Quantum Hall effect in graphene: A functional determinant approach

Abstract

We start the paper with a brief presentation of the main characteristics of graphene, and of the Dirac theory of massless fermions in 2+1 dimensions obtained as the associated low-momentum effective theory, in the absence of external fields. We then summarize the main steps needed to obtain the Hall conductivity in the effective theory at finite temperature and density, with emphasis on its dependence on the phase of the Dirac determinant selected during the evaluation of the effective action. Finally, we discuss the behavior, under gauge transformations, of the contribution due to the lowest Landau level, and interpret gauge transformations as rotations of the corresponding spinors around the magnetic field.

Talk given at QFEXT07, Leipzig, Germany; discussion on the connection between phase of the determinant, Chern Simons and Berry's phase extended. Final version, to appear in Journal of Physics A

References in corpus (13)

• Electric Field Effect in Atomically Thin Carbon Films
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Landau level degeneracy and quantum Hall effect in a graphite bilayer
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Electronic Properties of Disordered Two-Dimensional Carbon
• Unconventional Integer Quantum Hall effect in graphene
• Dirac and Normal Fermions in Graphite and Graphene: Implications to the Quantum Hall Effect
• Dirac Functional Determinants in Terms of the Eta Invariant and the Noncommutative Residue
• Finite-temperature relativistic Landau problem and the relativistic quantum Hall effect
• The quantum Hall effect in graphene samples and the relativistic Dirac effective action
• Relativistic Landau problem at finite temperature

Cited by in corpus (5)

• Parity-odd effects and polarization rotation in graphene
• Planar QED at finite temperature and density: Hall conductivity, Berry's phases and minimal conductivity of graphene
• 2D massless QED Hall half-integer conductivity and graphene
• Aharonov-Bohm-Coulomb Problem in Graphene Ring
• Analytic solution for Gauged Dirac-Weyl equation in $(2+1)$-dimensions