Nonlinear optical conductivity of a two-band crystal I

The structure of the electronic nonlinear optical conductivity is elucidated in a detailed study time-reversal symmetric two-band model. decomposed as sum contributions related with different regions First Brillouin Zone, defined by single or multiphoton resonances. All are written terms same integrals, which contain all information specific to particular model under study. In this way, ready-to-use formulas provided that reduce often tedious calculations second and third order evaluation small set similar integrals. scenario where charge carriers present prior excitation, Fermi surface must also be considered shown have an universal frequency dependence, tunable doping. General characteristics made evident type resonance-based analysis: existence step functions determine chemical potential dependence electron-hole insulators; determination imaginary part Hilbert transforms, simpler than those Kramers-Kr\"{o}nig relations; absence Drude peaks diagonal elements conductivity, among others. As examples, analytical expressions derived for conductivities some simple systems: very basic direct gap semiconductors Dirac fermions monolayer graphene.