Optical Selection Rule of Excitons in Gapped Chiral Fermion Systems

TL;DR

This paper reveals how the topological winding number in gapped chiral fermion systems determines exciton optical selection rules, enabling electrical control of optical properties in 2D materials.

Contribution

It introduces a topological framework linking winding number to exciton selection rules and demonstrates tunable excitonic states in specific 2D systems.

Findings

Winding number governs exciton optical selection rules.

Gating can switch excitons from bright to dark.

The theory applies to topological crystalline insulators and MoS2 bilayers.

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 $w \pm 1 + nN$ 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.