nanoelectronics - Institut d'Études Scientifiques de Cargèse (IESC)

Friday
Friday, October 2
Metallic phase of the quantum Hall effect in four-dimensional space
Jonathan M. Edge, J. Tworzydlo, C. W. J. Beenakker
Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Hoza 69, 00--681
Warsaw, Poland
We study the phase diagram of the quantum Hall effect in four-dimensional (4D) space [1].
Unlike in 2D, in 4D there exists a metallic as well as an insulating phase, depending on the
disorder strength. The critical exponent ≈ 1.2 of the diverging localization length at the
quantum Hall insulator-to-metal transition differs from the semiclassical value = 1 of 4D
Anderson transitions in the presence of time-reversal symmetry. Our numerical analysis is
based on a mapping of the 4D Hamiltonian onto a 1D dynamical system, providing a route
towards the experimental realization of the 4D quantum Hall effect.
[1] J.M. Edge, J. Tworzydlo, C. W. J. Beenakker Metallic phase of the quantum Hall effect in
four-dimensional space arXiv:1206.0099 to be published in PRL (2012)
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Thermal metal in topological superconductors
Jakub Tworzydlo (1) , I. C. Fulga (2) , A. R. Akhmerov (2) , C.W.J. Beenakker (2) , B. Beri (3)
(1)
Faculty of Physics, University of Warsaw, Poland
(2)
Instituut-Lorentz, Universiteit Leiden, The Netherlands
(3)
TCM Group, Cavendish Laboratory, United Kingdom
The thermal quantum Hall effect appears in the absence of time-reversal symmetry in a
single layer of a chiral p-wave superconductor. The insulator-insulator transition associated
with this effect is generically present only for weak disorder. For stronger disorder we find a
transition to a delocalized phase, known as the thermal metal.
In contrast, for a helical superconductor in the presence of time-reversal symmetry the
transition between two topologically distinct thermal insulators occurs via the intervening
thermal metal phase, even for an arbitrarily weak disorder.
We present a detailed study of a phase diagram and the critical exponents for these
topologically induced transitions. We also point to an underling mechanism of Majorana
states formation in both chiral and helical systems.
[1] I. C. Fulga, A. R. Akhmerov, J. Tworzydlo, B. Beri, and C. W. J. Beenakker, Phys. Rev. B
86, 054505 (2012)
[2] M. V. Medvedyeva, J. Tworzydlo, and C. W. J. Beenakker, Phys. Rev. B 81, 214203
(2010)
[3] J. H. Bardarson, M. V. Medvedyeva, J. Tworzydło, A. R. Akhmerov, and C. W. J.
Beenakker, Phys.Rev. B 81, 121414(R) (2010)
[4] M. Wimmer, A. R. Akhmerov, M. V. Medvedyeva, J. Tworzydlo, C. W. J. Beenakker,
Phys. Rev. Lett. 105, 046803 (2010)