Relativistic Mott criticality in graphene

TL;DR

This paper develops a theoretical model for the semimetal-insulator transition in graphene, revealing that at criticality, Dirac fermions become incoherent and Coulomb interactions are irrelevant, with emergent Lorentz invariance affecting thermodynamic ratios.

Contribution

It formulates the Gross-Neveu-Yukawa theory for graphene's phase transition and analyzes its quantum critical behavior near three dimensions, highlighting the irrelevance of Coulomb interactions.

Findings

Dirac fermions do not remain coherent at the critical point.

The Coulomb interaction tail is irrelevant at criticality.

Emergent Lorentz invariance influences low-temperature thermodynamics.

Abstract

We formulate the effective Gross-Neveu-Yukawa theory of the semimetal-insulator transitions on the honeycomb lattice and compute its quantum critical behavior near three (spatial) dimensions. We find that at the critical point Dirac fermions do not survive as coherent excitations and that the $\sim 1/r$ tail of the weak Coulomb interaction is an irrelevant coupling. The emergent Lorentz invariance near criticality implies a universal ratio of the low-temperature specific heats of the metallic and the rotational-symmetry-broken insulating phase.