Fermion condensation around a Coulomb impurity in a Weyl semimetal as a manifestation of the Landau zero-charge problem

TL;DR

This paper investigates how a Coulomb impurity in an undoped Weyl semimetal leads to fermion condensation and charge screening, illustrating the Landau zero-charge problem through a theoretical analysis.

Contribution

It demonstrates that the impurity induces a neutral fermion cloud and connects the Thomas-Fermi approximation to the Gell-Mann-Low equation, revealing a zero-charge screening effect.

Findings

Impurity charge is completely screened at finite distances.

The system exhibits an experimentally accessible Landau zero-charge effect.

The Thomas-Fermi equation reduces to the Gell-Mann-Low equation in the zero-size limit.

Abstract

A Coulomb impurity placed in an undoped Weyl semimetal spontaneously surrounds itself with a cloud of condensed Weyl fermions. We study this system within the Thomas-Fermi approximation. We find that the ground-state of the system is electrically neutral and exhibits an experimentally accessible Landau zero-charge effect: the impurity charge is screened out at any finite distance in the limit of vanishing impurity size. Specifically, we show how in this limit the Thomas-Fermi equation for the electrostatic potential transforms into the Gell-Mann-Low equation for the charge.