Topological phase transitions between chiral and helical spin textures in a lattice with spin-orbit coupling and a magnetic field

¹ Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles (U.L.B.) B-1050 Brussels, Belgium, EU
² Institute for Theoretical Physics, Utrecht University - Leuvenlaan 4, 3584 CE Utrecht, The Netherlands, EU

^a ngoldman@ulb.ac.be

Received: 9 November 2011
Accepted: 12 December 2011

Abstract

We consider the combined effects of large spin-orbit couplings and a perpendicular magnetic field in a 2D honeycomb fermionic lattice. This system provides an elegant setup to generate versatile spin textures propagating along the edge of a sample. The spin-orbit coupling is shown to induce topological phase transitions between a helical quantum spin Hall phase and a chiral spin-imbalanced quantum Hall state. Besides, we find that the spin orientation of a single topological edge state can be tuned by a Rashba spin-orbit coupling, opening an interesting route towards quantum spin manipulation. We discuss the possible realization of our results using cold atoms trapped in optical lattices, where large synthetic magnetic fields and spin-orbit couplings can be engineered and finely tuned. In particular, this system would lead to the observation of a time-reversal symmetry-broken quantum spin Hall phase.