Spectral and transport properties of a half-filled Anderson impurity coupled to phase-biased superconducting and metallic leads

TL;DR

This paper develops a method to analyze a quantum dot coupled to superconducting and metallic leads, enabling phase-dependent spectral and transport property calculations using numerical techniques, and confirms results with quantum Monte Carlo simulations.

Contribution

It introduces a general scheme to map complex quantum dot setups onto an Anderson model, facilitating phase-dependent spectral and transport analysis with standard numerical methods.

Findings

Spectral properties interpreted via broadened Andreev bound states.

Phase-dependent Kondo temperature follows a previously conjectured form.

Transport properties agree with quantum Monte Carlo simulations.

Abstract

We derive and apply a general scheme for mapping a setup consisting of a half-filled single level quantum dot coupled to one normal metallic and two superconducting phase-biased leads onto an ordinary half-filled single impurity Anderson model with single modified tunneling density of states. The theory allows for the otherwise unfeasible application of the standard numerical renormalization group and enables to obtain phase-dependent local spectral properties as well as phase-dependent induced pairing and Josephson current. The resulting transport properties match well with the numerically exact continuous-time hybridization-expansion quantum Monte Carlo. For weakly coupled normal electrode, the spectral properties can be interpreted in terms of normal-electrode-broadened Andreev bound states with phase-dependent position analogous to the superconducting Anderson model, which coexist in the $\pi$-like phase with a Kondo peak whose phase-dependent Kondo temperature follows the form conjectured previously in Doma\'nski et al., Phys.~Rev.~B {\bf 95}, 045104 (2017)