Dynamic shear viscosity of undoped ABC-stacked multilayer graphene

We investigate the dynamic shear viscosity of the undoped, ABC-stacked multilayer graphene, whose low-energy behavior is captured by a chiral-$N$ effective Hamiltonian with $N$ equal to the number of layers. Electron-electron interactions are analyzed using Feynman diagrams and the random phase approximation (RPA). Evaluating the three leading-order diagrams (self-energy, vertex, and ``honey'' diagrams), we find that the electron-electron interaction can remarkably enhance the shear viscosity at the low dynamic frequency, where states near charge neutrality dominate the response. In the absence of screening, the interaction-induced contribution diverges in the zero-frequency limit for large layer numbers; this infrared divergence is removed by RPA screening of the Coulomb potential. The resulting viscosity exhibits a nonmonotonic frequency dependence, increasing at low frequency and decreasing at high frequency. Furthermore, in the high frequency regime, where the response is governed by the noninteracting contribution, the viscosity scales linearly with the layer number $N$. Our results demonstrate that electron viscous effects in multilayer graphene can be tuned by frequency and layer number.