Chiral-Symmetric Higher-Order Topological Phases of Matter

TL;DR

This paper introduces new higher-order topological phases in chiral-symmetric systems, characterized by multipole chiral numbers that predict corner states and are robust against certain disorders.

Contribution

The work defines bulk topological invariants called multipole chiral numbers for class AIII systems, revealing phases often overlooked by existing theories.

Findings

Higher-order topological phases with corner states identified

Multipole chiral numbers serve as bulk invariants

Phases are robust under chiral-symmetry-preserving disorder

Abstract

We introduce novel higher-order topological phases of matter in chiral-symmetric systems (class AIII of the tenfold classification), most of which would be misidentified as trivial by current theories. These phases are protected by "multipole chiral numbers", bulk integer topological invariants that in 2D and 3D are built from sublattice multipole moment operators, as defined herein. The integer value of a multipole chiral number indicates how many degenerate zero-energy states localize at each corner of a system. These higher-order phases of matter are generally boundary-obstructed and robust in the presence of chiral-symmetry-preserving disorder.