The honeycomb lattice with multi-orbital structure: topological and quantum anomalous Hall insulators with large gaps

Gu-Feng Zhang; Yi Li; Congjun Wu

doi:10.1103/PhysRevB.90.075114

paper

The honeycomb lattice with multi-orbital structure: topological and quantum anomalous Hall insulators with large gaps

arXiv:1403.0563 · doi:10.1103/PhysRevB.90.075114

Abstract

We construct a minimal four-band model for the two-dimensional (2D) topological insulators and quantum anomalous Hall insulators based on the $p_{x}$ - and $p_{y}$ -orbital bands in the honeycomb lattice. The multiorbital structure allows the atomic spin-orbit coupling which lifts the degeneracy between two sets of on-site Kramers doublets $j_{z} = \pm \frac{3}{2}$ and $j_{z} = \pm \frac{1}{2}$ . Because of the orbital angular momentum structure of Bloch-wave states at $Γ$ and $K (K^{'})$ points, topological gaps are equal to the atomic spin-orbit coupling strengths, which are much larger than those based on the mechanism of the $s$ - $p$ band inversion. In the weak and intermediate regime of spin-orbit coupling strength, topological gaps are the global gap. The energy spectra and eigen wave functions are solved analytically based on Clifford algebra. The competition among spin-orbit coupling $λ$ , sublattice asymmetry $m$ and the Néel exchange field $n$ results in band crossings at $Γ$ and $K (K^{'})$ points, which leads to various topological band structure transitions. The quantum anomalous Hall state is reached under the condition that three gap parameters $λ$ , $m$ , and $n$ satisfy the triangle inequality. Flat bands also naturally arise which allow a local construction of eigenstates. The above mechanism is related to several classes of solid state semiconducting materials.

14 pages, 6 figures

The honeycomb lattice with multi-orbital structure: topological and quantum anomalous Hall insulators with large gaps

Abstract

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