We predict that long-lived excitons with very large binding energies can also exist in a single or few layers of monochalcogenides such as GaSe. Our theoretical study shows that excitons confined by a radial local strain field are unable to recombine despite of electrons and holes co-existing in space. The localized single-particle states are calculated in the envelope function approximation based on a three-band $boldsymbol{k}cdot boldsymbol{p}$ Hamiltonian obtained from DFT calculations. The binding energy and the decay rate of the exciton ground state are computed after including correlations in the basis of electron-hole pairs. The interplay between the localized strain and the caldera-type valence band, characteristic of few-layered monochalcogenides, creates localized electron and hole states with very different quantum numbers which hinders the recombination even for singlet excitons.
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