Quantum Geometry and Topology of Bulk Plasmons in Weyl Metals

We address the quantum geometric structure of plasmons in Fermi surfaces enclosing a topological charge. We demonstrate that Weyl fermion plasmons have monopole structure, are topological and have a finite vorticity $\zeta =2{\mathsf{C}}_{\text{w}}$, where ${\mathsf{C}}_{\text{w}}$ is the Chern number of the Fermi surface enclosing the Weyl point. We show that these plasmons selectively couple to light linearly polarized along the plasmon effective dipole moment $\mathbf{d}$, which has quantum geometric origin and points along the direction of the plasmon center of mass momentum $\widehat{\mathbf{Q}}$. We suggest that Weyl metal topological plasmons have distinctive optical properties compared to conventional plasmons.