Interaction of static charges in graphene within Monte-Carlo simulation

TL;DR

This paper uses Monte-Carlo simulations to analyze how static charges interact in graphene, revealing temperature-dependent screening effects and phase transition indicators in a lattice gauge theory framework.

Contribution

It introduces a detailed Monte-Carlo simulation approach to study charge interactions in graphene, highlighting the role of Debye screening and phase transition behavior.

Findings

Interaction is well described by Debye screening at all temperatures.

Debye mass indicates the insulator-semimetal phase transition.

Graphene behaves as a weakly interacting 2D plasma at high temperatures.

Abstract

The study of the interaction potential between static charges within Monte-Carlo simulation of graphene is carried out. The numerical simulations are performed in the effective lattice field theory with noncompact $3 + 1$-dimensional Abelian lattice gauge fields and $2 + 1$-dimensional staggered lattice fermions. It is shown that for all considered temperatures the interaction can be well described by the Debye screened potential created by two-dimensional electron-hole excitations. At low temperatures Debye mass $m_D$ plays a role of order parameter of the insulator-semimetal phase transition. In the semimetal phase at high temperature graphene reveals the properties of weakly interacting two-dimensional plasma of fermions excitations.