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

Abstract

Atomically thin films of III-VI post-transition metal chalcogenides (InSe and GaSe) form an interesting class of two-dimensional semiconductor that feature strong variations of their band gap as a function of the number of layers in the crystal [1-4] and, specifically for InSe, an earlier predicted crossover from a direct gap in the bulk [5,6] to a weakly indirect band gap in monolayers and bilayers [7-11]. Here, we apply angle resolved photoemission spectroscopy with submicrometer spatial resolution ($\mu$ARPES) to visualise the layer-dependent valence band structure of mechanically exfoliated crystals of InSe. We show that for 1 layer and 2 layer InSe the valence band maxima are away from the $\mathbf{\Gamma }$-point, forming an indirect gap, with the conduction band edge known to be at the $\mathbf{\Gamma }$-point. In contrast, for six or more layers the bandgap becomes direct, in good agreement with theoretical predictions. The high-quality monolayer and bilayer samples enables us to resolve, in the photoluminescence spectra, the band-edge exciton (A) from the exciton (B) involving holes in a pair of deeper valence bands, degenerate at $\mathbf{\Gamma }$, with the splitting that agrees with both $\mu$ARPES data and the results of DFT modelling. Due to the difference in symmetry between these two valence bands, light emitted by the A-exciton should be predominantly polarised perpendicular to the plane of the two-dimensional crystal, which we have verified for few-layer InSe crystals.

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• Tutorial: Exciton resonances for atomically-thin optics
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• Electrical detection of the flat band dispersion in van der Waals field-effect structures
• Spatially-Resolved Band Gap and Dielectric Function in 2D Materials from Electron Energy Loss Spectroscopy
• Tunable spin-orbit coupling in two-dimensional InSe
• Structures of bulk hexagonal post-transition-metal chalcogenides from dispersion-corrected density-functional theory
• Light sources with bias tunable spectrum based on van der Waals interface transistors
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• Nonperturbative self-consistent electron-phonon spectral functions and transport
• Electronic structure of 2D van der Waals crystals and heterostructures investigated by spatially- and angle-resolved photoemission
• Strong atomic reconstruction in twisted bilayers of highly flexible InSe: Machine-Learned Interatomic Potential and continuum model approaches
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