Hall viscosity and electromagnetic response of electrons in graphene

Abstract

We derive an analytic expression for the geometric Hall viscosity of non-interacting electrons in a single graphene layer in the presence of a perpendicular magnetic field. We show that a recently-derived formula in [C. Hoyos and D. T. Son, Phys. Rev. Lett. {\bf 108}, 066805 (2012)], which connects the coefficient of $q^2$ in the wave vector expansion of the Hall conductivity ${\sigma }_{xy}(q)$ of the two-dimensional electron gas (2DEG) to the Hall viscosity and the orbital diamagnetic susceptibility of that system, continues to hold for graphene -- in spite of the lack of Galilean invariance -- with a suitable definition of the effective mass. We also show that, for a sufficiently large number of occupied Landau levels in the positive energy sector, the Hall conductivity of electrons in graphene reduces to that of a Galilean-invariant 2DEG with an effective mass given by $\hslash k_F/v_F$ (cyclotron mass). Even in the most demanding case, i.e. when the chemical potential falls between the zero-th and the first Landau level, the cyclotron mass formula gives results accurate to better than 1$\%$. The connection between the Hall conductivity and the viscosity provides a possible avenue to measure the Hall viscosity in graphene.

10 pages including one Appendix, one figure. As main modifications, in this version the result for the Hall viscosity and Hall conductivity of graphene reflect the expected electron-hole symmetry and a detailed discussion section has been added to compare our results with those obtained earlier in the literature

References in corpus (5)

• The electronic properties of graphene
• Unconventional Integer Quantum Hall effect in graphene
• Lorentz shear modulus of a two-dimensional electron gas at high magnetic field
• Many-body orbital paramagnetism in doped graphene sheets
• Magnetoelasticity theory of incompressible quantum Hall liquids

Cited by in corpus (10)

• Non-local transport and the Hall viscosity of 2D hydrodynamic electron liquids
• Dissipative and Hall viscosity of a disordered 2D electron gas
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• Viscosity Enhancement by Electron-Hole Collisions in Dirac Electron Fluid
• Terahertz Radiation from the Dyakonov-Shur Instability of Hydrodynamic Electrons in a Corbino Geometry
• Hydrodynamics of the electronic Fermi liquid: a pedagogical overview
• Optical N-plasmon: Topological hydrodynamic excitations in Graphene from repulsive Hall viscosity
• Geometric and computational aspects of chiral topological quantum matter
• Hydrodynamic Coulomb drag in odd electron liquids
• Nonlinear Odd Viscoelastic Effect