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

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 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-WuZhang-type model, the edge modes abruptly disappear, although the nontrivial Chern number does not change. In the Haldane-type model, for varying the model parameters, the edge modes do not necessarily disappear, and the nontrivial 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.