Bulk-edge correspondence with generalized chiral symmetry

TL;DR

This paper extends the bulk-edge correspondence concept to systems with generalized chiral symmetry, revealing unconventional edge state behaviors and critical phenomena when symmetry is broken by mass in topological models.

Contribution

It introduces a generalized chiral symmetry framework and analyzes edge state behavior and phase transitions in topological systems with broken symmetry.

Findings

Edge states exhibit unconventional behavior with symmetry breaking.

Localization length diverges at critical mass where edge and bulk states touch.

Imaginary wave vector of edge states becomes real at the touching energy.

Abstract

The bulk-edge correspondence in topological phases is extended to systems with the generalized chiral symmetry, where the conventional chiral symmetry is broken. In such systems, we find that the edge state exhibits an unconventional behavior in the presence of the symmetry breaking by the mass, which is explored explicitly in the case of a deformed Su-Schrieffer-Heeger model. The localization length of the edge states diverges at a certain critical mass, where the edge state touches to the bulk band. The edge state is specified by an imaginary wave vector that becomes real at the touching energy.