Strong enhancement of third harmonic generation in a double layer graphene system caused by electron-hole pairing

A manifestation of electron-hole pairing in nonlinear electromagnetic response of a double layer graphene system is studied. It is shown that the pairing causes the appearance of a number of peaks in the frequency dependence of the intensity of the third harmonic generation (THG). The highest peak corresponds to \hbar\omega = (2/3)\Delta, where \omega\ is the incident wave frequency, and \Delta\ is the order parameter of the electron-hole pairing. The absolute value of the THG intensity in the systems with electron-hole pairing is in several orders of magnitude greater than the THG intensity in the unpaired state. It is shown that huge enhancement of the THG intensity occurs both in the double monolayer and double bilayer graphene systems.