Topology of Andreev Bound States with Flat Dispersion

TL;DR

This paper develops a theoretical framework for understanding dispersionless Andreev bound states in unconventional superconductors, deriving criteria from bulk-edge correspondence, and explores their properties including a novel Majorana fermion with unique magnetic response.

Contribution

It introduces a generalized criterion and index theorems for dispersionless Andreev bound states, providing new insights into their stability and properties in various superconductor types.

Findings

Derived a bulk-edge correspondence criterion for dispersionless Andreev states

Identified a time-reversal invariant Majorana fermion with unique magnetic response

Analyzed specific superconductor models including dxy-wave, px-wave, and noncentrosymmetric types

Abstract

A theory of dispersionless Andreev bound states on surfaces of time-reversal invariant unconventional superconductors is presented. The generalized criterion for the dispersionless Andreev bound state is derived from the bulk-edge correspondence, and the chiral spin structure of the dispersionless Andreev bound states is argued from which the Andreev bound state is stabilized. Then we summarize the criterion in a form of index theorems. The index theorems are proved in a general framework to certify the bulk-edge correspondence. As concrete examples, we discuss (i) dxy-wave superconductor (ii) px-wave superconductor, and (iii) noncentrosymmetric superconductors. In the last example, we find a peculiar time-reversal invariant Majorana fermion. The time-reversal invariant Majorana fermion shows an unusual response to the Zeeman magnetic field, which can be used to identify it experimentally.