Bulk-edge correspondence in two-dimensional topological semimetals: A transfer matrix study of antichiral edge modes

TL;DR

This paper investigates the bulk-edge correspondence in two-dimensional topological semimetals with antichiral edge modes, revealing parameter ranges where edge modes vanish or spectral flows break down despite unchanged Chern numbers.

Contribution

It provides an analytical transfer matrix approach to study edge modes in specific topological semimetal models, uncovering breakdowns of bulk-edge correspondence.

Findings

Edge modes can abruptly disappear without changing Chern number.

Spectral flow of edge modes can break down independently of topological invariants.

Bulk-edge correspondence is not universally valid in these models.

Abstract

We study edge modes in topological semimetals which have an energy band structure of ordinary semimetals but can be characterized by a Chern number. More specifically, we focus on a Qi-Wu-Zhang-type square-lattice model and a Haldane-type honeycomb model, both of which exhibit antichiral edge modes whose wave packets propagate in the same direction at both parallel edges of the strip. To obtain these analytical solutions of the edge modes, we apply the transfer matrix method which was developed in the previous work [Phys. Rev. B \textbf{101}, 014442 (2020)]. As a result, we show that the bulk-edge correspondence is broken down for a certain range of the model parameters. More precisely, when increasing the strength of a hopping amplitude of the Qi-Wu-Zhang-type model, the edge modes abruptly disappear, although the non-trivial Chern number does not change. In the Haldane-type model, for varying the model parameters, the edge modes do not necessarily disappear, and the non-trivial Chern number does not change. However, the energy spectral flows of the edge modes from the valence band to the conduction band are abruptly broken at a certain set of the model parameters.