Topological properties of subsystem-symmetry-protected edge states in an extended quasi-one-dimensional dimerized lattice

TL;DR

This paper explores the topological properties of a complex quasi-one-dimensional lattice with multiple legs and sublattices, revealing conditions for various topological edge states and their symmetry classifications.

Contribution

It introduces a theoretical analysis of subsystem-symmetry-protected topological phases in a multi-leg, multi-sublattice dimerized lattice, highlighting new conditions for edge states.

Findings

Existence of zero- and finite-energy topological edge states.

Zero-energy edge states depend on the relation between legs and sublattices.

Different topological phases are characterized by subsystem symmetry.

Abstract

We investigate theoretically the topological properties of dimerized quasi-one-dimensional (1D) lattice comprising of multi legs $(L)$ as well as multi sublattices $(R)$. The system has main and subsidiary exchange symmetries. In the basis of latter one, the system can be divided into $L$ 1D subsystems each of which corresponds to a generalized $SSH_R$ model having $R$ sublattices and on-site potentials. Chiral symmetry is absent in all subsystems except when the axis of main exchange symmetry coincides on the central chain. We find that the system may host zero- and finite-energy topological edge states. The existence of zero-energy edge state requires a certain relation between the number of legs and sublattices. As such, different topological phases, protected by subsystem symmetry, including zero-energy edge states in the main gap, no zero-energy edge states, and zero-energy edge states in the bulk states are characterized. Despite the classification symmetry of the system belongs to $BDI$ but each subsystem falls in either $AI$ or $BDI$ symmetry class.