Square-root topological phase with time-reversal and particle-hole symmetry

TL;DR

This paper explores a new class of topological phases arising from the squared Hamiltonian in systems with time-reversal and particle-hole symmetry, revealing novel edge and surface states in 2D and 3D.

Contribution

It introduces the concept of square-root topological phases in systems with specific symmetries, expanding the understanding beyond chiral symmetry cases.

Findings

2D class CII systems host helical edge states due to nontrivial squared Hamiltonian topology

Surface states emerge in 3D systems with nontrivial squared Hamiltonian topology

Toy model analysis demonstrates the emergence of these edge and surface states

Abstract

Square-root topological phases have been discussed mainly for systems with chiral symmetry. In this paper, we analyze the topology of the squared Hamiltonian for systems preserving the time-reversal and particle-hole symmetry. Our analysis elucidates that two-dimensional systems of class CII host helical edge states due to the nontrivial topology of the squared Hamiltonian in contrast to the absence of ordinary topological phases. The emergence of the helical edge modes is demonstrated by analyzing a toy model. We also show the emergence of surface states induced by the non-trivial topology of the squared Hamiltonian in three dimensions.