Effective Field Theory of Relativistic Quantum Hall Systems

Abstract

Motivated by the observation of the fractional quantum Hall effect in graphene, we consider the effective field theory of relativistic quantum Hall states. We find that, beside the Chern-Simons term, the effective action also contains a term of topological nature, which couples the electromagnetic field with a topologically conserved current of $2+1$ dimensional relativistic fluid. In contrast to the Chern-Simons term, the new term involves the spacetime metric in a nontrivial way. We extract the predictions of the effective theory for linear electromagnetic and gravitational responses. For fractional quantum Hall states at the zeroth Landau level, additional holomorphic constraints allow one to express the results in terms of two dimensionless constants of topological nature.

4 pages

References in corpus (1)

• The Euler current and relativistic parity odd transport

Cited by in corpus (11)

• The Euler current and relativistic parity odd transport
• Exact Electromagnetic Response of Landau Level Electrons
• Horava-Lifshitz Gravity and Effective Theory of the Fractional Quantum Hall Effect
• Hall viscosity, spin density, and torsion
• Quantum Hall effective action for anisotropic Dirac semi-metal
• Weiss Oscillations in the Galilean-Invariant Dirac Composite Fermion Theory for Even-Denominator Filling Fractions of the Lowest Landau Level
• Universal nonlinear responses of quantum Hall systems with Galilean invariance
• Relativistic Gravity and Parity-Violating Non-Relativistic Effective Field Theories
• Motion-driven quantum dissipation in an open electronic system with nonlocal interaction
• Viscosities and shift in a chiral superfluid: a holographic study
• Flux-induced midgap states between strain-engineered flat bands