Quasi-bound States and Resonant Skew Scattering in Two-Dimensional Materials with a Mexican-Hat Dispersion

TL;DR

This paper investigates how Mexican-hat dispersion in 2D materials leads to quasi-bound states near defects, significantly affecting electron scattering and causing resonant skew scattering phenomena.

Contribution

It reveals the formation of quasi-bound states due to opposite signs of effective mass inside and outside the dispersion region, and analyzes their impact on electron scattering.

Findings

Quasi-bound states can form near defects in Mexican-hat dispersions.

Resonant skew scattering is significantly enhanced near quasi-bound state energies.

Under certain conditions, quasi-bound states can become true bound states in the continuum.

Abstract

Mexican-hat dispersion of band electrons in two-dimensional materials attracts a lot of interest, mainly due to the Van Hove singularity of the density of states near the band edge. In this paper, we show that there is one more feature of such a dispersion, which also leads to nontrivial effects. It consists in the fact that the sign of the effective mass in the momentum space near the central extremum is opposite to the sign of the mass outside this region. For this reason, any localized potential that repels quasiparticles in the outer region attracts quasiparticles in the central region and thereby creates quasi-bound states. We study these states in the case when the Mexican-hat dispersion is formed due to the hybridization of the inverted electron and hole bands, and the potential is created by a point defect. The energy and width of the resonance of the local density of states corresponding to a quasi-bound state are found, and it is shown that, under certain conditions, a quasi-bound state can transform into a bound state in a continuum of band states. The presence of quasi-bound states leads to nontrivial effects in the spin-dependent scattering of electrons. Due to the quasi-bound state, the skew scattering is strongly enhanced for electrons with energy near the resonance, and the skewness angle varies over a wide range depending on the energy. In addition, in a certain energy range, a nontrivial effect of scattering suppression appears in the direction opposite to the skewness angle.