Nonlinear optical effects in intrinsic and doped 2D semiconductors

We present a general method to compute the nonlinear optical response, using the length gauge that avoids unphysical divergences otherwise present in the evaluation of the nonlinear current density response.
Moreover, we disentangle the dispersive part of the nonlinear optical spectrum from Drude like nonlinear response.
The dependence of the nonlinear response of several 2D materials, including mono- and few-layer graphene and black phosphorus, on doping and temperature is studied.
Furthermore, our results explain the dominant role of mixed inter-intraband motion in the nonlinear resonances of systems with few bands.
In addition, we compare the effects of truncation of the Hamiltonian basis set on the calculation of the nonlinear response using either the velocity and length gauge.