Fig. 3: PLE of 5L and 7L InSe at T = 4.2K.

a, b Left - 2D band structure of 5L and 7L InSe around \(\Gamma\) computed using DFT-parametrized tight-binding dispersion with spin-orbit interaction taken into account. Right - PL (red), PLE measured at the black arrow (blue) and projected optical DoS (purple) of lamellae for 5 and 7L InSe. Relevant optical transitions from \({v}_{i}\) to \({c}_{j}\) are labeled as i, j. Orange dotted line shows ARPES intensity around \(\Gamma\)-point¹³, plotted to match \({v}_{0}\)-\({c}_{0}\) optical transition in PLE with the first valence subband in ARPES. Inset shows scanning electron micrograph of the lamella overlaid with its PL map sampled at 1.30(2) eV, scale bar is \(5\ \upmu {\rm{m}}\). c Amplitude \(\Delta {\psi }_{{\rm{In}}}=\psi ({{\rm{In}}}_{1})-\psi ({{\rm{In}}}_{2})\), of In \(S\)-orbital contribution to the subbands \({c}_{n}\) across the layers for \(N=5\). Band edges in bulk InSe are at Z points of the 3D Brillouin zone, hence the number of nodes in the layer-dependent microscopic wavefunction counts down from 4 for the lowest energy subband to 0 for the highest. d Solid lines - out-of-plane dispersion of bulk InSe at in-plane \(\Gamma\) point. Orange dots - \(\Gamma\)-point subbands for 5L InSe at \({k}_{z}\) given by quantization of momentum in quantum well picture (dashed lines). Insets: center - 3D Brillouin zone of InSe, bottom left - amplitude \(\Delta {\psi }_{{\rm{Se}}}=\psi ({{\rm{Se}}}_{1})-\psi ({{\rm{Se}}}_{2})\), of Se \({P}_{z}\)-orbital contribution to top valence subband. e Exciton binding energy (\({E}_{X}\)) extracted from PLE (see inset) as a function of number of layers in the film. The error bars correspond to the width of continuum absorption step. Colors indicate different samples. The dashed curve is displayed as a guide to the eye.