Monte Carlo simulation of monolayer graphene at non-zero temperature

TL;DR

This paper uses lattice simulations to study the phase transitions and thermal properties of monolayer graphene at non-zero temperature, revealing an insulating phase, a Berezinskii-Kosterlitz-Thouless transition, and a pseudogap phase.

Contribution

It provides the first lattice simulation results for monolayer graphene at finite temperature, identifying phase transition characteristics and thermal behavior.

Findings

Identification of an excitonic insulating phase at low temperatures and strong coupling.

Determination of the Berezinskii-Kosterlitz-Thouless transition temperature relative to the zero-temperature gap.

Evidence for a pseudogap phase with a non-zero thermal mass extending to high temperatures.

Abstract

We present results from lattice simulations of a monolayer graphene model at non-zero temperature. At low temperatures for sufficiently strong coupling the model develops an excitonic condensate of particle-hole pairs corresponding to an insulating phase. The Berezinskii-Kosterlitz-Thouless phase transition temperature is associated with the value of the coupling where the critical exponent delta governing the response of the order parameter at criticality to an external source has a value close to 15. The critical coupling on a lattice with temporal extent N_t=32 (T=1/(N_t a_t) where a_t is the temporal lattice spacing) and spatial extent N_s=64 is very close to infinite coupling. The value of the transition temperature normalized with the zero temperature fermion mass gap Delta_0 is given by T_BKT/Delta_0=0.055(2). This value provides an upper bound on the transition temperature, because simulations closer to the continuum limit where the full U(4) symmetry is restored may result in an even lower value. In addition, we measured the helicity modulus Upsilon and the fermion thermal mass Delta_T(T), the later providing evidence for a pseudogap phase with Delta_T>0 extending to arbitrarily high T.