Quantum Anomalous Hall Phase and Time‐Reversal‐Symmetry‐Broken Quantum Spin Hall Phase on the Square–Hexagon Lattice

The topological properties of the square–hexagon lattice are studied when the time‐reversal (TR) symmetry is broken. Based on the Chern number and spin Chern number, the topological trivial and nontrivial phases can be determined. When the spin‐dependent and ‐independent staggered potentials are taken into consideration, rich phase diagrams are obtained. A number of topological nontrivial phases, including the TR‐symmetry‐broken quantum spin Hall phase and quantum anomalous Hall (QAH) phase, can be achieved by tuning the spin‐dependent staggered potential. When the spin‐independent staggered potential is varied, it is possible to observe the topological phase transition from the metal phase to the QAH phase. The evolutions of the bulk bandgap and spin spectrum gap are also presented together. To support the identification of the topological phases, helical and chiral edge states are given numerically. Moreover, the corresponding density distribution and spin polarization are analyzed and discussed. The topological phase transitions on the square–hexagon lattice in the presence of the spin‐dependent and ‐independent staggered potentials are investigated. In terms of Chern number and spin Chern number, a variety of topological nontrivial phases can be found, such as the quantum anomalous Hall phase and time‐reversal‐symmetry‐broken quantum spin Hall phase.