$Z_2$ antiferromagnetic topological insulators with broken $C_4$ symmetry

Abstract

A two-dimensional topological insulator may arise in a centrosymmetric commensurate Néel antiferromagnet (AF), where staggered magnetization breaks both the elementary translation and time reversal, but retains their product as a symmetry. Fang et al.[Phys. Rev. B 88, 085406 (2013)] proposed an expression for a $Z_2$ topological invariant to characterize such systems. Here, we show that this expression does not allow to detect all the existing phases if a certain lattice symmetry is lacking. We implement numerical techniques to diagnose topological phases of a toy Hamiltonian, and verify our results by computing the Chern numbers of degenerate bands, and also by explicitly constructing the edge states, thus illustrating the efficiency of the method.

References in corpus (5)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• The Quantum Spin Hall Effect: Theory and Experiment
• Antiferromagnetic topological insulators
• New classes of topological crystalline insulators with unpinned surface Dirac cones

Cited by in corpus (3)

• Symmetry-protected line nodes and Majorana flat bands in nodal crystalline superconductors
• ${\mathcal{Z}}_2$ classification for a novel antiferromagnetic topological insulating phase in three-dimensional topological Kondo insulator
• Zeeman spin-orbit coupling in antiferromagnetic conductors