Dynamic Viscosity of the ABC-stacked Multilayer Graphene in the Collisionless Regime

We explore the dynamic shear viscosity of the undoped ABC-stacked multilayer graphene based on the chiral-$N$ effective Hamiltonian, where the chirality $N$ is equivalent to the layer number. We investigate the dependence of the dynamic shear viscosity on the frequency in the collisionless regime and calculate Coulomb interaction corrections by three leading order Feynman diagrams: self-energy diagram, vertex diagram, and honey diagram. We propose that the dynamic shear viscosity is generated by the relaxation of momentum flux polarization through electron-hole excitations, and that the interaction can amplify this effect. Furthermore, our research indicates that the dynamic shear viscosity exhibits a robust linear positive dependence on $N$. This finding suggests that by making modifications to the number of layers in graphene, it is possible to finely tune the electron viscous effects.