Shiba impurity bound states as a probe of topological superconductivity and Fermion parity changing quantum phase transitions

TL;DR

This paper explores how impurity-induced Shiba states in spin-orbit coupled superconductors can serve as local probes for topological superconductivity and quantum phase transitions involving Fermion parity changes, detectable via tunneling spectroscopy.

Contribution

It introduces the concept that Shiba states in time-reversal broken spin-orbit superconductors can be tuned to reveal topological phases and quantum phase transitions through their zero-energy crossings.

Findings

Shiba states can be tuned across the gap using magnetic field or gate voltage.

Zero-energy crossings of Shiba states indicate Fermion parity changing quantum phase transitions.

Shiba states provide a local spectroscopic signature of topological superconductivity.

Abstract

Spin-orbit coupled superconductors are potentially interesting candidates for realizing topological and potentially non-Abelian states with Majorana Fermions. We argue that time-reversal broken spin-orbit coupled superconductors generically can be characterized as having sub-gap states that are bound to localized non-magnetic impurities. Such bound states, which are referred to as Shiba states, can be detected as sharp resonances in the tunneling spectrum of the spin-orbit coupled superconductors. The Shiba state resonance can be tuned using a gate-voltage or a magnetic field from being at the edge of the gap at zero magnetic fields to crossing zero energy when the Zeeman splitting is tuned into the topological superconducting regime. The zero-crossing signifies a Fermion parity changing first order quantum phase transition, which is characterized by a Pfaffian topological invariant. These zero-crossings of the impurity level can be used to locally characterize the topological superconducting state from tunneling experiments.