Markovian kinetic equation approach to electron transport through quantum dot coupled to superconducting leads

TL;DR

This paper derives a Markovian master equation for a quantum dot connected to superconducting leads, analyzing transport, proximity effects, and Andreev bound states in various equilibrium and non-equilibrium conditions.

Contribution

It introduces a novel Markovian approach to model electron transport in quantum dots coupled to superconductors with detailed treatment of superconducting properties.

Findings

Derived a master equation for quantum dot-superconductor systems

Analyzed transport and proximity effects in equilibrium and non-equilibrium

Identified conditions for Andreev bound states formation

Abstract

We present a derivation of Markovian master equation for the out of equilibrium quantum dot connected to two superconducting reservoirs, which are described by the Bogoliubov-de Gennes Hamiltonians and have the chemical potentials, the temperatures, and the complex order parameters as the relevant quantities. We consider a specific example in which the quantum dot is represented by the Anderson impurity model and study the transport properties, proximity effect and Andreev bound states in equilibrium and far from equilibrium setups.