Anomalous screening in two-dimensional materials with an extremum ring in the dispersion law

TL;DR

This paper investigates how a ring-shaped extremum in the band structure of certain two-dimensional materials leads to unusual screening behaviors, especially at low doping levels, using Thomas-Fermi theory.

Contribution

It introduces a theoretical analysis of anomalous screening effects caused by extremal rings in 2D materials' band structures, highlighting unique doping-dependent behaviors.

Findings

Screening response is enhanced as doping decreases.

At zero doping, the screening cloud size scales with the cube root of impurity charge.

Topological band features significantly influence electrostatic screening.

Abstract

A variety of two-dimensional materials possess a band structure with an energy extremal ridge along a ring in momentum space. Examples are biased bilayer graphene, and surfaces and interfaces with a Rashba spin-orbit interaction where at low doping the carriers fill an annulus. This topological feature causes an anomalous screening behavior, which we study using the Thomas-Fermi theory. Specifically, reducing the doping is predicted to enhance the linear screening response, while at zero doping the size of the screening cloud surrounding a Coulomb impurity is found to increase as the cube root of the impurity charge.