Numerical simulation of graphene in external magnetic field

TL;DR

This paper presents numerical simulations of monolayer graphene under external magnetic fields using lattice field theory, revealing how magnetic fields influence phase transitions and conductivity.

Contribution

It introduces a lattice simulation approach to study graphene in magnetic fields, showing the magnetic field's effect on phase transition points and phase diagram.

Findings

Magnetic field shifts insulator-semimetal transition to higher dielectric permittivity.

Phase diagram of graphene in magnetic field is constructed.

Conductivity dependence on substrate permittivity is analyzed.

Abstract

In this paper the results of numerical simulation of monolayer graphene in external magnetic field are presented. The numerical simulation is performed in the effective lattice field theory with noncompact $3 + 1$-dimensional Abelian lattice gauge fields and $2 + 1$-dimensional staggered lattice fermions. The dependences of fermion condensate and graphene conductivity on the dielectric permittivity of substrate for different values of external magnetic field are calculated. It is found that magnetic field shifts insulator-semimetal phase transition to larger values of the dielectric permittivity of substrate. The phase diagram of graphene in external magnetic field is drawn.