Formulation of the Relativistic Quantum Hall Effect and "Parity Anomaly"

Abstract

We present a relativistic formulation of the quantum Hall effect on Haldane sphere. An explicit form of the pseudopotential is derived for the relativistic quantum Hall effect with/without mass term. We clarify particular features of the relativistic quantum Hall states with the use of the exact diagonalization study of the pseudopotential Hamiltonian. Physical effects of the mass term to the relativistic quantum Hall states are investigated in detail. The mass term acts as an interpolating parameter between the relativistic and non-relativistic quantum Hall effects. It is pointed out that the mass term unevenly affects the many-body physics of the positive and negative Landau levels as a manifestation of the "parity anomaly". In particular, we explicitly demonstrate the instability of the Laughlin state of the positive first relativistic Landau level with the reduction of the charge gap.

We have corrected the typographic errors in our article. There are three corrections: (1)2g -> 2j in Fig.3 (2)2g -> 2j in the caption of Fig.3 (3)2g=12 -> 2j = 64 in the caption of Fig.5

References in corpus (9)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Substrate-induced band gap opening in epitaxial graphene
• Quantum Hall Ferromagnetism in Graphene
• First direct observation of Dirac fermions in graphite
• Observation of topological surface state quantum Hall effect in an intrinsic three-dimensional topological insulator
• Modeling disorder in graphene
• Quantum Hall Effect on Top and Bottom Surface States of Topological Insulator (Bi1-xSbx)2Te3 Films
• The Fractional Quantum Hall States of Dirac Electrons in Graphene
• Fractional Quantum Hall Effect in Graphene

Cited by in corpus (6)

• Relativistic Landau Models and Generation of Fuzzy Spheres
• Probing non-Hermitian phase transitions in curved space via quench dynamics
• Landau quantization of multilayer graphene on a Haldane sphere
• Landau level quantization for massless Dirac fermions in the spherical geometry: graphene fractional quantum Hall effect on the Haldane sphere
• Disorder-induced topological superconductivity in a spherical quantum-Hall--superconductor hybrid
• Fractional quantum Hall effects in graphene on a h-BN substrate