The nontrivial topological phases of indirect excitons in semiconductor coupled quantum wells

Abstract

Motivated by the experimental realization of two-dimensional electrostatic lattices for indirect excitons using patterned interdigitated electrodes [M. Remeika et al., Appl. Phys. Lett. 100, 061103 (2012)] and the observation of spin currents governed by spin-orbit interaction and controlled by an applied magnetic field in a coherent gas of indirect excitons [A. A. High et al., Phys. Rev. Lett. 110, 246403 (2013)], we investigate in details the nontrivial topological phases of indirect excitons in a one-dimensional dimerized lattice, known as Su-Schrieffer-Heeger model. The studies focus on the interplay between the spin-orbit coupling of electrons and holes and Zeeman field. We find that a uniform (staggered) perpendicular Zeeman field can turn trivial regions into nontrivial through a topological phase transition. In the nontrivial region of the band, a pair of zero-energy boundary states can survive due to the protection of time-reversal, particle-hole, chiral, and inversion symmetries. The topological class of the system is BDI and can be characterized by Z index. The winding number is used to distinguish the different topological regions of a band. We justify how the topological edge states can be realized by applying a Zeeman field in x -direction to balance the splitting of bright state and dark state, and discuss the exciton polarization degree of the edge states.