Electron-boson-interaction induced particle-hole symmetry breaking of conductance into subgap states in superconductors

F Setiawan,Jay D Sau

doi:10.1103/physrevresearch.3.l032038

Abstract

Particle-hole symmetry (PHS) of conductance into subgap states in superconductors is a fundamental consequence of a noninteracting mean-field theory of superconductivity. The breaking of this PHS has been attributed to a noninteracting mechanism, i.e., quasiparticle poisoning (QP), a process detrimental to the coherence of superconductor-based qubits.Here, we show that the ubiquitous electron-boson interactions in superconductors can also break the PHS of subgap conductances. We study the effect of such couplings on the PHS of subgap conductances in superconductors using both the rate equation and Keldysh formalism, which have different regimes of validity. In both regimes, we found that such couplings give rise to a particle-hole $asymmetry$ in subgap conductances which increases with increasing coupling strength, increasing subgap-state particle-hole content imbalance and decreasing temperature. Our proposed mechanism is general and applies even for experiments where the subgap-conductance PHS breaking cannot be attributed to QP.

Highlights

Subgap states in superconductors are key features of topological superconducting phases [1,2,3,4,5,6,7,8,9,10,11,12,13] which offer great promise for quantum information processing [14,15]. Tunneling transport into such Andreev bound states (ABSs) provides the most direct and commonly employed method to detect them [16,17,18,19]. (Hereafter ABS refers to any subgap state in superconductors.) Most of our understanding of tunneling into superconductors is based on the celebrated Blonder-Tinkham-Klapwijk (BTK) formalism [20]
We propose a generic mechanism for particle-hole symmetry (PHS) breaking of subgap conductances without changing the superconductor’s parity state, namely, the coupling between ABSs and bosonic modes
Contrary to widely held belief, we show that the PHS breaking of subgap conductances in superconductors can arise without quasiparticle poisoning (QP)

Summary

INTRODUCTION

Subgap states in superconductors are key features of topological superconducting phases [1,2,3,4,5,6,7,8,9,10,11,12,13] which offer great promise for quantum information processing [14,15]. Our study of transport into an ABS coupled to bosonic modes and its relation to PHS breaking of subgap conductances has not been undertaken before To this end, we present ways to enforce fermion-parity conservation in treating interaction effects on transport into ABSs. We consider two different limits: weak and strong tunneling regimes where the ABS-lead tunnel strength is smaller and larger than the thermal broadening ∼kBT , respectively. The simplest application of FGR [23,53,54] considers the conductance into an ABS at positive [Fig. 1(a)] and negative subgap energies [Fig. 1(b)] to arise from the tunneling of electrons and holes, respectively, into the ABS (changing the ABS occupancy n from 0 → 1). The ratio /kBT determines two different transport regimes: weak ( /kBT < 1) and strong ( /kBT > 1) tunneling regimes

Rate equation

Keldysh

CONCLUSIONS