Bicircular Light Induced Multi-State Geometric Current

We investigate the photocurrent induced by bicircular light (BCL) in materials, with a focus on its multi-state geometric nature. BCL, a combination of left- and right-circularly polarized light, can generate both injection and shift currents, originating from the geometric properties of gauge-invariant shift vectors, quantum geometric tensors, and triple-phase products. Crucially, the real parts of the quantum geometric tensors and triple-phase products remain nonzero in centrosymmetric systems, facilitating photocurrent generation in contrast to the traditional shift current bulk photovoltaic effect. Using a diagrammatic approach, we systematically analyze the BCL-induced photocurrents and demonstrate the multi-state geometric nature within a one-dimensional three-site Rice-Mele model. Our findings provide a quantum geometric understanding of BCL-induced photocurrents, underscoring the importance of considering multi-band contributions in real materials.