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The singular density of states and the two Fermi wavevectors resulting from aring-shaped or "Mexican hat" valence band give rise to unique trends in thecharged impurity scattering rates and charged impurity limited mobilities. Ringshaped valence bands are common features of many monolayer and few-layertwo-dimensional materials including the III-VI materials GaS, GaSe, InS, andInSe. The wavevector dependence of the screening, calculated within the randomphase approximation, is so strong that it is the dominant factor determiningthe overall trends of the scattering rates and mobilities with respect totemperature and hole density. Charged impurities placed on the substrate and inthe 2D channel are considered. The different wavevector dependencies of thebare Coulomb potentials alter the temperature dependence of the mobilities.Moving the charged impurities 5 $\AA$ from the center of the channel to thesubstrate increases the mobility by an order of magnitude.

Charged impurity scattering in two-dimensional materials with ring-shaped valence bands: GaS, GaSe, InS, and InSe