Elastic response of the electron fluid in intrinsic graphene: The collisionless regime

TL;DR

This paper calculates the frequency-dependent electron viscosity in intrinsic graphene at charge neutrality, revealing significant interaction effects and linking viscosity to energy flow, using a theoretical approach based on the Kubo formalism.

Contribution

It provides the first detailed calculation of the collisionless electron viscosity in graphene, including interaction corrections and the role of pseudo-spin symmetry.

Findings

Interaction corrections to viscosity are larger than those to optical conductivity.

Viscosity is directly related to nonlocal energy-flow response.

Pseudo-spin symmetry influences the viscosity tensor.

Abstract

The elastic response of an electron fluid at finite frequencies is defined by the electron viscosity $\eta(\omega)$. We determine $\eta(\omega)$ for graphene at the charge neutrality point in the collisionless regime, including the leading corrections due to the electron-electron Coulomb interaction. We find interaction corrections to $\eta(\omega)$ that are significantly larger if compared to the corresponding corrections to the optical conductivity. In addition, we find comparable contributions to the dynamic momentum flux due to single-particle and many-particle effects. We also demonstrate that $\eta(\omega)$ is directly related to the nonlocal energy-flow response of graphene at the Dirac point. The viscosity in the collisionless regime is determined with the help of the strain generators in the Kubo formalism. Here, the pseudo-spin of graphene describing its two sublattices plays an important role in obtaining a viscosity tensor that fulfills the symmetry properties of a rotationally symmetric system.