Sound of Fermi arcs: a linearly dispersing gapless surface plasmon mode in undoped Weyl semimetals

Using Green's function of semi-infinite Weyl semimetals, we present the quantum theory of the collective charge dynamics of Fermi arcs. We find that the Fermi arc plasmons in undoped Weyl semimetals are linearly dispersing gapless plasmon modes. The gaplessness comes from proper consideration of the deep penetration of surface states near the end of the Fermi arcs into the interior of the Weyl semimetal. The linear dispersion---rather than square root dispersion of pure 2D electron systems with extended Fermi surface---arises from the strong anisotropy introduced by the Fermi arc itself, due to which the continuum of surface particle-hole (PH) excitations in this system will have a strong resemblance to a stack of one-dimensional (1D) electron systems. This places the Fermi arc electron liquid in between the 1D and 2D electron liquids. Contamination with the bulk PH excitations in the doped case gives rise to the damping of the Fermi arc sounds.