Transport in topological surface-states emerging from an interplay between isotropic and anisotropic exchange interactions*

Recently, 5d and 4d oxides and halides with honeycomb lattice structures are of great interest for sizeable anisotropic exchange interaction leading to new magnetic ground states. We will discuss an interplay between the isotropic Heisenberg and anisotropic Kitaev type exchange interactions in these materials, leading to a transition from ordinary insulator to topological edge states. The intrinsic magnetic ordering induces a magnetic gap in the electronic structure of the edge states. We specifically focus on the zigzag antiferromagnetic order under strong anisotropic interaction, where consecutive atomic chains exhibit altering magnetic orientation. We argue that the two edges have the same chirality in a sample with an odd number of atomic chains leading to a quantized anomalous Hall conductance. However, the two edges have opposite chirality when the number of atomic chains is even, leading to a cancellation of phases, giving a zero Hall conductance and a substantial longitudinal resistance, typically known as the axion insulator state.