  In many atomically thin materials their optical absorption is dominated by
excitonic transitions. It was recently found that optical selection rules in
these materials are influenced by the band topology near the valleys. We
propose that gate-controlled band ordering in a single atomic monolayer,
through changes in the valley winding number and excitonic transitions, can be
probed in helicity-resolved absorption and photoluminescence. This predicted
tunable band topology is confirmed by combining an effective Hamiltonian and a
Bethe-Salpeter equation for an accurate description of excitons, with
first-principles calculations suggesting its realization in Sb-based
monolayers.
