Time-dependent Landauer-B\"uttiker formalism for superconducting junctions at arbitrary temperatures

TL;DR

This paper extends the time-dependent Landauer-Büttiker formalism to superconducting junctions at arbitrary temperatures, providing a computationally efficient method and numerical results for simple normal metal-superconductor systems.

Contribution

It introduces a formalism that applies the Landauer-Büttiker approach to superconducting regions, simplifying calculations at finite temperatures.

Findings

Extended formalism to superconducting junctions.

Expressed frequency integrals with special functions for faster computation.

Numerical simulations of normal metal-superconductor junctions.

Abstract

We discuss an extension of our earlier work on the time-dependent Landauer--B\"uttiker formalism for noninteracting electronic transport. The formalism can without complication be extended to superconducting central regions since the Green's functions in the Nambu representation satisfy the same equations of motion which, in turn, leads to the same closed expression for the equal-time lesser Green's function, i.e., for the time-dependent reduced one-particle density matrix. We further write the finite-temperature frequency integrals in terms of known special functions thereby considerably speeding up the computation. Numerical simulations in simple normal metal -- superconductor -- normal metal junctions are also presented.