Weak localization corrections to the thermal conductivity in s -wave superconductors

Physical review. B./Physical review. B, vol. 101

Abstract

We study the thermal conductivity in disordered $s$-wave superconductors. Expanding on previous works for normal metals, we develop a formalism that tackles particle diffusion as well as the weak localization (WL) and weak antilocalization (WAL) effects focusing on the two-dimensional case. Using a Green's functions diagrammatic technique, which takes into account the superconducting nature of the system by working in Nambu space, we identify the system's low-energy modes, the diffuson and the cooperon. The timescales that characterize the diffusive regime are energy dependent; this is in contrast to the normal state, where the relevant timescale is the impurity scattering time ${\ensuremath{\tau}}_{e}$, independent of energy. The energy dependence introduces a novel energy scale ${\ensuremath{\varepsilon}}_{*}$, which for dirty superconductors $({\ensuremath{\tau}}_{e}\mathrm{\ensuremath{\Delta}}\ensuremath{\ll}1$, with $\mathrm{\ensuremath{\Delta}}$ the gap) is given by ${\ensuremath{\varepsilon}}_{*}=\sqrt{\mathrm{\ensuremath{\Delta}}/{\ensuremath{\tau}}_{e}}$. From the diffusive behavior of the low-energy modes, we obtain the WL correction to the thermal conductivity. We give explicit expressions in two dimensions. We determine the regimes in which the correction depends manifestly on ${\ensuremath{\varepsilon}}_{*}$ and propose an optimal regime to verify our results in an experiment. In particular, we find a parametrically large reduction of the weak localization correction in a dirty superconductor, in comparison with its value in the normal state, when the temperature is lowered by 10% below the transition temperature.

Authors 3

1. L. González Rosado Aachen JARA-Institute for Quantum Information

   RWTH Aachen University · Forschungszentrum Jülich · Jülich Aachen Research Alliance

   Affiliation as printed

   JARA Institute for Quantum Information (PGI-11), Forschungszentrum Jülich, 52425 Jülich, Germany

   JARA Institute for Quantum Information, RWTH Aachen University, 52056 Aachen, Germany

2. Fabian Hassler Aachen JARA-Institute for Quantum Information

   RWTH Aachen University

   Affiliation as printed

   JARA Institute for Quantum Information, RWTH Aachen University, 52056 Aachen, Germany

3. Gianluigi Catelani

   Forschungszentrum Jülich · Jülich Aachen Research Alliance

   Affiliation as printed

   JARA Institute for Quantum Information (PGI-11), Forschungszentrum Jülich, 52425 Jülich, Germany