Chiral topological excitonic insulator in semiconductor quantum wells

We present a scheme to realize the chiral topological excitonic insulator in semiconductor heterostructures which can be experimentally fabricated with a coupled quantum well adjacent to two ferromagnetic insulating films. The different mean-field chiral topological orders, which are due to the change in the directions of the magnetization of the ferromagnetic films, can be characterized by the Thouless, Kohmoto, Nightingale, and Nijs numbers in the bulk system as well as by the winding numbers of the gapless states in the edged system. Furthermore, we propose an experimental scheme to detect the emergence of the chiral gapless edge state and distinguish different chiral topological orders by measuring the thermal conductance.