Conductance matrix symmetries of multiterminal semiconductor-superconductor devices

TL;DR

This paper explores how symmetries in the conductance matrix of multiterminal semiconductor-superconductor devices can reveal information about transmission probabilities and spin-orbit coupling, considering effects of bias and leakage.

Contribution

It introduces symmetry relations in conductance matrices and demonstrates their use in identifying spin-orbit coupling characteristics in hybrid devices.

Findings

Symmetry relations help extract transmission probabilities.

Symmetries can identify Rashba versus Dresselhaus spin-orbit coupling.

Voltage bias and leakage affect the symmetry relations and their signatures.

Abstract

Nonlocal tunneling spectroscopy of multiterminal semiconductor-superconductor hybrid devices is a powerful tool to investigate the Andreev bound states below the parent superconducting gap. We examine how to exploit both microscopic and geometrical symmetries of the system to extract information on the normal and Andreev transmission probabilities from the multiterminal electric or thermoelectric differential conductance matrix under the assumption of an electrostatic potential landscape independent of the bias voltages, as well as the absence of leakage currents. These assumptions lead to several symmetry relations on the conductance matrix. Next, by considering a numerical model of a proximitized semiconductor wire with spin-orbit coupling and two normal contacts at its ends, we show how such symmetries can be used to identify the direction and relative strength of Rashba versus Dresselhaus spin-orbit coupling. Finally, we study how a voltage-bias-dependent electrostatic potential as well as quasiparticle leakage break the derived symmetry relations and investigate characteristic signatures of these two contributions.