Family of third-order topological insulators from Su-Schrieffer-Heeger stacking

TL;DR

This paper introduces a family of third-order topological insulators constructed from stacked SSH chains, characterized by Bott indices, and explores their rich topological phases including higher-order and nodal semimetal states.

Contribution

It presents a unified topological framework for third-order insulators via stacking SSH chains and classifies ten distinct models with analytical corner state solutions.

Findings

Certain surfaces and hinges exhibit nontrivial second- and first-order topology.

Phase diagram analysis reveals multiple topological phases, including third-order, second-order, and nodal semimetals.

Abstract

We construct a family of chiral symmetry-protected third-order topological insulators by stacking Su-Schrieffer-Heeger (SSH) chains and provide a unified topological characterization by a series of Bott indices. Our approach is informed by the analytical solution of corner states for the model Hamiltonians written as a summation of the extended SSH model along three orthogonal directions. By utilizing the generalized Pauli matrices, an enumeration of the constructed model Hamiltonians generates ten distinct models, including the well-studied three-dimensional Benalcazar-Bernevig-Hughes model. By performing a boundary projection analysis for the ten models, we find that certain surfaces and hinges of the systems can exhibit, respectively, nontrivial second-order and first-order topology in the phase of the third-order topological insulators. Furthermore, we analyze the phase diagram for one of the predicted models and reveal a rich set of topological phases, including the third-order topological insulators, second-order weak topological insulators, and second-order nodal semimetals.