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Scientific Report 2007-2009<br />
Condensed matter physics and biophysics<br />
C1. Superconductivity in low-dimensional materials<br />
Large part of the experimental and theoretical research<br />
on new superconducting (SC) materials focuses<br />
nowadays on systems that are effectively low dimensional.<br />
To this category belong layered materials<br />
with weakly-coupled planes, like the high-temperature<br />
cuprate superconductors, as well as confined 2D structures,<br />
like thin films or conducting layers at the interface<br />
of artificial heterostructures. Besides the low dimensionality,<br />
a common characteristic of many of these systems<br />
is the low superfluid density, i.e. the energy scale which<br />
controls the phase fluctuations of the SC order parameter.<br />
Under these conditions, the SC transition could<br />
share a Berezinsky-Kosterlitz-Thouless (BKT) character,<br />
where vortex excitations play a crucial role.<br />
The BKT transition has in principle very specific signatures,<br />
both below and above the SC transition temperature<br />
T BKT . For example the superfluid density J s<br />
vanishes with an “universal” jump approaching T BKT<br />
from below, while the SC correlation length ξ(T ), that<br />
is probed by several quantities like paraconductivity, diamagnetism<br />
or Nerst effect, should diverge exponentially<br />
as T → T BKT from above. This form would be in marked<br />
contrast with the typical power-law behavior of ξ(T ) due<br />
to Ginzburg-Landau (GL) SC fluctuations, where modulus<br />
and phase fluctuate simultaneously.<br />
The observation of clear signatures of BKT physics<br />
in these new systems is still debated. In cuprates<br />
contradicting conclusions emerge from different probes:<br />
while Nerst effect and diamagnetism point towards a<br />
relevance of BKT physics, no clear signature of the<br />
would be universal jump of the superfluid density has<br />
been <strong>report</strong>ed. Moreover paraconductivity in underdoped<br />
compounds provides evidence of a more traditional<br />
Aslamazov-Larkin GL-behavior [1]. This scenario<br />
calls for a deepr theoretical investigation of the additional<br />
effects that can affect the “universal” character<br />
of the BKT transition, mainly related to the quasi-2D<br />
structure and/or disorder. We have investigated these<br />
issues [2-3] using the sine-Gordon description of the BKT<br />
transition, which allows us to go beyond standard results<br />
derived in the XY model. First we discussed the role<br />
played by the energy µ of the vortex core in a weaklycoupled<br />
layered system. Here two ratios are relevant:<br />
µ/J s , which fixes the temperature where vortices would<br />
like to unbind, driving the J s to zero, and J ⊥ /J s , where<br />
J ⊥ is the interlayer Josephson coupling, which tends to<br />
keep J s finite. While in the XY model µ/J s has a fixed<br />
value, we showed that in the more general case the behavior<br />
of the system strongly depend on the ratio µ/J s ,<br />
the increasing of which effectively enhances J ⊥ /J s [2].<br />
As a consequence, even though the transition can ultimatively<br />
have a BKT character (i.e. vortex excitations<br />
are relevant) the jump of the superfluid-density J s is reduced<br />
and smoothed, and does not occur any more at the<br />
“universal” temperature. A similar ’non-universal’ µ/J s<br />
dependence of the BKT transition was found in the analysis<br />
of the magnetic-field effect [3]. Indeed, we showed<br />
that the standard linear scaling of the field-induced diamagnetism<br />
M ≃ −ξ 2 (T )H above T c is restricted to a<br />
range of fields that decreases as µ/J s increases, accounting<br />
thus for the persistent non-linear effects <strong>report</strong>ed in<br />
experiments in high-T c superconductors.<br />
R/R N<br />
1<br />
0.9<br />
0.8<br />
0.7<br />
0.6<br />
0.5<br />
0.4<br />
0.3<br />
0.2<br />
0.1<br />
0<br />
T(K)<br />
Data<br />
Hom<br />
Inhom<br />
0.15 0.2 0.25 0.3 0.35 0.4<br />
Figure 1: Resistivity in the presence of GL+BKT fluctuations,<br />
in the absence (Hom) and in the presence (Inhom)<br />
of inhomoegenity, compared to experimental data in SC heterostructures.<br />
[4]<br />
Interestingly, a revised approach to the BKT transition<br />
can be necessary also in the case of low-temperature<br />
superconductivity, as it is shown by our recent analysis<br />
of 2D superconducting heterostructures [4]. Our work<br />
shows that the contribution of SC BKT fluctuations<br />
to the conductivity cannot be computed neglecting the<br />
prominent role of the intrinsic sample inhomogeneity<br />
(see Fig. 1). This result could give new insight also on<br />
the nature of the superconductor-insulator transition,<br />
that in these systems can be induced in field-effect<br />
devices, which represent a promising candidate for<br />
future technological applications.<br />
References<br />
1. S. Caprara et al., Phys. Rev. B 79, 024506 (2009).<br />
2. L. Benfatto et al., Phys. Rev. Lett. 98, 117008 (2007).<br />
3. L. Benfatto et al., Phys. Rev. Lett. 99, 207002 (2007).<br />
4. L. Benfatto et al., Phys. Rev. B 80, 214506 (2009).<br />
Authors<br />
L. Benfatto 3 , S. Caprara, C. Castellani, M. Grilli<br />
http://theprestige.phys.uniroma1.it/clc/<br />
<strong>Sapienza</strong> Università di Roma 54 Dipartimento di Fisica