Massive Dirac fermions and the zero field quantum Hall effect

2008/07/04 by Alfredo Raya, Edward D. Reyes, Edward Daniel Reyes-Ramírez · 1 citation
Physics and Astronomy · #Noncommutative and Quantum Gravity Theories #Quantum and electron transport phenomena #Topological Materials and Phenomena #cond-mat.mes-hall #hep-th

paper · pdf · doi:10.1088/1751-8113/41/35/355401

published as J.Phys.A41:355401,2008 · 15 pages. Accepted in Jour. Phys. A

arxiv created 2008/07/04 · openalex publication_date 2008/07/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Through an explicit calculation for a Lagrangian in quantum electrodynamics in (2+1)-spacetime dimensions (QED3), 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 QED3 Lagrangian, for both 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). PACS numbers: 73.43.−f, 10.10.Kk, 11.30.Er 1.

Citations

• The fractional quantum Hall effect
• Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems
• Transport of Dirac quasiparticles in graphene: Hall and optical conductivities
• On the generalized ward identity
• Zitterbewegung, chirality, and minimal conductivity in graphene
• Algebraic Fermi Liquid from Phase Fluctuations: “Topological” Fermions, Vortex “Berryons,” andQED3Theory of Cuprate Superconductors

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• 2D massless QED Hall half-integer conductivity and graphene