Eur. Phys. J. B (2016) 89: 192
https://doi.org/10.1140/epjb/e2016-70176-5

Regular Article

The topological quantum phase transitions in Lieb lattice driven by the Rashba SOC and exchange field

¹ Department of Electronic Information Science and Engineering, Zhejiang Ocean University, Zhoushan 316022, P.R. China
² College of Physics Science and Technology, Shenzhen University, Shenzhen 518060, P.R. China
³ College of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan 316022, P.R. China
⁴ Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA
⁵ Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803, USA

^a e-mail: wangrui@zjou.edu.cn

Received: 21 March 2016
Received in final form: 16 June 2016
Published online: 7 September 2016

Abstract

The quantum spin Hall (QSH) effect and the quantum anomalous Hall (QAH) effect in Lieb lattice are investigated in the presence of both Rashba spin-orbit coupling (SOC) and uniform exchange field. The Lieb lattice has a simple cubic symmetry, which is characterized by the single Dirac-cone per Brillouin zone and the middle flat band in the band structure. The intrinsic SOC is essentially needed to open the full energy gap in the bulk. The QSH effect could survive even in the presence of the exchange field. In terms of the first Chern number and the spin Chern number, we study the topological nature and the topological phase transition from the time-reversal symmetry broken QSH effect to the QAH effect. For Lieb lattice ribbons, the energy spectrum and the wave-function distributions are obtained numerically, where the helical edge states and the chiral edge states reveal the non-trivial topological QSH and QAH properties, respectively.