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 τe, independent of energy. The energy dependence introduces a novel energy scale ε * , which in disordered superconductors (τe∆ 1, with ∆ the gap) is given by ε * = ∆/τe. 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 ε * and propose an optimal regime to verify our results in an experiment.

Solution of master equations by fermionic-duality: Time-dependent charge and heat currents through an interacting quantum dot proximized by a superconductor

“…(41a)] and actual one, |z) [Eq. (42)], differ, but only by inverting the polarization. This is expected since the duality mapping inverts the energy spectrum, swapping the Andreev states |τ) = | − τ) and thus inverting the polarization of their occupations.…”

“…[38], but time-dependent charge and heat currents were not addressed. Yet, we find these two quantities particularly interesting, since they provide experimental access to the complex dynamic behaviour of the proximized quantum dot state, noting also the continued interest in heat transport in superconductors [40][41][42][43]. Importantly, for such time-dependent decay the proximity effect requires a careful consideration of the physical procedure of state preparation which enters the master equation as an initial condition.…”