Weyl semimetals possess unique electrodynamic properties due to a combination of strongly anisotropic and gyrotropic bulk conductivity, surface conductivity, and surface dipole layer. In particular, the gyrotropy caused by Weyl node separation in momentum space gives rise to the optical Hall effect for surface polaritons at the boundaries parallel to the gyrotropic axis. We explore the potential of popular tip-enhanced optical spectroscopy techniques for studies of bulk and surface topological electron states in these materials. Strong anisotropy, anomalous dispersion, and the optical Hall effect for surface polaritons launched by a nanotip provide information about Weyl node position and separation in the Brillouin zone, the value of the Fermi momentum, and the matrix elements of the optical transitions involving both bulk and surface electron states.

• Received 2 September 2019
• Revised 9 December 2019

DOI:https://doi.org/10.1103/PhysRevB.100.235451