical system, providing a route<br />
towards the experimental realization of the 4D quantum Hall effect.<br />
[1] J.M. Edge, J. Tworzydlo, C. W. J. Beenakker Metallic phase of the quantum Hall effect in<br />
four-dimensional space arXiv:1206.0099 to be published in PRL (2012)<br />
__________________________________________________________________________<br />
Thermal metal in topological superconductors<br />
Jakub Tworzydlo (1) , I. C. Fulga (2) , A. R. Akhmerov (2) , C.W.J. Beenakker (2) , B. Beri (3)<br />
(1)<br />
Faculty of Physics, University of Warsaw, Poland<br />
(2)<br />
Instituut-Lorentz, Universiteit Lei<strong>de</strong>n, The Netherlands<br />
(3)<br />
TCM Group, Cavendish Laboratory, United Kingdom<br />
The thermal quantum Hall effect appears in the absence of time-reversal symmetry in a<br />
single layer of a chiral p-wave superconductor. The insulator-insulator transition associated<br />
with this effect is generically present only for weak disor<strong>de</strong>r. For stronger disor<strong>de</strong>r we find a<br />
transition to a <strong>de</strong>localized phase, known as the thermal metal.<br />
In contrast, for a helical superconductor in the presence of time-reversal symmetry the<br />
transition between two topologically distinct thermal insulators occurs via the intervening<br />
thermal metal phase, even for an arbitrarily weak disor<strong>de</strong>r.<br />
We present a <strong>de</strong>tailed study of a phase diagram and the critical exponents for these<br />
topologically induced transitions. We also point to an un<strong>de</strong>rling mechanism of Majorana<br />
states formation in both chiral and helical systems.<br />
[1] I. C. Fulga, A. R. Akhmerov, J. Tworzydlo, B. Beri, and C. W. J. Beenakker, Phys. Rev. B<br />
86, 054505 (2012)<br />
[2] M. V. Medvedyeva, J. Tworzydlo, and C. W. J. Beenakker, Phys. Rev. B 81, 214203<br />
(2010)<br />
[3] J. H. Bardarson, M. V. Medvedyeva, J. Tworzydło, A. R. Akhmerov, and C. W. J.<br />
Beenakker, Phys.Rev. B 81, 121414(R) (2010)<br />
[4] M. Wimmer, A. R. Akhmerov, M. V. Medvedyeva, J. Tworzydlo, C. W. J. Beenakker,<br />
Phys. Rev. Lett. 105, 046803 (2010)
Friday<br />
Nanoscale inhomogeneities in diluted magnetic systems : Effects on Curie<br />
temperature and spontaneous magnetization<br />
Akash Chakraborty (1,2) , Richard Bouzerar (3) , Paul Wenk (4) , Stefan Kettemann (2,5) , and<br />
Georges Bouzerar (3,2)<br />
(1)<br />
Karlsruhe <strong>Institut</strong>e of Technology, 76128 Karlsruhe, Germany<br />
(2)<br />
Jacobs University Bremen, 28759 Bremen, Germany<br />
(3)<br />
<strong>Institut</strong> Néel, CNRS, 38042 Grenoble Ce<strong>de</strong>x 09, France<br />
(4)<br />
Universitaet Regensburg, 93040 Regensburg, Germany<br />
(5)<br />
Pohang University of Science and Technology (POSTECH), Pohang 790-784, South<br />
Korea<br />
The presence of nanoscale inhomogeneities has been experimentally evi<strong>de</strong>nced in several<br />
diluted magnetic systems, which in turn often leads to interesting physical phenomena.<br />
Among them room-temperature ferromagnetism is one of the most interesting and sought<br />
after topics in today’s emerging field of spintronics. However, until now, in the dilute regime it<br />
has been difficult to obtain Curie temperatures larger than that measured in well annealed<br />
samples of (Ga,Mn)As (∼190K for 12% doping). Here we suggest an innovative path to roomtemperature<br />
ferromagnetism in diluted magnetic semiconductors. We theoretically show that<br />
even a small concentration of nanoscale inhomogeneities can result in a gigantic increase of<br />
the critical temperatures [1]. We give a plausible explanation for the wi<strong>de</strong> variation of the<br />
critical temperatures measured in (Ga,Mn)N and provi<strong>de</strong> a better un<strong>de</strong>rstanding of the likely<br />
origin of very high Curie temperatures measured occasionally. We also show that nano-sized<br />
clusters of magnetic impurities can lead to drastic effects on the temperature <strong>de</strong>pen<strong>de</strong>nt<br />
magnetization compared to that of homogeneously diluted compounds [2]. The unusual and<br />
unconventional nature of the magnetization curves is found to strongly <strong>de</strong>pend on the relative<br />
concentration of the inhomogeneities as well as the effective range of the exchange<br />
interactions.<br />
[1] A. Chakraborty, R. Bouzerar, S. Kettemann, and G. Bouzerar, Nanoscale<br />
inhomogeneities: A new path toward high Curie temperature ferromagnetism in diluted<br />
materials, Phys. Rev. B 85 014201 (2012).<br />
[2] A. Chakraborty, P. Wenk, R. Bouzerar, and G. Bouzerar, Spontaneous magnetizationin in<br />
presence of nanoscale inhomogeneities in diluted magnetic systems, (submitted to Phys.<br />
Rev. B).<br />
__________________________________________________________________________<br />
Onsager relations in a two-dimensional electron gas with spin-orbit coupling<br />
Roberto Raimondi, Cosimo Gorini, and Peter Schwab<br />
CNISM and Dipartimento di Fisica "E. Amaldi", via <strong>de</strong>lla Vasca Navale 84, Università Roma<br />
Tre, 00146 Roma, Italy<br />
<strong>Institut</strong> <strong>de</strong> Physique et Chimie <strong>de</strong>s Matériaux <strong>de</strong> Strasbourg (UMR 7504), CNRS and<br />
Université <strong>de</strong> Strasbourg, 23 rue du Loess, BP 43, F-67034 Strasbourg Ce<strong>de</strong>x 2, France<br />
<strong>Institut</strong> für Physik, Universität Augsburg, 86135 Augsburg, Germany<br />
Theory predicts for the two-dimensional electrons gas with only Rashba spin-orbit interaction<br />
a vanishing spin Hall conductivity and at the same time a finite inverse spin Hall effect. We<br />
show how these seemingly contradictory results are compatible with the Onsager relations:<br />
the latter do hold for spin and particle (charge) currents in the two-dimensional electron gas,<br />
although (i) their form <strong>de</strong>pends on the experimental setup and (ii) a vanishing bulk spin Hall
Friday<br />
conductivity does not necessarily imply a vanishing spin Hall effect. We also discuss the<br />
situation in which extrinsic spin orbit from impurities is present and the bulk spin Hall<br />
conductivity can be different from zero.<br />
[1] C. Gorini, R. Raimondi, P. Schwab, arXiv:1207.1289<br />
__________________________________________________________________________<br />
Spin-orbit coupling assisted by flexural phonons in graphene<br />
H. Ochoa (1) , A. H. Castro Neto (2,3) , V. I. Fal'ko (4,5) , F. Guinea (1)<br />
(1)<br />
<strong>Institut</strong>o <strong>de</strong> Ciencia <strong>de</strong> Materiales <strong>de</strong> Madrid. CSIC. Sor Juana Inés <strong>de</strong> la Cruz 3. 28049<br />
Madrid. Spain.<br />
(2)<br />
Graphene Research Centre and Physics Department, National University of Singapore, 2<br />
Science Drive 3, 117542, Singapore.<br />
(3)<br />
Department of Physics, Boston University, 590 Commonwealth Ave., Boston MA 02215,<br />
USA.<br />
(4)<br />
Physics Department, Lancaster University, Lancaster, LA1 4YB, UK.<br />
(5)<br />
DPMC, University of Geneva, 24 Quai Ernest-Ansermet, CH1211 Geneve 4, Switzerland<br />
We present a complete analysis of the possible couplings between spins and flexural, out of<br />
plane, vibrations [1]. From tight-binding mo<strong>de</strong>ls we obtain analytical and numerical estimates<br />
of their strength. We show that dynamical effects, induced by quantum and thermal<br />
fluctuations, significantly enhance the spin-orbit gap. We also compute the spin relaxation<br />
rates due to flexural phonon scattering. Our results confirm that graphene is an excellent<br />
candidate for spintronics <strong>de</strong>vices.<br />
[1] H. Ochoa, A. H. Castro Neto, V. I. Fal'ko, F. Guinea, Spin-orbit coupling assisted by<br />
flexural phonons in graphene, arXiv:1209.4382 [cond-mat.mes-hall]<br />
__________________________________________________________________________<br />
Massless Dirac bosons in honeycomb plasmonic lattices<br />
G. Weick, 1 C. Woollacott, 2 W.L. Barnes, 3 O. Hess, 4 E. Mariani 2<br />
1<br />
<strong>Institut</strong> <strong>de</strong> Physique et Chimie <strong>de</strong>s Matériaux <strong>de</strong> Strasbourg, Université <strong>de</strong> Strasbourg &<br />
CNRS<br />
2<br />
Centre for Graphene Science, School of Physics, University of Exeter<br />
3<br />
School of Physics, University of Exeter<br />
4<br />
The Blackett Laboratory, Department of Physics, Imperial College London<br />
We consi<strong>de</strong>r a two-dimensional honeycomb lattice of metallic nanoparticles, each supporting<br />
a localized surface plasmon, and study the properties of the collective plasmons resulting<br />
from the near field dipolar interaction between the nanoparticles. We analytically investigate<br />
the dispersion, the effective Hamiltonian and the eigenstates of the collective plasmons for<br />
an arbitrary orientation of the individual dipole moments. When the polarization points close<br />
to the normal to the plane the spectrum presents Dirac cones, similar to those present in the<br />
electronic band structure of graphene. Moreover, we show that the corresponding<br />
eigenstates of the collective plasmons represent Dirac-like massless bosonic excitations. We<br />
further discuss how one can manipulate the Dirac points in the Brillouin zone and open a gap<br />
in the collective plasmon dispersion by modifying the polarization of the localized surface<br />
plasmons, paving the way for a fully tunable plasmonic analogue of graphene.
Friday<br />
Electron focusing in grapheme<br />
Csaba Péterfalvi 1,2 , László Oroszlány 1 , József Cserti 1 , Colin Lambert 2<br />
1 Department of Physics of Complex Systems, Eötvös University, Budapest, H-1117,<br />
Hungary<br />
2 Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK<br />
We propose an implementation of a valley selective electronic Veselago lens, as a planar<br />
potential step in bilayer graphene. We <strong>de</strong>monstrate that low energy electrons radiating from<br />
a point source and being scattered by an appropriately oriented potential step can be<br />
focused again coherently within the same band. The phenomenon is due to the negative<br />
refraction in<strong>de</strong>x which is a consequence of the anisotropy in the dispersion relation caused<br />
by the trigonal warping effect. We also consi<strong>de</strong>r an effective Hamiltonian in which the<br />
electron-electron interaction [1], as well as external mechanical strain [2] is taken into<br />
account, and we show how this affects the focusing phenomenon. Recent studies on the<br />
electron-phonon interaction in bilayer graphene [3] suggest that the electrons' free path can<br />
be long enough even on room temperatures to enable the focusing.<br />
[1] Y. Lemonik, I. L. Aleiner, C. Toke, and V. I. Fal’ko, Spontaneous symmetry breaking and<br />
Lifshitz transition in bilayer graphene, Phys. Rev. B 82, 201408 (2010)<br />
[2] M. Mucha-Kruczyński, I. L. Aleiner and V. I. Fal’ko, Strained bilayer graphene: Band<br />
structure topology and Landau level spectrum, Phys. Rev. B 84, 041404 (2011)<br />
[3] K. M. Borysenko, J. T. Mullen, X. Li, Y. G. Semenov et al, Electron-phonon interactions in<br />
bilayer graphene, Phys. Rev. B 83, 161402 (2011)<br />
__________________________________________________________________________<br />
Theory of scanning gate microscopy<br />
C. Gorini 1 , R. A. Jalabert 1 , W. Szewc 1 , S. Tomsovic 2 and D. Weinmann 1<br />
1 <strong>Institut</strong> <strong>de</strong> Physique et Chimie <strong>de</strong>s Matérieux <strong>de</strong> Strasbourg, UMR 7504, CNRS-UdS, 23 rue<br />
du Loess, BP 43, 67034 Strasbourg Ce<strong>de</strong>x 2, France<br />
2 Department of Physics and Astronomy, PO Box 642814, Washington State University,<br />
Pullman, WA 99164-2814, USA<br />
The conductance change due to a local perturbation in a phase-coherent nanostructure is<br />
calculated [1]. The general expressions to first and second or<strong>de</strong>r in the perturbation are<br />
applied to the scanning gate microscopy of a two-dimensional electron gas containing a<br />
quantum point contact. The relation between the conductance change and the local current<br />
<strong>de</strong>nsity is discussed relying on an extension of the Szafer-Stone mo<strong>de</strong>l for a constriction [2].<br />
[1] R. A. Jalabert, W. Szewc, S. Tomsovic and D. Weinmann, What is measured in the<br />
scanning gate microscopy of a quantum point contact? Phys. Rev. Lett. 105 166802 (2010)<br />
[2] A. Szafer and A. D. Stone, Theory of Quantum Conduction through a Constriction Phys.<br />
Rev. Lett. 62 300 (1989)
Friday<br />
Electron interferometry with a Quantum Point Contact: Effect of electron-electron<br />
interaction and temperature<br />
Andrii Kleshchonok, Geneviève Fleury, Jean-Louis Pichard<br />
Service <strong>de</strong> Physique <strong>de</strong> l’Etat Con<strong>de</strong>nsé, IRAMIS / SPEC, CEA Saclay, 91191 Gif-sur-<br />
Yvette, France<br />
Motivated by experiments recently ma<strong>de</strong> in Harvard [1], Stanford [2], Zurich [3] and Grenoble<br />
[4], we study a simplified mo<strong>de</strong>l for <strong>de</strong>scribing an electron interferometer formed with a<br />
quantum point contact and the <strong>de</strong>pletion region induced by the charged tip of a scanning<br />
gate microscope. The contact is ma<strong>de</strong> of a single site with Hubbard interaction U (An<strong>de</strong>rson<br />
impurity) coupling two semi-infinite square lattices. A local moment [5] can take place in the<br />
contact above the Kondo temperature. We study how this moment can be manipulated when<br />
one scans the tip around the contact. We discuss also how the conductance of this<br />
interferometer <strong>de</strong>pends on the location the tip, on the strength U of the interaction and on the<br />
temperature, in regimes where the Hartree-Fock approximation remains valid [6]. In certain<br />
cases, an enhancement of the interference fringes can be yiel<strong>de</strong>d by an increase of the<br />
temperature [7] or an increase of the strength U of the interaction.<br />
[1] M.A. Topinka, et al. Coherent Branched Flow in a Two-Dimensional Electron Gas, Nature<br />
410 183 (2001)<br />
[2] M. P. Jura, et al. Unexpected features of branched flow through high-mobility twodimensional<br />
electron gases , Nature Physics 3 841-845 (2007)<br />
[3] A. A. Kozikov, et al. Interference of electrons in backscattering through a quantum point<br />
contact, arXiv:1206.1371v1<br />
[4] M. G.Pala , et al. Scanning gate microscopy of quantum rings: effects of an external<br />
magnetic field and of charged <strong>de</strong>fects, Nanotechnology 20, 26 (2009)<br />
[5] An<strong>de</strong>rson P. W. Localized Magnetic States in Metals, Physical Review 124 41-53 (1961)<br />
[6] Tsvelick A. M., Wiegmann P. B. Exact results in the theory of magnetic alloys, Advances<br />
in Physics 32 453 (1983)<br />
[7] About A., Lemarié G., Pichard J.-L. Thermal Enhancement of Interference Effects in<br />
Quantum Point Contacts Phys. Rev. Lett. 106 156810 (2011)<br />
__________________________________________________________________________<br />
Symmetry-induced interference effects in metalloporphyrins wires<br />
R.Ferradás 1,2 , V.M.García-Suárez 1,2,3 and J.Ferrer 1,2,3<br />
1<br />
Departamento <strong>de</strong> Física, Universidad <strong>de</strong> Oviedo, 33007 Oviedo, Spain<br />
2<br />
Nanomaterials and Nanotechnology Research Center, CSIC-Universidad <strong>de</strong> Oviedo, Spain<br />
3<br />
Department of Physics, Lancaster University, Lancaster LA1 4YW, United Kingdom<br />
Organo-metallic molecular structures where a single metallic atom is embed<strong>de</strong>d in the<br />
organic backbone are i<strong>de</strong>al systems to study the effect of strong correlations on their<br />
electronic structure. In this work we calculate the electronic and transport properties of a<br />
series of metalloporphyrin molecules sandwiched by gold electro<strong>de</strong>s using a combination of<br />
<strong>de</strong>nsity functional theory and scattering theory. The impact of strong correlations at the<br />
central metallic atom is gauged by comparing our results obtained using conventional DFT<br />
and DFT+U approaches. The zero bias transport properties may or may not show spinfiltering<br />
behavior, <strong>de</strong>pending on the nature of the d state closest to the Fermi energy. The<br />
type of d state <strong>de</strong>pends on the metallic atom and gives rise to interference effects that<br />
produce different Fano features. The inclusion of the U term opens a gap between the d<br />
states and changes qualitatively the conductance and spin-filtering behavior in some of the
Friday<br />
molecules. We explain the origin of the quantum interference effects found as due to the<br />
symmetry-<strong>de</strong>pen<strong>de</strong>nt coupling between the d states and other molecular orbitals and<br />
propose the use of these systems as nanoscale chemical sensors. We also <strong>de</strong>monstrate that<br />
an a<strong>de</strong>quate treatment of strong correlations is really necessary to correctly <strong>de</strong>scribe the<br />
transport properties of metalloporphyrins and similar molecular magnets.<br />
[1] D. Dolphin, The Porphyrins Handbook, Aca<strong>de</strong>mic, New York (1978)<br />
[2] M. Liao and S.Scheiner, Electronic structure and bonding in metal porphyrins, Journal of<br />
chemical Physics 117, 205 (2002)<br />
[3] J. Otsuki, STM studies on Porphyrins, Chemical Review 254, 2311 (2010)<br />
[4] V.I. Anisimov, J. Zaanen and O.K. An<strong>de</strong>rsen, Band theory and Mott insulators: Hubbard<br />
instead of Stoner I, Physical Review B 44, 943 (1991)<br />
[5] A.I. Liechtenstein,V.I. Anisimov and J. Zaanen, DFT and strong interactions: Orbital<br />
or<strong>de</strong>ring in Mott-Hubbard insulators, Physical Review B 52, 5467 (1995)<br />
[6] C. Tablero, Representations of the occupation number matrix on the LDA/GGA+U<br />
method, J. Phys.:Con<strong>de</strong>nsed Matter 20, 325205<br />
[7] M. Cococcioni and S. Gironcoli, Linear response approach to the calculation of the<br />
effective interaction parameters in LDA+U method, Physical Review B 71, 035105 (2005)<br />
[8] R.E. Sparks, V.M. García-Suárez, D.Zs. Manrique and C.J. Lambert, Quantum<br />
interference in single molecule electronic systems, Physical Review B 83, 075437 (2011)<br />
__________________________________________________________________________<br />
Ac magnetic fields coupled to spin qubits<br />
Álvaro Gómez León and Gloria Platero<br />
Sor Juana Inés <strong>de</strong> la Cruz, 3, Cantoblanco, 28049, Madrid, Spain<br />
Quantum systems coupled to periodic ac electric or magnetic fields present new interesting<br />
coherence properties not present in the undriven system. We will show that the presence of<br />
an external periodic ac magnetic field applied to a two coupled two-level systems, such as a<br />
double quantum dot, is able to induce charge localization, spin locking or both, by tuning the<br />
ac field parameters, i.e., the frequency, intensity or phase difference, as well as by tuning its<br />
polarization.<br />
In contrast with ac electric fields, the possibility of induce dynamical spin locking will allow to<br />
freeze the spin projection of the initial state for some values of the parameter space [2,3]. We<br />
show how the symmetries of the Hamiltonian in the presence of the driving field influence the<br />
quasi-energy spectrum and how they <strong>de</strong>termine the electronic charge and spin dynamics.<br />
Finally we discuss how the application of an ac magnetic field to these systems allows to<br />
tune the topological properties for both the adiabatic and the non adiabatic regime [4]. Our<br />
results generalize those on geometrical phases for the spin by Berry [5] including the spatial<br />
<strong>de</strong>gree of freedom and spatial anisotropy for the magnetic field.<br />
[1] Charge localization and dynamical spin locking in double quantum dots driven by ac<br />
magnetic fields, A. Gómez-León and G. Platero, Phys. Rev. B (Rapid Communications) 84,<br />
121310 (2011).<br />
[2] Transport blocking and topological phases using ac magnetic fields, A. Gómez-León and<br />
G. Platero, Phys. Rev. B 85, 245319 (2012).<br />
[3] Topological phases in adiabatic and nonadiabatic driven systems, A. Gómez-León and G.<br />
Platero, Phys. Rev. B 86, 115318 (2012).<br />
[4] Quantal Phase Factors Accompanying Adiabatic Changes, M. V. Berry, Proc. R. Soc.<br />
Lond. A 392, 45-57 (1984).
Friday<br />
Nonequilibrium transport response from equilibrium transport theory<br />
Víctor García Suárez and Jaime Ferrer<br />
Department of Physics, University of Oviedo and CINN (CSIC).Oviedo (Spain).<br />
Department of Physics, Lancaster University. Lancaster (UK).<br />
We propose a simple scheme [1] that <strong>de</strong>scribes accurately essential non-equilibrium effects<br />
in nanoscale electronics <strong>de</strong>vices using equilibrium transport theory. The scheme, which is<br />
based on the alignment and <strong>de</strong>alignment of the junction molecular orbitals with the shifted<br />
Fermi levels of the electro<strong>de</strong>s, simplifies drastically the calculation of current-voltage<br />
characteristics compared to typical non-equilibrium algorithms. We probe that the scheme<br />
captures a number of non-trivial transport phenomena such as the negative differential<br />
resistance and rectification effects. It applies to those atomic-scale junctions whose relevant<br />
states for transport are spatially placed on the contact atoms or near the electro<strong>de</strong>s.<br />
[1] V. M. García-Suárez and J. Ferrer, Nonequilibrium transport response from equilibrium<br />
transport theory, Phys. Rev. B. 86 125456 (2012)<br />
__________________________________________________________________________<br />
Quantum chaos in disor<strong>de</strong>red graphene<br />
Spiros Evangelou<br />
University of Ioannina, Physics Department, Ioannina-45110 Greece<br />
I shall report on the energy-level statistics in disor<strong>de</strong>red graphene lattices of various<br />
shapes[1] close to the Dirac point. The level-spacing distribution function, shown for various<br />
flakes with armchair, zigzag and Klein edges, will be consistent with weakly chaotic behavior.<br />
The obtained level-spacing distribution is also related to critical fractal eigenstates while<br />
An<strong>de</strong>rson localization occurs for strong disor<strong>de</strong>r.<br />
[1] H.Amanatidis, I.Kleftogiannis, D.E.Katsanos and S.N.Evangelou (to be submitted).<br />
.
Posters<br />
Posters<br />
Ab-initio study of the thermopower of biphenyl-based single-molecule junctions<br />
M. Bürkle 1, 2 , L. A. Zotti 3 , J. K. Viljas 4, 5 , D. Vonlanthen 6 , A. Mishchenko 7<br />
T. Wandlowski 7 M. Mayor 2, 6, 8 G. Schön 1, 2, 8 1, 2, 9<br />
and F. Pauly<br />
1<br />
<strong>Institut</strong>e of Theoretical Solid State Physics, Karlsruhe <strong>Institut</strong>e of Technology, D-76131<br />
Karlsruhe, Germany<br />
2<br />
DFG Center for Functional Nanostructures, Karlsruhe <strong>Institut</strong>e of Technology, D-76131<br />
Karlsruhe, Germany<br />
3<br />
Departamento <strong>de</strong> Física Teórica <strong>de</strong> la Materia Con<strong>de</strong>nsada,<br />
Universidad Autónoma <strong>de</strong> Madrid, E-28049 Madrid, Spain<br />
4<br />
Low Temperature Laboratory, Aalto University, P.O. Box 15100, FIN-00076 Aalto, Finland<br />
5<br />
Department of Physics, P.O. Box 3000, FIN-90014 University of Oulu, Finland<br />
6<br />
Department of Chemistry, University of Basel, CH-4056 Basel, Switzerland<br />
7<br />
Department of Chemistry and Biochemistry, University of Bern, CH-3012 Bern, Switzerland<br />
8<br />
<strong>Institut</strong>e for Nanotechnology, Karlsruhe <strong>Institut</strong>e of Technology, D-76344 Eggenstein-<br />
Leopoldshafen, Germany<br />
9<br />
Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720<br />
By employing ab initio electronic-structure calculations combined with the nonequilibrium<br />
Green's function technique, we study the <strong>de</strong>pen<strong>de</strong>nce of the thermopower Q on the<br />
conformation in biphenyl-based single-molecule junctions. For the series of experimentally<br />
available biphenyl molecules, alkyl si<strong>de</strong> chains allow us to gradually adjust the torsion angle<br />
between the two phenyl rings from 0 ° to 90 ° and to control in this way the <strong>de</strong>gree of π-<br />
electron conjugation. Studying different anchoring groups and binding positions, our theory<br />
predicts that the absolute values of the thermopower <strong>de</strong>crease slightly towards larger torsion<br />
angles, following an a+bcos2 <strong>de</strong>pen<strong>de</strong>nce. The anchoring group <strong>de</strong>termines the sign of Q<br />
and a,b simultaneously. Sulfur and amine groups give rise to Q,a,b>0, while for cyano,<br />
Q,a,b
Posters<br />
Non-adiabatically driven electron in quantum wire<br />
T. Ca<strong>de</strong>z 1 , J. H. Jefferson 2 and A. Ramsak 1,3<br />
1<br />
J. Stefan <strong>Institut</strong>e, Ljubljana, Slovenia<br />
2<br />
Department of Physics, Lancaster University, Lancaster LA1 4YB, UK<br />
3<br />
Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia<br />
An exact solution is <strong>de</strong>rived for the wave function of an electron in a semiconductor quantum<br />
wire with spin-orbit interaction and driven by external time <strong>de</strong>pen<strong>de</strong>nt harmonic confining<br />
potential [1]. The formalism allows analytical expressions for various quantities to be <strong>de</strong>rived,<br />
such as spin and pseudo-spin rotations, energy and occupation probabilities for excited<br />
states. It is <strong>de</strong>monstrated how perfect spin and pseudo-spin flips can be achieved at high<br />
frequencies of or<strong>de</strong>r , the confining potential level spacing. By an appropriately chosen<br />
driving term, spin manipulation can be exactly performed far into the non-adiabatic regime.<br />
Implications for spin-polarised emission and spin-<strong>de</strong>pen<strong>de</strong>nt transport are also discussed.<br />
[1] T. Ca<strong>de</strong>z, J. H. Jefferson and A. Ramsak, Non-adiabatically driven electron in quantum<br />
wire, arXiv: 1208.5359<br />
__________________________________________________________________________<br />
Spin-orbit effects in nanowire-based wurtzite semiconductor quantum dots<br />
Guido Intronati (1,2,3) , Pablo Tamborenea (1) , Rodolfo Jalabert (2) , Dietmar Weinmann (2)<br />
(1) Departamento <strong>de</strong> Física, Universidad <strong>de</strong> Buenos Aires, Ciudad Universitaria, Pab. I,<br />
C1428EHA Buenos Aires, Argentina<br />
(2) <strong>Institut</strong> <strong>de</strong> Physique et Chimie <strong>de</strong>s Matériaux <strong>de</strong> Strasbourg, UMR 7504, CNRS-UdS, 23<br />
rue du Loess, BP 43, 67034 Strasbourg Ce<strong>de</strong>x 2, France<br />
(3) Service <strong>de</strong> Physique <strong>de</strong> l'Etat Con<strong>de</strong>nsé CNRS URA 2464, CEA Saclay, 91191 Gif-sur-<br />
Yvette, France<br />
We study the effects of spin-orbit interaction on the electronic states and spin relaxation<br />
rates of cylindrical quantum dots <strong>de</strong>fined on wurtzite quantum wires. The linear and cubic<br />
contributions of the bulk Dresselhaus spin-orbit coupling are taken into account, along with<br />
the influence of an external magnetic field. An analytic solution for the electronic states that<br />
was previously found for cylindrical pillbox zincblen<strong>de</strong> quantum dots with Rashba interaction<br />
is exten<strong>de</strong>d here to the case of wurtzite dots. The energy spectrum is computed, and the<br />
electronic states for InAs are characterized. This may be a useful aspect of this compound<br />
from the point of view of applications to spin manipulation.
Posters<br />
Nonclassical photon-pair production in a voltage-biased Josephson junction<br />
Juha Leppäkangas 1 , Göran Johansson 1 , Michael Marthaler 2 , and Mikael Fogelström 1<br />
1<br />
Microtechnology and Nanoscience, MC2, Chalmers University of Technology, SE-412 96<br />
Göteborg, Swe<strong>de</strong>n<br />
2<br />
<strong>Institut</strong> für Theoretische Festkörperphysik and DFG-Center for Functional Nanostructures<br />
(CFN), Karlsruhe <strong>Institut</strong>e of Technology, D-76128 Karlsruhe, Germany<br />
We investigate electromagnetic radiation emitted by a small voltage-biased Josephson<br />
junction connected to a superconducting transmission line. For weak tunneling couplings and<br />
frequencies below the well known emission peak at the Josephson frequency (2eV/h), extra<br />
radiation is triggered by quantum noise in the electromagnetic environment. For typical ohmic<br />
transmission lines, the corresponding photon flux spectrum becomes symmetric around half<br />
the Josephson frequency, indicating that the photons are predominately created in pairs. By<br />
establishing an input-output formalism for the microwave field in the transmission line, we<br />
give further evi<strong>de</strong>nce for this non-classical photon pair production, <strong>de</strong>monstrating that it<br />
violates the classical Cauchy-Schwarz inequality for two-mo<strong>de</strong> flux cross correlations. In<br />
connection to recent experiments [1], we also consi<strong>de</strong>r a stepped transmission line, where<br />
resonances increase the signal-to-noise ratio.<br />
[1] M. Hofheinz, F. Portier, Q. Baudouin, P. Joyez, D. Vion, P. Bertet, P. Roche, and D.<br />
Esteve Bright Si<strong>de</strong> of the Coulomb Blocka<strong>de</strong>, Phys. Rev. Lett. 106 217005 (2011)<br />
__________________________________________________________________________<br />
Gap Generation in Topological Insulator Surface States by non-Ferromagnetic<br />
Magnets<br />
László Oroszlány 1 , Alberto Cortijo 2<br />
1<br />
Department of Physics of Complex Systems, Eotvos University,<br />
H-1117 Budapest, Pázmány Péter sétány 1/A, Hungary<br />
2<br />
<strong>Institut</strong>o <strong>de</strong> Ciencia <strong>de</strong> Materiales <strong>de</strong> Madrid, CSIC, Cantoblanco, 28049 Madrid, Spain.<br />
Within a tight binding approach, it is shown that, contrary to the naive expectation, single<br />
particle spectral gaps can be opened on the surface states of three dimensional topological<br />
insulators by using commensurate out- and in-plane antiferromagnetic or ferromagnetic<br />
insulating thin films [1].<br />
[1] L. Oroszlány, A. Cortijo arXiv:1208.4615<br />
__________________________________________________________________________<br />
Optical conductivity of bilayer graphene in the far-infrared (FIR) spectral range<br />
Gábor Széchenyi, József Cserti<br />
Department of Physics of Complex Systems, Eötvös University, Budapest, Hungary<br />
Using Kubo formula we study theoretically the frequency <strong>de</strong>pen<strong>de</strong>nt optical conductivity in<br />
bilayer graphene with symmetry breaking mechanisms. We <strong>de</strong>monstrate that in the FIR<br />
spectral range (1.2-80 meV) the spectrum is strongly sensitive to the rate of the symmetry<br />
breaking, the trigonal warping and the polarization of the light. We show analytically a<br />
connection between the minimal conductivity and the zero frequency limit of the optical<br />
spectrum.
Posters<br />
Entanglement and the Kondo effect in triple quantum dots<br />
S. B. Tooski 1, 2, 3 , B. Bulka 3 , R. Zitko 1,2 , and A. Ramsak 1, 2<br />
1 Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia<br />
2 J. Stefan <strong>Institut</strong>e, Ljubljana, Slovenia<br />
3 <strong>Institut</strong>e of Molecular Physics, Polish Aca<strong>de</strong>my of Sciences, ul. M. Smoluchowskiego 17,<br />
Poznan, Poland<br />
We analyze a system of triple quantum dots in a triangular geometry, in which one of the<br />
quantum dots is connected to metallic leads, Fig. 1. We expect that the Kondo effect<br />
between the leads and central dot C (with intra-dot Coulomb interactions) can induce perfect<br />
spin entangled states between dots A and B (dots without intra-dot interactions). Using<br />
Wilson’s numerical renormalization group technique [1], we investigate various spin-spin<br />
correlation functions, probabilities for antiparallel and parallel spin alignment, and the<br />
concurrence [2] to quantify quantum entanglement in the triple quantum dot system [3], in the<br />
regime where each dot is essentially singly occupied by adjusting a global back-gate voltage.<br />
As a consequence of quantum phase transition an abrupt switch between fully entangled and<br />
separate states between A and B dots takes place. By tuning the interdot coupling t and the<br />
dot-lead coupling Γ, one can switch abruptly ferromagnetic and antiferromagnetic interaction<br />
between A and B dots. The effective Ru<strong>de</strong>rman-Kittel-Kasuya-Yoshida (RKKY) interaction<br />
between these dots is ferromagnetic in our simplified mo<strong>de</strong>l. Here the spins or<strong>de</strong>r<br />
ferromagnetically into a triplet state and un<strong>de</strong>rgo the S=1 Kondo screening at low<br />
temperatures. This yields an uncompensated S=1/2 residual spin, and since half a unit of<br />
spin is quenched by the conduction band via the Kondo effect, there clearly cannot be any<br />
entanglement between the electrons on noninteracting dots. For t t , the antiferromagnetic<br />
or<strong>de</strong>ring wins and the electrons form an entangled singlet state on A and B dots. The<br />
transition from the regime dominated by the RKKY interaction between A and B dots to the<br />
Kondo singlet phase for C dot is in this case a true quantum phase transition and the<br />
concurrence falls abruptly from C AB 1 to C AB 0.<br />
c<br />
A<br />
t<br />
B<br />
t’ t’<br />
L<br />
C<br />
R<br />
Fig. 1. A triangle of quantum dots attached to the leads.<br />
[1] R. Zitko, NRG_Ljubljana co<strong>de</strong>; H. R. Krishna-murthy, J. W. Wilkins and K. G. Wilson,<br />
Phys. Rev. B 21, 1003 (1980).<br />
[2] A. Ramšak, J. Mravlje, R. Žitko, and J. Bonča, Phys. Rev. B 74, 241305(R) (2006); J.<br />
Mravlje, A. Ramšak, and T. Rejec, Phys. Rev. B 73, 241305(R) (2006); T. Rejec and A.<br />
Ramšak, Phys. Rev. B 68, 035342 (2003); A. Ramšak, I. Sega, and J. H. Jefferson, Phys.<br />
Rev. A 74, 010304(R) (2006).<br />
[3] W. Wang, Phys. Rev. B 78, 235316 (2008); A. K. Mitchell, T. F. Jarrold, and D. E. Logan<br />
Phys. Rev. B 79, 085124 (2009).