Indirect momentum excitation of graphene using high transversal modes of light in hyperbolic media

Electrons in indirect semiconductors can optically transit between the valance and conduction band edges only when the momentum conservation is satisfied with help of a third quasi-particle, such as a phonon. In this report, we theoretically demonstrate that indirect interband transition of graphene electrons can be optically enabled only by light with highly enhanced transversal modes, which can be generated by scattering of point dipole radiation with periodic metal slits fabricated in a natural hyperbolic material. The light-matter interaction for graphene electrons is reformulated by using indirect transition matrix elements, and interband polarizations of graphene are obtained by solving quantum kinetic equations of motion in the semi-classical regime. The interband optical current density of graphene as a function of the polarization angle of the incident field shows clear hexagonal response to the high transversal modes of light, which results from the low dependence on dephasing rate and dominance of the indirect polarizations over the direct interband contributions.