Quantum anomalous Hall effect on star lattice with spin-orbit coupling and exchange field

TL;DR

This paper investigates the quantum anomalous Hall effect on a star lattice with spin-orbit coupling and exchange field, revealing multiple quantized Hall conductivities, a nearly flat band, and topological edge states, expanding understanding of topological phases.

Contribution

It introduces a star lattice model exhibiting quantum anomalous Hall effects with multiple energy gaps and topological features, connecting to honeycomb and kagome lattice systems.

Findings

Five quantized Hall conductivities at different energy gaps

Existence of a nearly flat band with nontrivial topology

Numerical confirmation of chiral edge states

Abstract

We study the star lattice with Rashba spin-orbit coupling and exchange field and find that there exists the quantum anomalous Hall effect in this system and there are five energy gaps at Dirac points and quadratic band crossing points. We calculate the Berry curvature distribution and obtain the Hall conductivity (Chern number $\nu$) quantized as integers, and find that $\nu=-1,2,1,1,2$, respectively, when the Fermi level lies in these five gaps. Our model can be view as a general quantum anomalous Hall system and, in limit cases, can give what the honeycomb lattice and kagome lattice gave. We also find there exists a nearly flat band with $\nu=1$ which may provide an opportunity to realize the fractional quantum anomalous Hall effect. Finally, the chiral edge states on a zigzag star lattice are given numerically to confirm the topological property of this system.