Screening of a charged impurity in graphene in a magnetic field

TL;DR

This study numerically investigates how a charged impurity affects electron states in graphene under a magnetic field, revealing modifications to Landau levels, wave functions, and screening effects that depend on chemical potential, with implications for tuning impurity charge.

Contribution

The paper provides a detailed numerical analysis of impurity effects in graphene's Landau levels, highlighting how chemical potential influences impurity charge screening and electron spectrum modifications.

Findings

Charged impurities convert Landau levels into bandlike structures.

Effective impurity charge can be tuned by chemical potential.

Screening behavior varies depending on the chemical potential position.

Abstract

The electron states in the field of a charged impurity in graphene in a magnetic field are studied numerically. It is shown that a charged impurity removes the degeneracy of Landau levels converting them into bandlike structures. As the charge of impurity grows, the repulsion of sublevels of different Landau levels with the same value of orbital momentum takes place leading to the redistribution of the wave function profiles of these sublevels near the impurity. By studying the polarization effects, it is shown in agreement with the recent experiments that the effective charge of impurity can be very effectively tuned by chemical potential. If the chemical potential is situated inside a Landau level, then the charge of impurity is strongly diminished. In addition, the polarization function in this case has a peak at zero momentum, which leads to the sign-changing oscillations of the screened potential as a function of distance. If the chemical potential lies between the Landau levels, then the screened potential does not change sign, the screening is minimal, and the charged impurity can strongly affect the electron spectrum.