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

## TL;DR

This study uses advanced ARPES techniques to reveal how the band gap nature in InSe transitions from indirect in monolayers to direct in multilayers, confirming theoretical predictions and exploring excitonic properties.

## Contribution

The paper provides experimental visualization of the layer-dependent valence band structure of InSe, confirming the crossover from indirect to direct band gap with increasing layers using $b1$ARPES.

## Key findings

- Valence band maxima are away from $b3$-point in 1-2 layers, indicating an indirect gap.
- Bandgap becomes direct in 6 or more layers, matching theoretical models.
- Resolved exciton features in photoluminescence spectra, with polarization properties verified.

## 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.