Symmetry origins of the 'caldera' valence band distortion in 2D semiconductors

The electronic structures of many two-dimensional van der Waals semiconductors exhibit various fascinating properties distinct from their three-dimensional bulk counterparts. Through an examination of their lattice symmetries, we identify several universal rules dictating their band dispersion in the monolayer limit, where in-plane mirror symmetry and quantum confinement play critical roles. Taking group-III metal monochalcogenides (such as GaSe) as an example, we reveal the origin of the unusual `caldera' shape of the valence band edge (otherwise inelegantly dubbed an `upside down Mexican hat'), which we show is surprisingly common among other 2D semiconductors (such as in phosphorene for {\$}k{\$} along its zigzag direction). Reference: arXiv:1508.06963