Anti-Stokes luminescence of bulk and thin-film $\beta$-InSe under infrared optical excitation

A new mechanism of low-temperature radiative recombination in bulk crystals of $\beta$-InSe and thin films exfoliated from them, resulting in the appearance of intense anti-Stokes luminescence with a photon energy of 2.54 eV, is revealed. The position of the corresponding spectral line is close to the exciton resonance of the $k$-space-direct band-to-band transition associated with the recombination of electrons at the bottom of the conduction band and holes in the Se $p_{xy}$ orbitals. The observed anti-Stokes emission presumably results from Auger recombination of $k$-space-indirect electron-hole pairs, which leads to the population of the lower lying states in the valence band. It is established that the relative intensity of anti-Stokes luminescence increases by more than two orders of magnitude in InSe films with thicknesses of several tens of nanometers as compared to bulk InSe.