Band Topology, Orbital Phase Winding, and Selection Rules in Excitonic Physics in Two Dimensions

TL;DR

This paper reveals how band topology and orbital phase winding influence excitonic optical properties in 2D semiconductors, leading to novel selection rules and valley-specific circular dichroism detectable via spectroscopy.

Contribution

It introduces the concept of optical matrix element winding number as a key factor in excitonic physics in topological 2D materials, with specific analysis of graphene systems.

Findings

Winding number determines excitonic optical strength and helicity.

Multiple bright excitons per valley with different helicities.

Valley-specific circular dichroism observable through spectroscopy.

Abstract

We show that band topology can dramatically change the photophysics of two-dimensional (2D) semiconductors. For systems in which states near the band extrema are of multiple orbitals character and the spinors describing the orbital components (pseudospins) pick up nonzero winding numbers (topological invariants) around the extremal k-point, the optical strength and nature (i.e., helicity) of the excitonic states are dictated by the optical matrix element winding number, a unique and heretofore unrecognized characteristic. We illustrate these findings in three gapped graphene systems - monolayer graphene with inequivalent sublattices and biased bi- and tri-layer graphene, where the pseudospin textures manifest into a unique optical matrix element winding pattern associated with different valley and photon circular polarization. This winding-number physics leads to novel exciton series and optical selection rules, with each valley hosting multiple bright excitons coupled to light of different helicity. This valley-exciton selective circular dichroism can be unambiguously detected using optical spectroscopy.