Monte-Carlo study of the phase transition in the AA-stacked bilayer graphene

TL;DR

This study uses Hybrid Monte Carlo simulations to analyze the phase transition in AA-stacked bilayer graphene, revealing a spontaneous mass gap formation linked to antiferromagnetic ordering influenced by electron interactions.

Contribution

It provides the first detailed Monte Carlo analysis of the phase transition and magnetic ordering in AA-stacked bilayer graphene with screened Coulomb interactions.

Findings

Observation of a phase transition with spontaneous mass gap generation.

Dependence of antiferromagnetic order on electron-electron interaction strength.

Validation of the Hubbard-Stratonovich transformation in this context.

Abstract

Tight-binding model of the AA-stacked bilayer graphene with screened electron-electron interactions has been studied using the Hybrid Monte Carlo simulations on the original double-layer hexagonal lattice. Instantaneous screened Coulomb potential is taken into account using Hubbard-Stratonovich transformation. G-type antiferromagnetic ordering has been studied and the phase transition with spontaneous generation of the mass gap has been observed. Dependence of the antiferromagnetic condensate on the on-site electron-electron interaction is examined.