Symmetry, distorted band structure, and spin-orbit coupling of group-III metal-monochalcogenide monolayers

The electronic structure of (group-III) metal-monochalcogenide monolayers exhibits many unusual features. Some, such as the unusually distorted upper valence-band dispersion we describe as a ``caldera,'' are primarily the result of purely orbital interactions. Others, including spin splitting and wave-function spin mixing, are directly driven by spin-orbit coupling. We employ elementary group theory to explain the origin of these properties, and use a tight-binding model to calculate the phenomena enabled by them, such as the band-edge carrier effective $g$ factors, optical absorption spectrum, conduction electron spin orientation, and a relaxation-induced upper-valence-band population inversion and spin polarization mechanism.