Theory of Nonlocal Transport from Nonlinear Valley Responses

TL;DR

This paper develops a theoretical framework for understanding nonlocal transport signals arising from nonlinear valley Hall effects, highlighting the distinct symmetry and mechanisms involved, and predicts sizable signals in bilayer T_d-WTe2.

Contribution

It introduces a symmetry-based theory for nonlinear nonlocal valley responses, distinguishing them from linear effects and providing formulas and first-principles predictions.

Findings

Nonlocal signals require valley-even symmetry.

Distinct scaling behaviors differentiate responses.

Predicted sizable signals in bilayer T_d-WTe2.

Abstract

We develop a theory for the nonlocal measurement of nonlinear valley Hall effect. Different from the linear case where the direct and the inverse processes are reciprocal, we unveil that the nonlinear inverse valley Hall effect needed to generate nonlocal voltage signal must have a distinct symmetry character and involve distinct mechanisms compared to the nonlinear valley Hall response it probes. Particularly, it must be valley-even, in contrast to both linear and nonlinear valley Hall effects which are valley-odd. Layer groups that permit such nonlocal valley responses are obtained via symmetry analysis, and formulas for the nonlocal signals are derived. In the presence of both linear and nonlinear valley responses, we show that the different responses can be distinguished by their distinct scaling behaviors in the different harmonic components, under a low-frequency ac driving. Combined with first-principles calculations, we predict sizable nonlocal transport signals from nonlinear valley responses in bilayer $T_{d}$-WTe$_{2}$. Our work lays a foundation for nonlocal transport studies on the emerging nonlinear valleytronics.