Critical behaviour of reduced QED$_{4,3}$ and dynamical fermion gap generation in graphene

A. V. Kotikov; S. Teber

doi:10.1103/PhysRevD.94.114010

paper

Critical behaviour of reduced QED $_{4, 3}$ and dynamical fermion gap generation in graphene

arXiv:1610.00934 · doi:10.1103/PhysRevD.94.114010

Abstract

The dynamical generation of a fermion gap in graphene is studied at the infra-red Lorentz-invariant fixed point where the system is described by an effective relativistic-like field theory: reduced QED $_{4, 3}$ with $N$ four component fermions ( $N = 2$ for graphene), where photons are $(3 + 1)$ -dimensional and mediate a fully retarded interaction among $(2 + 1)$ -dimensional fermions. A correspondence between reduced QED $_{4, 3}$ and QED $_{3}$ allows us to derive an exact gap equation for QED $_{4, 3}$ up to next-to-leading order. Our results show that a dynamical gap is generated for $α > α_{c}$ where $1.03 < α_{c} < 1.08$ in the case $N = 2$ or for $N < N_{c}$ where $N_{c}$ is such that $α_{c} \to \infty$ and takes the values $3.24 < N_{c} < 3.36$ . The striking feature of these results is that they are in good agreement with values found in models with instantaneous Coulomb interaction. At the fixed point: $α = 1/137 ≪ α_{c}$ , and the system is therefore in the semi-metallic regime in accordance with experiments.

(v2) Accepted for publication in PRD. Short discussion and some references added at the end of Sec V (per referee's comments). No change in results. 7 pages. (v1) 7 pages

Critical behaviour of reduced QED $_{4, 3}$ and dynamical fermion gap generation in graphene

Abstract

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Cited by in corpus (13)

Critical behaviour of reduced QED4,3​ and dynamical fermion gap generation in graphene

Abstract

References in corpus (10)

Cited by in corpus (13)

Critical behaviour of reduced QED $_{4, 3}$ and dynamical fermion gap generation in graphene