Bound states around impurities in a superconducting bilayer

TL;DR

This paper investigates how impurities induce bound states in a superconducting bilayer with s-wave pairing, revealing distinct behaviors for even and odd parity states and emphasizing the role of superconducting fitness.

Contribution

It provides a comprehensive analysis of impurity-induced bound states in a bilayer superconductor, highlighting differences between even and odd parity pairing and introducing the superconducting fitness framework.

Findings

Bound states occur only for time-reversal symmetry-breaking impurities in even-parity s-wave.

All impurity potentials induce bound states in odd-parity s-wave states.

Bound states are categorized into six types, applicable even for nodal gaps.

Abstract

We theoretically study the appearance of bound states around impurities in a superconducting bilayer. We focus our attention on $s$-wave pairing, which includes unconventional odd-parity states permitted by the layer degree of freedom. Utilizing numerical mean-field and analytical $T$-matrix methods, we survey the bound state spectrum produced by momentum-independent impurity potentials in this model. For even-parity $s$-wave pairing bound states are only found for impurities which break time-reversal symmetry. For odd-parity $s$-wave states, in contrast, bound states are generically found for all impurity potentials, and fall into six distinct categories. This categorization remains valid for nodal gaps. Our results are conveniently understood in terms of the ``superconducting fitness'' concept, and show an interplay between the pair-breaking effects of the impurity and the normal-state band structure.