Finite-temperature relativistic Landau problem and the relativistic quantum Hall effect

Abstract

This paper presents a study of the free energy and particle density of the relativistic Landau problem, and their relevance to the quantum Hall effect. We study first the zero temperature Casimir energy and fermion number for Dirac fields in a 2+1-dimensional Minkowski space-time, in the presence of a uniform magnetic field perpendicular to the spatial manifold. Then, we go to the finite-temperature problem, with a chemical potential, introduced as a uniform zero component of the gauge potential. By performing a Lorentz boost, we obtain Hall's conductivity in the case of crossed electric and magnetic fields.

arXiv commentFinal version, to appear in Journal of Physics A: Mathematical and General

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• Magnetic Field Effects on the Superconducting and Quantum Critical Properties of Layered Systems with Dirac Electrons
• Relativistic and nonrelativistic Landau levels for the noncommutative quantum Hall effect with anomalous magnetic moment in a conical Gödel-type spacetime
• Quantum Hall effect in graphene: A functional determinant approach
• Relativistic persistent currents in ideal Aharonov-Bohm rings
• Relativistic currents on ideal Aharonov-Bohm cylinders
• Casimir Effect of rough plates under a magnetic field in Hořava-Lifshitz theory
• Vacuum polarization at the boundary of a topological insulator
• Aharonov-Bohm rings in de Sitter expanding universe
• One-Loop Quantum Corrections to the Casimir Effect for Smoothly Rough Plates in the Low-Temperature Regime