Anti-chiral edge states and hinge states based on the Haldane model

TL;DR

This paper demonstrates that antichiral edge and hinge states, which propagate in the same direction on opposite edges or hinges, can be realized using the original Haldane model by combining subsystems with opposite chirality, and these states are topologically protected.

Contribution

The study shows how to achieve antichiral edge and hinge states using the original Haldane model and stacking into three dimensions, expanding the understanding of topological states.

Findings

Antichiral edge states can be realized with the original Haldane model.

Antichiral hinge states can be implemented in three-dimensional stacking.

These states are robust against disorder and topologically protected.

Abstract

Different from the chiral edge states, antichiral edge states propagating in the same direction on the opposite edges are theoretically proposed based on the modified Haldane model, which is recently experimentally realized in photonic crystal and electric lattice systems. Here, we instead present that the antichiral edge states in the two-dimensional system can also be achieved based on the original Haldane model by combining two subsystems with the opposite chirality. Most importantly, by stacking these two-dimensional systems into three-dimension, it is found that the copropagating antichiral hinge states localized on the two opposite diagonal hinge cases of the system can be implemented. Interestingly, the location of antichiral hinge states can be tuned via hopping parameters along the third dimension. By investigating the local Chern number/layer Chern number and transmission against random disorders, we confirm that the proposed antichiral edge states and hinge states are topologically protected and robust against disorders. Our proposed model systems are expected to be realized in photonic crystal and electric lattice systems.