We propose a theory for nonlocal measurements of the nonlinear valley Hall effect (VHE). In contrast to the well-known reciprocity between direct and inverse VHEs in linear responses, we unveil that the nonlinear inverse VHE needed to generate nonlocal voltage is not reciprocal to the nonlinear VHE it probes, but rather has distinct symmetry characters and physical origins. Particularly, while all previously studied VHEs are valley-odd, the nonlinear inverse VHE is valley-even. This fundamental distinction gives rise to unprecedented scaling behaviors in valley mediated nonlocal transport, providing essential experimental hallmarks of nonlinear valley responses. Layer groups that permit the proposed nonlocal valley responses are identified. Sizable nonlocal signals from nonlinear valley responses are revealed in bilayer $T_d\text{−}{\mathrm{WTe}}_2$ through first-principles calculations. Our work lays a foundation for all-electrical detection of nonlinear valley-charge interconversion, which constitutes the basis of emerging nonlinear valleytronics.

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• Transport phenomena
• Valleytronics
• 2-dimensional systems
• First-principles calculations