Charged impurity scattering in two-dimensional topological insulators with Mexican-hat dispersion

TL;DR

This work investigates how charged impurities scatter electrons in two-dimensional topological insulators with Mexican-hat dispersion, where a ring-shaped Fermi surface and a Van Hove density-of-states singularity create significant inter- and intra-contour scattering. The authors develop a two-branch Boltzmann transport framework within the BHZ model to treat momentum that is not a single-valued function of energy, avoiding the relaxation-time approximation. They compute the screened impurity potential using RPA by evaluating the Lindhard polarization with quantum-metric effects, revealing three Friedel-oscillation modes and strong screening peculiarities at low energies. The study analyzes how temperature and electron density influence screening, scattering, and conductivity, showing nontrivial trends that depend on the relative strength of intra- vs inter-contour processes. Overall, the paper provides a specialized framework for transport in multi-contour, multi-orbital 2D topological materials and highlights the role of quantum geometry in screening and impurity scattering.

Abstract

Scattering by charged impurities is known to mainly determine transport properties of electrons in modern quantum materials, but it remains poorly studied for materials with Mexican hat dispersion. Due to such nontrivial features as a singular density of states and a ring-shaped Fermi surface, electron-electron interaction and electron transitions between different isoenergetic contours are of key importance in this materials. We show that these factors significantly affect both the spatial profile of the screened potential of Coulomb centers and the dependence of mobility on temperature and electron density. The screened potential is calculated within the random phase approximation. The transport properties are determined without using the usual relaxation time approximation, since the distribution function in energy space is a vector defined by a system of two equations.

Figures (5)

• Figure 1: MHD and ring-shaped Fermi surface for $a = 0.2$ and $\delta = -0.1$, conduction band minimum is at $E_0 =0.296$.
• Figure 2: Wave vector dependence of the screened charge impurity potential: a) at the electron density $n =0.5$ for two values of temperature and b) for two Fermi energies at the same temperature $T = 0.01$.
• Figure 3: Angular dependencies of intra-contour (green and yellow) and inter-contour (red and blue) scattering probabilities for $E_F=0.01$ (a) and $E_F = 0.5$ (b).
• Figure 4: Dependence of current (a) and carrier density (b) on the temperature for given Fermi levels shown near the curves.
• Figure 5: Dependencies of the conductivity on the Fermi level for fixed temperatures (a) and temperature dependencies of the conductivity for fixed electron densities (b).