Electrodynamics of tilted Dirac and Weyl materials: A unique platform for unusual surface plasmon polaritons

The electrodynamics of Weyl semimetals is an extension of Maxwell's theory where in addition to field strength tensor F-mu nu, an axion field enters the theory which is parametrized by a four-vector b(mu) = (b(0), b). In tilted Weyl materials (TWMs) an additional set of parameters zeta = (zeta(x), zeta(y), zeta(z)) enters the theory that can be encoded into the metric of the spacetime felt by electrons in TWMs. This allows an extension of Maxwell's electrodynamics that describes electric and magnetic fields in TWMs, and tilted Dirac materials (TDMs) that correspond to b(mu) = 0. The tilt parameter zeta appearing as an off-diagonal metric matrix element, mixing time and space components, which mingles E and B fields, whereby the inhomogeneous Maxwell's equations are modified. As an example of the application of the electrodynamics of TWMs, we study the surface plasmon polariton (SPP) in these systems. The peculiarity of the SPP on the surface of TWMs or TDMs is that it is not merely the propagation of electromagnetic modes on the surface of a conductor. It also describes the propagation of electromagnetic waves at the interface of two different spacetime geometries. In the case of TDMs, we find a characteristic dependence of the SPP spectrum on the tilt parameter zeta which can be used to map zeta from SPP measurements. In the case of TWMs, depending on whether the interface with vacuum supports a Fermi arc or not, and whether the propagation direction is along the Fermi arc or transverse to it, we find many unusual spectral features for SPP modes. These include (1) surface plasmons with much higher frequency than bulk plasmon frequency, (2) soft SPP modes at short length scales, (3) a tilt-controlled SPP window beyond which SPP modes are unstable, (4) a kink in the SPP dispersion, (5) uniform group velocity near the "horizon" (zeta = 1), and (6) possible negative group velocity. Our detailed study of the dependence of SPP spectra on the arrangements of three vectors (b, q, zeta), the first two of which are at our control, can be utilized to map the tilt characteristics and Fermi arc characteristics from SPP measurements.