Topology of critical chiral phases: multiband insulators and superconductors

TL;DR

This paper generalizes the understanding of symmetry-protected edge states at quantum critical points to multiband one-dimensional chiral topological insulators and superconductors across various symmetry classes.

Contribution

It extends the topological phase transition framework to multiband models in all chiral symmetry classes, revealing new insights into critical topological phases.

Findings

Edge states exist at gap-closing points in multiband models.

The topological classification applies to all chiral symmetry classes.

Critical models exhibit robust edge modes at phase transitions.

Abstract

Recent works have proved the existence of symmetry-protected edge states in certain one-dimensional topological band insulators and superconductors at the gap-closing points which define quantum phase transitions between two topologically nontrivial phases. We show how this picture generalizes to multiband critical models belonging to any of the chiral symmetry classes AIII, BDI, or CII of noninteracting fermions in one dimension.