  There is a need for compact, dynamically tunable nonreciprocal optical
elements to enable on-chip-compatible optical isolators and more efficient
radiative energy transfer systems. Plasmon Fizeau drag, the drag of electrical
current on propagating surface plasmon polaritons, has been proposed to induce
nonreciprocal surface modes to enable one-way energy transport. However,
relativistic electron drift velocities are required to induce appreciable
contrast between the dispersion characteristics of co-propagating and
counter-propagating surface plasmon modes. The high electron drift velocity of
graphene previously allowed for the experimental demonstration of
current-induced nonreciprocity in a two-dimensional (2D) Dirac material. The
high electron drift and Fermi velocities in three-dimensional (3D) Dirac
materials make them ideal candidates for the effect, however, both the theory
of the Fizeau drag effect and its experimental demonstrations in 3D Dirac
materials are missing. Here we develop a comprehensive theory of Fizeau drag in
DC-biased 3D Weyl semimetals (WSM) or Dirac semimetals (DSM), both under local
and non-local approximation and with dissipative losses. We predict that under
practical assumptions for loss, Fizeau drag in the DSM Cd$_3$As$_2$ opens
windows of pseudo-unidirectional transport. We additionally introduce new
figures of merit to rank nonreciprocal plasmonic systems by their potential for
directional SPP transport. Further, we propose a new approach for achieving
appreciable plasmonic Fizeau drag via optically pumping bulk inversion symmetry
breaking WSMs or DSMs.
