Intraband effects in excitonic second-harmonic generation

A theory for the nonlinear excitonic optical response of semiconductors is developed. By adopting the length gauge, intraband effects are rigorously taken into account. We show that the second-order nonlinear response mixing intra- and interband transitions can be expressed in terms of generalized derivatives of the exciton Green's function. The theory is applied to hexagonal boron-nitride monolayers. For both the linear and nonlinear response, a dramatic influence of excitons is found. Hence, new discrete resonances appear as well as pronounced changes in the continuum spectrum.