Spin-valley collective modes of the electron liquid in graphene

We develop the theory of collective modes supported by a Fermi liquid of electrons in pristine graphene. Under reasonable assumptions regarding the electron-electron interaction, all the modes but the plasmon are overdamped. In addition to the $SU\left(2\right)$-symmetric spin mode, these include also the valley imbalance modes obeying a $U\left(1\right)$ symmetry, and a $U\left(2\right)$-symmetric valley spin imbalance mode. We derive the interactions and diffusion constants characterizing the overdamped modes. The corresponding relaxation rates set fundamental constraints on graphene valley- and spintronics applications.

Figure 1

Position of scattered particles on the Fermi surface and associated angles, for collinear (left) and head-on (right) scattering processes. Note that the momenta $\mathbf{p}$ and ${\mathbf{p}}^{\prime }$ do not lie on the Fermi surface.