Critical exponents of the semimetal-insulator transition in graphene: A Monte Carlo study

TL;DR

This study uses lattice Monte Carlo simulations to determine the critical exponents of the semimetal-insulator transition in graphene, revealing how these exponents vary with the number of Dirac flavors and discussing implications for experiments.

Contribution

First Monte Carlo determination of critical exponents for the graphene semimetal-insulator transition as a function of Dirac flavor number, providing insights into the phase transition's nature.

Findings

Critical exponent δ varies with Dirac flavor number N_f.

γ remains approximately 1 across different N_f.

Results align with some analytical predictions and inform experimental scenarios.

Abstract

The low-energy theory of graphene exhibits spontaneous chiral symmetry breaking due to pairing of quasiparticles and holes, corresponding to a semimetal-insulator transition at strong Coulomb coupling. We report a Lattice Monte Carlo study of the critical exponents of this transition as a function of the number of Dirac flavors $N_f^{}$, finding $\delta = 1.25 \pm 0.05$ for $N_f^{} = 0$, $\delta = 2.26 \pm 0.06$ for $N_f^{} = 2$ and $\delta = 2.62 \pm 0.11$ for $N_f^{} = 4$, with $\gamma \simeq 1$ throughout. We compare our results with recent analytical work for graphene and closely related systems, and discuss scenarios for the fate of the chiral transition at finite temperature and carrier density, an issue of relevance for upcoming experiments with suspended graphene samples.