DC photocurrent in a ferroelectric excitonic insulator

We theoretically investigate the linear and nonlinear optical responses in a non-centrosymmetric excitonic insulator (EI). The ordered state in the EI is characterized by the spontaneous orbital hybridization triggered by the excitonic instability, which can realize electronic ferroelectricity in its EI ground state. We show the optically active collective modes in the linear response regime. Then, using time-dependent mean-field theory, we compute the shift and injection currents as second-order optical responses. We demonstrate that the collective mode of the ferroelectric EI leads to a shift current which shows sharp resonances at sub-bandgap collective mode frequencies. We also find a nonvanishing injection current and discuss its origin associated with optically active collective modes.