Time-reversal odd transport in bilayer graphene: Hall conductivity and Hall viscosity

Abstract

We consider the time-reversal odd dynamics of the bilayer graphene at low energies in the quantum Hall regime. A generating functional for the effective action that captures the electromagnetic response to all orders in momentum and frequency is presented and evaluated to the third order in the space-time gradient $\mathcal{O}({\partial }^3)$. In addition, we calculate the Hall viscosity and derive an explicit relationship with the $q^2$ coefficient of the Hall conductivity. It is reminiscent of the Hoyos--Son relation in the Galilean invariant systems, which can be recovered in the limit of large filling factor $N$.

arXiv comment9 pages, 3 figures

References in corpus (27)

• The electronic properties of graphene
• Landau level degeneracy and quantum Hall effect in a graphite bilayer
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Unconventional Integer Quantum Hall effect in graphene
• The electronic properties of bilayer graphene
• Hall Viscosity and Electromagnetic Response
• Measuring Hall Viscosity of Graphene's Electron Fluid
• Kubo formulas for viscosity: Hall viscosity, Ward identities, and the relation with conductivity
• Collision-dominated nonlinear hydrodynamics in graphene
• Lorentz shear modulus of a two-dimensional electron gas at high magnetic field
• Interaction Induced Quantum Valley Hall Effect in Graphene
• Magnetohydrodynamics in graphene: shear and Hall viscosities
• Topological Phases in the Zeroth Landau Level of Bilayer Graphene
• Hall viscosity in quantum systems with discrete symmetry: point group and lattice anisotropy
• Pseudo-zero-mode Landau levels and collective excitations in bilayer graphene
• Hall viscosity and electromagnetic response of electrons in graphene
• Duality and Universal Transport in a Mixed-Dimension Electrodynamics
• Electromagnetic response and pseudo-zero-mode Landau levels of bilayer graphene in a magnetic field
• Bosonic Analogue of Dirac Composite Fermi Liquid
• Euler - Heisenberg effective action and magnetoelectric effect in multilayer graphene
• Optical conductivity in graphene: hydrodynamic regime
• Exact Electromagnetic Response of Landau Level Electrons
• Self-Dual $\nu =1$ Bosonic Quantum Hall State in Mixed Dimensional QED
• Quantum Boltzmann equation for bilayer graphene
• Landau quantization of multilayer graphene on a Haldane sphere
• Abelian Chern-Simons Theory for the Fractional Quantum Hall Effect in Graphene
• Finite-wavevector Electromagnetic Response in Lattice Quantum Hall Systems

Cited by in corpus (3)

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