Chiral symmetry breaking in monolayer graphene by strong coupling expansion of compact and non-compact U(1) lattice gauge theories

Journal Article · Wed Jun 15 00:00:00 EDT 2011 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2011.01.002· OSTI ID:21579909

Araki, Yasufumi ^[1]

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1. Department of Physics, The University of Tokyo, Tokyo 113-0033 (Japan)

Research Highlights: > Monolayer graphene is treated by strong coupling expansion of lattice gauge theory. > Spontaneous gap generation is shown in the strong coupling regime. > Results from compact and non-compact gauge formulations are compared. > Dispersion relation of the collective excitations are derived. - 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.

• OSTI ID: 21579909
• Journal Information: Annals of Physics (New York), Vol. 326, Issue 6; Other Information: DOI: 10.1016/j.aop.2011.01.002; PII: S0003-4916(11)00010-8; Copyright (c) 2011 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AMPLITUDES
CHIRAL SYMMETRY
CHIRALITY
COLLECTIVE EXCITATIONS
CONDENSATES
COUPLING
DISPERSION RELATIONS
EXCITONS
FERMIONS
FLUCTUATIONS
GAUGE INVARIANCE
MASS FORMULAE
ORDER PARAMETERS
PIONS
QUANTUM CHROMODYNAMICS
RELATIVISTIC RANGE
SEMIMETALS
SPECTRA
STRONG-COUPLING MODEL
SYMMETRY BREAKING
BOSONS
DIMENSIONLESS NUMBERS
ELEMENTARY PARTICLES
ELEMENTS
ENERGY RANGE
ENERGY-LEVEL TRANSITIONS
EXCITATION
FIELD THEORIES
HADRONS
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
MESONS
PARTICLE MODELS
PARTICLE PROPERTIES
PSEUDOSCALAR MESONS
QUANTUM FIELD THEORY
QUASI PARTICLES
SYMMETRY
VARIATIONS