Gap generation and semimetal-insulator phase transition in graphene

TL;DR

This paper investigates the conditions under which a gap forms in suspended graphene, revealing a critical coupling constant close to lattice simulation results and identifying a second order phase transition.

Contribution

It introduces a continuum model incorporating dynamical polarization and four-fermion interactions to accurately predict the semimetal-insulator transition in graphene.

Findings

Critical coupling constant =0.92 close to lattice results

Second order phase transition identified

Critical exponents align with lattice simulations

Abstract

The gap generation is studied in suspended clean graphene in the continuum model for quasiparticles with the Coulomb interaction. We solve the gap equation with the dynamical polarization function and show that, comparing to the case of the static polarization function, the critical coupling constant lowers to the value \alpha_c=0.92, which is close to that obtained in lattice Monte Carlo simulations. It is argued that additional short-range four-fermion interactions should be included in the continuum model to account for the lattice simulation results. We obtain the critical line in the plane of electromagnetic and four-fermion coupling constants and find a second order phase transition separating zero gap and gapped phases with critical exponents close to those found in lattice calculations.