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Atomically thin films of III-VI post-transition metal chalcogenides (InSe andGaSe) form an interesting class of two-dimensional semiconductor that featurestrong variations of their band gap as a function of the number of layers inthe crystal [1-4] and, specifically for InSe, an earlier predicted crossoverfrom a direct gap in the bulk [5,6] to a weakly indirect band gap in monolayersand bilayers [7-11]. Here, we apply angle resolved photoemission spectroscopywith submicrometer spatial resolution ($\mu$ARPES) to visualise thelayer-dependent valence band structure of mechanically exfoliated crystals ofInSe. We show that for 1 layer and 2 layer InSe the valence band maxima areaway from the $\mathbf{\Gamma}$-point, forming an indirect gap, with theconduction band edge known to be at the $\mathbf{\Gamma}$-point. In contrast,for six or more layers the bandgap becomes direct, in good agreement withtheoretical predictions. The high-quality monolayer and bilayer samples enablesus to resolve, in the photoluminescence spectra, the band-edge exciton (A) fromthe exciton (B) involving holes in a pair of deeper valence bands, degenerateat $\mathbf{\Gamma}$, with the splitting that agrees with both $\mu$ARPES dataand the results of DFT modelling. Due to the difference in symmetry betweenthese two valence bands, light emitted by the A-exciton should be predominantlypolarised perpendicular to the plane of the two-dimensional crystal, which wehave verified for few-layer InSe crystals.

Indirect to direct gap crossover in two-dimensional InSe revealed by ARPES