Chiral Symmetry Breaking in Monolayer Graphene by Strong Coupling Expansion of Compact and Non-compact U(1) Lattice Gauge Theories

TL;DR

This paper investigates how strong Coulomb interactions in monolayer graphene can induce chiral symmetry breaking, leading to an insulating state, using lattice gauge theory models to analyze collective excitations and phase transitions.

Contribution

It demonstrates chiral symmetry breaking in graphene via strong coupling U(1) lattice gauge theories, providing analytical formulas for excitations and connecting to effective field theory.

Findings

Chiral condensate becomes finite in strong coupling limit.

Pseudo-Nambu-Goldstone mode mass formula derived.

Energy scales of excitations estimated from lattice parameters.

Abstract

Due to effective enhancement of the Coulomb coupling strength in the vacuum-suspended graphene, the system may turn from a semimetal into an insulator by the formation of a gap in the fermionic spectrum. This phenomenon is analogous to the spontaneous breaking of chiral symmetry in the strong-coupling relativistic field theories. We study this "chiral symmetry breaking" and associated collective excitations on graphene in the strong coupling regime by taking U(1) lattice gauge theory as an effective model for graphene. Both compact and non-compact formulations of the U(1) gauge action show chiral symmetry breaking with equal magnitude of the chiral condensate (exciton condensate) in the strong coupling limit, while they start to deviate from the next-to-leading order in the strong coupling expansion. Phase and amplitude fluctuations of the order parameter are also investigated: in particular, a mass formula for the pseudo-Nambu--Goldstone mode ($\pi$-exciton), which is analogous to Gell-Mann--Oakes--Renner relation for the pion in quantum chromodynamics (QCD), is derived from the axial Ward-Takahashi identity. To check the applicability of the effective field theory description, typical energy scales of fermionic and bosonic excitations are estimated by identifying the lattice spacing of the U(1) gauge theory with that of the original honeycomb lattice of graphene.