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

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.

6 pages, 7 figures

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• Flat bands and nontrivial topological properties in an extended Lieb lattice
• Excited quantum Hall effect: enantiomorphic flat bands in a Yin-Yang Kagome lattice
• Sumanene monolayer of pure carbon: a two-dimensional Kagome-analogy lattice with desirable band gap, ultrahigh carrier mobility and strong exciton binding energy
• High Chern numbers and topological flat bands in high-field polarized Kitaev magnets on the star lattice
• Triply degenerate nodal lines in topological and non-topological metals
• Engineering flux-controlled flat bands and topological states in a Stagome lattice
• Unconventional transport properties in systems with triply degenerate quadratic band crossings
• Topological phases of monolayer and bilayer depleted Lieb lattices