Velocity renormalization in graphene from lattice Monte Carlo

TL;DR

This study uses lattice Monte Carlo simulations to analyze how strong Coulomb interactions renormalize the Fermi velocity of Dirac quasiparticles in graphene, revealing a significant increase near the critical coupling for a phase transition.

Contribution

It provides the first lattice Monte Carlo calculation of Fermi velocity renormalization in graphene considering long-range Coulomb interactions at charge neutrality.

Findings

Fermi velocity increases approximately linearly with Coulomb coupling alpha_g

Renormalized velocity v_FR exceeds the bare velocity v_F by a factor of about 3.3 at the critical coupling

Results are consistent with experimental observations in ultra-clean suspended graphene

Abstract

We compute the Fermi velocity of the Dirac quasiparticles in clean graphene at the charge neutrality point for strong Coulomb coupling alpha_g. We perform a Lattice Monte Carlo calculation within the low-energy Dirac theory, which includes an instantaneous, long-range Coulomb interaction. We find a renormalized Fermi velocity v_FR > v_F, where v_F = c/300. Our results are consistent with a momentum-independent v_FR which increases approximately linearly with alpha_g, although a logarithmic running with momentum cannot be excluded at present. At the predicted critical coupling alpha_gc for the semimetal-insulator transition due to excitonic pair formation, we find v_FR/v_F = 3.3, which we discuss in light of experimental findings for v_FR/v_F at the charge neutrality point in ultra-clean suspended graphene.