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

Abstract

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 quantummore » 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.« less

Authors:
 [1]
  1. Department of Physics, The University of Tokyo, Tokyo 113-0033 (Japan)
Publication Date:
OSTI Identifier:
21579909
Resource Type:
Journal Article
Journal Name:
Annals of Physics (New York)
Additional Journal Information:
Journal Volume: 326; Journal 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.; Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
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

Citation Formats

Araki, Yasufumi. Chiral symmetry breaking in monolayer graphene by strong coupling expansion of compact and non-compact U(1) lattice gauge theories. United States: N. p., 2011. Web. doi:10.1016/j.aop.2011.01.002.
Araki, Yasufumi. Chiral symmetry breaking in monolayer graphene by strong coupling expansion of compact and non-compact U(1) lattice gauge theories. United States. https://doi.org/10.1016/j.aop.2011.01.002
Araki, Yasufumi. 2011. "Chiral symmetry breaking in monolayer graphene by strong coupling expansion of compact and non-compact U(1) lattice gauge theories". United States. https://doi.org/10.1016/j.aop.2011.01.002.
@article{osti_21579909,
title = {Chiral symmetry breaking in monolayer graphene by strong coupling expansion of compact and non-compact U(1) lattice gauge theories},
author = {Araki, Yasufumi},
abstractNote = {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.},
doi = {10.1016/j.aop.2011.01.002},
url = {https://www.osti.gov/biblio/21579909}, journal = {Annals of Physics (New York)},
issn = {0003-4916},
number = 6,
volume = 326,
place = {United States},
year = {Wed Jun 15 00:00:00 EDT 2011},
month = {Wed Jun 15 00:00:00 EDT 2011}
}