Optical Spin Hall Effect in 2D tilted anisotropic Dirac systems and probing of quantum capacitance

The optical spin Hall effect (OSHE) is the optical analogue of the electronic spin Hall effect. Instead of a spin-dependent separation of electronic spins, are the photons with opposite spin angular momentum, i.e. left and right circular polarization, which suffer a lateral shift in opposite direction by reflection or transmission of an incident light field on an interface. This spatial separation is attributed to an effective spin-orbit interaction of light, which describes the mutual influence of the spin (optical polarization) and the trajectory of the light beam. The OSHE phenomenon has been investigated mainly on 3D material interfaces and metasurfaces.

Recently, research has been extended to the case of atomically thin media, such as graphene, phosphorene, or semi-Dirac type. Here, we consider 2D Dirac materials described by low-energy model Hamiltonians with gapped bands displaying anisotropic and tilted dispersion. The breaking of the particle-hole symmetry in each valley modifies the density of states significantly, while the presence of a mass leads to a band gap of indirect nature. Besides the velocity anisotropy, this characteristic is an additional source of the anisotropy in the system. These elements lead to distinctive features in the optical conductivity, due to the strong modification of the spectrum of interband transitions around the indirect gap.

We explore how this optical response of a massive tilted Dirac system manifests on the longitudinal and transverse shift in the spin Hall effect of light. In semi-Dirac systems, for instance, a large OSHE was predicted. A comparison of the results from graphene and similar systems is presented to evaluate the influence of the tilting, the mass, and the anisotropy of the bands.

Also, in the insulating regime (when the Fermi level is lower than the energy gap), the optical conductivity is given as a function of the quantum capacitance, so given their mutual dependence, the possibility of probing these quantities based on the measurement of the displacements due to the OSHE in the THz regime has been explored.