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

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 anti-localization (WAL) effects. 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 time scales that characterize the diffusive regime are energy dependent; this is in contrast with the the normal state, where the relevant time scale is the mean free time ${\tau }_e$, independent of energy. The energy dependence introduces a novel energy scale ${\epsilon }_{\ast }$, which in disordered superconductors (${\tau }_e\Delta \ll 1$, with $\Delta$ the gap) is given by ${\epsilon }_{\ast }=\sqrt{\Delta /{\tau }_e}$. From the diffusive behavior of the low-energy modes, we obtain the WL correction to the thermal conductivity. We give explicitly expressions in two dimensions. We determine the regimes in which the correction depends explicitly on ${\epsilon }_{\ast }$ and propose an optimal regime to verify our results in an experiment.

15 pages, 6 figures

References in corpus (4)

• Failure of the Wiedemann-Franz Law in Mesoscopic Conductors
• Thouless energy of a superconductor from non local conductance fluctuations
• Mesoscopic effects in the heat conductance of superconducting-normal-superconducting and normal-superconducting junctions
• Nonlocal transport mediated by nonlocal Hikami boxes: Condensation of evanescent quasiparticles injected into the superconducting gap

Cited by in corpus (2)

• Long-range exchange interaction between spin qubits mediated by a superconducting link at finite magnetic field
• Solution of master equations by fermionic-duality: Time-dependent charge and heat currents through an interacting quantum dot proximized by a superconductor