Regular Article

Topological phase transitions on the square-octagon lattice with next-nearest-neighbor hopping

¹ School of Zhangjiagang, Jiangsu University of Science and Technology, Zhangjiagang 215600, P.R. China
² National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, P.R. China

^a e-mail: yuanyangnju@126.com

Received: 7 October 2019
Received in final form: 16 November 2019
Published online: 18 December 2019

Abstract

We investigate the topological phase transitions on the square-octagon lattice with an intrinsic spin-orbit coupling and an additional real next-nearest-neighbor hopping. We study the evolution of the band structure under the next-nearest-neighbor hopping parameters. Based on the spin Chern numbers, we present the phase diagrams of our model and find that a quantum spin Hall phase can be realized at different filling factors. Upon the inclusion of the staggered potential, we also discuss the effect of the time-reversal symmetry breaking term on the stability of the quantum spin Hall state. The variation of the spin-dependent staggered potential is shown to induce the time-reversal symmetry-broken quantum spin Hall phases, and the spin-imbalanced and spin-filtered quantum anomalous Hall phases. The phase transitions are always accompanied by closing of the bulk band gap. We finally demonstrate the edge-state properties of different topological phases.