Shear viscosity at finite magnetic field for graphene, non-relativistic and ultra-relativistic cases

Abstract

The present article has addressed the finite magnetic field extension of the previous work by Cho et al. (Phys. Rev. B 108, 235172, 2023) on microscopic calculation of shear viscosity for electron fluid in graphene system. Our calculation is based on the kinetic theory approach in the relaxation time approximation. In the absence of a magnetic field, transport is governed by a single shear viscosity coefficient, whereas the application of a finite magnetic field induces anisotropy, giving rise to five independent shear viscosity coefficients associated with distinct velocity gradient tensors. These coefficients can be physically categorized into perpendicular, parallel, and Hall components relative to the magnetic field direction. When the scattering time equals the cyclotron time, the perpendicular component is suppressed by 80% and the parallel component by 50% and the Hall effect can reach maximum. Corresponding magnetic field strength for electron fluid in graphene is around 0.01-0.1 Tesla, and the same for non-relativistic electron fluid and ultra-relativistic quark fluid are around 10 Tesla and 10^{14} Tesla respectively. They may be considered as the required magnetic field strength in three different fluid systems to observe noticeable magnetic field response in their shear viscosity coefficients.