  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.
