Optical Hall effect and anomalous dispersion of surface polaritons in Type-I Weyl semimetals

We theoretically study the bulk and surface polariton modes in Type-I Weyl semimetals with broken time-reversal symmetry. We apply the fully quantum-mechanical approach to derive the bulk and surface conductivity tensors by not only considering both intraband and interband optical transitions, but also taking into account all possible combinations of bulk-to-bulk, bulk-to-surface, and surface-to-surface transitions. 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 the 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.