Optical Selection Rule of Excitons in Gapped Chiral Fermion Systems.

Abstract

We show that the exciton optical selection rule in gapped chiral fermion systems is governed by their winding number w, a topological quantity of the Bloch bands. Specifically, in a C_{N}-invariant chiral fermion system, the angular momentum of bright exciton states is given by w±1+nN with n being an integer. We demonstrate our theory by proposing two chiral fermion systems capable of hosting dark s-like excitons: gapped surface states of a topological crystalline insulator with C_{4} rotational symmetry and biased 3R-stacked MoS_{2} bilayers. In the latter case, we show that gating can be used to tune the s-like excitons from bright to dark by changing the winding number. Our theory thus provides a pathway to electrical control of optical transitions in two-dimensional material.