Controlling Quantum Transport in a Superconducting Device via Dissipative Baths

TL;DR

This paper develops a theoretical framework for controlling quantum transport in superconducting devices using dissipative baths, revealing how dissipation influences steady states, conductance, and Majorana mode signatures.

Contribution

It generalizes the Meir-Wingreen formula and Onsager matrix for superconducting systems with multiple fermionic baths, providing new insights into dissipative effects on quantum transport.

Findings

Dissipation reduces degeneracy of non-equilibrium steady states.

Quantized conductance peaks are affected by dissipation.

Dissipation explains zero-bias peak suppression in Majorana modes.

Abstract

Within the quantum field-theoretical approach describing the evolution of a quadratic Liouvillian in the basis of Keldysh contour coherent states, we investigate the spectral and transport properties of a dissipative superconducting system coupled to normal Fermi reservoirs. We derive a generalization of the Meir-Wingreen formula and Onsager matrix for a superconducting system subject to an arbitrary number of fermionic baths. Following Kirchhoff's rule, we obtain an expression describing the dissipation induced loss current and formulate modified quantum kinetic equations. For wide-band contacts locally coupled to individual sites, we find that each contact reduces the degeneracy multiplicity of the non-equilibrium steady state by one. These results are numerically verified through several cases of the extended Kitaev model at symmetric points with a single contact. Furthermore, in the linear response regime at low temperatures, we demonstrate that (non-)degenerate non-equilibrium steady states correspond to (non-)quantized conductance peaks. Revisiting a paradigmatic problem of resonant transport in the Majorana mode of the Kitaev model we demonstrate that the dissipation accounts for the zero-bias peak suppression and its asymmetry.