Optical Selection Rule of Excitons in Gapped Chiral Fermion Systems

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.