Comparison of spatially dispersive models for dyadic intraband conductivity of graphene

Analytical expressions are presented for the intraband dyadic conductivity of graphene, fully taking into account its spatially dispersive nature for arbitrary values of the wavevector and the presence of a possible non-zero Fermi energy level. Such expressions are derived from the semi-classical Boltzmann transport equation solved both within the relaxationtime approximation and using the Bhatnagar-Gross-Krook model (which allows an extra degree of freedom to enforce the current continuity equation). Numerical results show that ignoring spatial dispersion lead to dramatic errors in the propagation properties and current profiles of fundamental modes in graphene nanoribbons.