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.

二维材料中能带电子的墨西哥帽色散引起了很多兴趣，主要是由于能带边缘附近状态密度的范霍夫奇点。在本文中，我们展示了这种分散还有一个特征，这也导致了非平凡的影响。它在于中心极值附近的动量空间中的有效质量的符号与该区域外的质量的符号相反。因此，任何排斥准粒子的局部电位外部区域的准粒子吸引中心区域的准粒子，从而产生准束缚态。我们在由于反转电子和空穴带的杂化而形成墨西哥帽色散的情况下研究这些状态，并且电位是由点缺陷产生的。求出了准束缚态对应的局部态密度共振的能量和宽度，表明在一定条件下，准束缚态可以转变为连续带态的束缚态. 准束缚态的存在导致电子的自旋相关散射中的非平凡效应。由于准束缚态，对于能量接近共振的电子，偏斜散射强烈增强，并且偏斜角根据能量在很宽的范围内变化。此外，