Nonlinear Spectroscopy of Collective Modes in an Excitonic Insulator

The nonlinear optical response of an excitonic insulator coupled to lattice degrees of freedom is shown to depend in strong and characteristic ways on whether the insulating behavior originates primarily from electron-electron or electron-lattice interactions. Linear response optical signatures of the massive phase mode and the amplitude (Higgs) mode are identified. Upon nonlinear excitation resonant to the phase mode, a new in-gap mode at twice the phase mode frequency is induced, leading to a huge second harmonic response. Excitation of in-gap phonon modes leads to different and much smaller effects. A Landau-Ginzburg theory analysis explains these different behaviors and reveals that a parametric resonance of the strongly excited phase mode is the origin of the photoinduced mode in the electron-dominant case. The difference in the nonlinear optical response serves as a measure of the dominant mechanism of the ordered phase.