Generalized Topology in Lattice Models without Chiral Symmetry

TL;DR

This paper introduces a new 1D lattice model with generalized topology that breaks chiral symmetry, extends to 2D to realize a second-order topological insulator, and is applicable to various crystalline materials.

Contribution

A new versatile 1D lattice model with generalized topology that extends to 2D SOTI phases, breaking chiral symmetry and robust against boundary variations.

Findings

Model characterized by a projected winding number W_{1D,P}=1

Extension to 2D yields a second-order topological insulator

Topology protected by opposite winding numbers W_{2D,P}^{ ext{±}}=±1

Abstract

The Su-Schrieffer-Heeger (SSH) model is a fundamental lattice model used to study topological physics. Here, we propose a new versatile one-dimensional (1D) lattice model that extends beyond the SSH model. Our 1D model breaks chiral symmetry and has generalized topology characterized by a projected winding number $W_{1D,P}=1$. When this model is extended to 2D, it can generate a second-order topological insulator (SOTI) phase. The generalized topology of the SOTI phase is protected by a pair of opposite winding numbers $W_{2D,P}^{\pm}=\pm1$, which count the opposite phase windings of a projected vortex and antivortex pair defined in the manifold of the entire parameter space. Thus, the topology of our models is robust and the end (corner) modes are independent of the selection of unit cells and boundary configurations. More significantly, we demonstrate that the model is very general and can be inherently realized in many categories of crystalline materials such as BaHCl.