Enhanced Valley Polarization via Nonlinear Cascaded Quantum-Geometric Selection Rules

Abstract: The quantum geometric properties of Bloch electrons fundamentally govern light-matter interactions and optical selection rules in solids. In semiconducting transition-metal dichalcogenides, circularly polarized excitation near the band edge enables valley-selective interband transitions, providing the basis for valleytronics. While nonlinear optical protocols are being developed to manipulate and probe valley selection rules, they largely rely on band-edge transitions that proceed via virtual intermediate states. Here, we demonstrate a doubly resonant cascaded nonlinear pathway from the valence band to high-lying states, mediated by a real intermediate state whose participation substantially reshapes the valley optical selection rules. Using time- and angle-resolved extreme-ultraviolet photoemission spectroscopy in combination with a time-dependent Lindblad master-equation formalism, we show that this cascaded nonlinear photoexcitation produces a substantially enhanced high-lying valley polarization compared to the conventional linear optical response near the band edge. The extension of the quantum-geometry-based selection rules to the nonlinear regime and high-lying bands offers new perspectives for ultrafast valleytronics and should play a determinant role in strong-field-driven phenomena in quantum materials.