Massive Dirac fermions and the zero field quantum Hall effect

Abstract

Through an explicit calculation for a Lagrangian in quantum electrodynamics in (2+1)-space--time dimensions (QED${}_3$), making use of the relativistic Kubo formula, we demonstrate that the filling factor accompanying the quantized electrical conductivity for massive Dirac fermions of a single species in two spatial dimensions is a half (in natural units) when time reversal and parity symmetries of the Lagrangian are explicitly broken by the fermion mass term. We then discuss the most general form of the QED${}_3$ Lagrangian, both for irreducible and reducible representations of the Dirac matrices in the plane, with emphasis on the appearance of a Chern-Simons term. We also identify the value of the filling factor with a zero field quantum Hall effect (QHE).

15 pages. Accepted in Jour. Phys. A

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Cited by in corpus (21)

• Planar QED at finite temperature and density: Hall conductivity, Berry's phases and minimal conductivity of graphene
• Fermion Condensate and Vacuum Current Density Induced by Homogeneous and Inhomogeneous Magnetic Fields in (2+1)-Dimensions
• Chiral and Parity Symmetry Breaking for Planar Fermions: Effects of a Heat Bath and Uniform External Magnetic Field
• Gauge Covariance Relations and the Fermion Propagator in Maxwell-Chern-Simons QED3
• Confinement in Maxwell-Chern-Simons Planar Quantum Electrodynamics and the 1/N approximation
• New point-like sources and a conducting surface in Maxwell-Chern-Simons electrodynamics
• Landau Levels as a Limiting Case of a Model with the Morse-Like Magnetic Field
• Electron-polaron--electron-polaron bound states in mass-gap graphene-like planar quantum electrodynamics: $s$-wave bipolarons
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• Finite temperature fermion condensate, charge and current densities in a (2+1)-dimensional conical space
• Light absorption in deformed graphene
• Off-shell Green functions at one-loop level in Maxwell-Chern-Simons quantum electrodynamics
• Infrared behavior of dynamical fermion mass generation in QED${}_3$
• The quantum scale invariance in graphene-like quantum electrodynamics
• 2D massless QED Hall half-integer conductivity and graphene
• Quantum parity conservation in planar quantum electrodynamics
• Renormalization of fermion velocity in finite temperature QED_{3}
• Vacuum instability by a chromoelectric field in 2 + 1-dimensions
• The spectrum consistency of fractional quantum Hall effect model
• Parity anomaly in Dirac equation in (1+2) dimensions, quantum electrodynamics and pair production