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
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.
Key words: Mesoscopic and Nanoscale Systems
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2016