We report a theoretic study of the topological properties of the $\alpha \text{−}{T}_3$ lattice by taking the intrinsic spin orbit interaction into account. It is shown that when $0<\alpha <1$, the electronic band structure is spin-valley split and the original flat band is distorted to display a nonzero dispersion that imparts the system to be metallic. The gapped valence or conduction band shows the quantum spin Hall phase and experiences a topological phase transition from the spin Chern number $C_s=1$ to $C_s=2$ at the critical point $\alpha =\frac{1}{2}$. When a staggered magnetization order is considered in the system, a bunch of topological phases appear such as the quantum spin quantum anomalous Hall phase with variation of $\alpha$ or the magnetization strength.

• Received 15 November 2020
• Accepted 1 February 2021

DOI:https://doi.org/10.1103/PhysRevB.103.075419