Year: 2020
Type: article
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: L. González Rosado, F. Hassler, G. Catelani
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
Award: G1259380839
OpenAlex ID: W3005936072