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

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