Valence band inversion and spin-orbit effects in the electronic structure of monolayer GaSe

Two-dimensional monochalcogenides (MX) have been identified as a unique and promising class of layered materials in recent years. The valence band of single-layer MX, as predicted by theory, is inverted into a bow-shaped (often referred to as an inverted sombrero) and relatively flat dispersion, which is expected to give rise to strongly correlated effects. The inversion leads to an indirect band gap, which is consistent with photoluminescence (PL) experiments, but PL provides no direct evidence of the band inversion in the valence band. Here we demonstrate for a hexagonal MX crystal, gallium selenide (GaSe), using a combination of angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT), that the valence band of monolayer (ML) GaSe exhibits a robust inversion of the valence dispersion at the Γ point forming a bow-shaped dispersion with a depth of 120 ± 10 meV between the double valence band maximum along the ΓK direction. We also demonstrate that the deeper-lying bands detected in the ARPES spectrum are consistent with DFT calculations only if spin-orbit coupling is considered. The presented ARPES evidence that spin-orbit coupling leads to the splitting of two fourfold-degenerate states into four Kramers doublets is of significance for PL measurements, as the change in energy of the second highest valence state at the Γ point has a measurable effect on the PL energies in high-energy luminescence. We predict the optical absorption coefficients for the principal transitions in ML GaSe using a four-band k·p model parametrized from first-principles theory with spin-orbit effects considered.