Observation of giant nonlinear valley Hall effect

The valley Hall effect (VHE) holds great promise for valleytronic applications by leveraging the valley degree of freedom. To date, research on VHE has focused on its linear response to an applied current, leaving nonlinear valley responses undetected and nonlinear valleytronic devices undeveloped. Here, we report the experimental observation of a nonlinear VHE in a graphene-hBN moire superlattice, evidenced by the generation of second-harmonic nonlocal voltages under AC currents. Remarkably, the nonlinear VHE has magnitude surpassing the linear VHE and is highly tunable via a gate voltage, which exhibits a pair of opposite peaks on the two sides of a Dirac gap. The nonlinear signal shows quadratic scaling with driving current and quartic scaling with local resistance, setting it apart from the linear counterpart. These experimental features are consistent with the theoretical picture of nonlocal transport mediated by nonlinear VHE and linear inverse VHE. We further reveal a nonlinear inverse VHE by observing the third- and fourth-harmonic nonlocal voltages. The nonlinear VHE provides a novel mechanism for valley manipulation and enables a novel valleytronic device, the valley rectifier, that converts AC charge current into DC valley current.