Systematic analysis method for nonlinear response tensors

TL;DR

This paper introduces a systematic method combining the Keldysh formalism and Chebyshev polynomial expansion to identify key parameters in nonlinear response tensors, demonstrated through the nonlinear Hall effect in SnTe monolayer.

Contribution

The method decomposes response tensors into model-independent and dependent parts, revealing essential parameters and providing microscopic insights into nonlinear responses.

Findings

Second-neighbor hopping is essential for the nonlinear Hall effect in SnTe.

Spin-orbit coupling is unnecessary for the nonlinear Hall effect in this case.

The method interprets the nonlinear Hall effect via orbital magneto-current and linear anomalous Hall effects.

Abstract

We propose a systematic analysis method for identifying essential parameters in various linear and nonlinear response tensors without which they vanish. By using the Keldysh formalism and the Chebyshev polynomial expansion method, the response tensors are decomposed into the model-independent and dependent parts, in which the latter is utilized to extract the essential parameters. An application of the method is demonstrated by analyzing the nonlinear Hall effect in the ferroelectric SnTe monolayer for example. It is shown that in this example the second-neighbor hopping is essential for the nonlinear Hall effect whereas the spin-orbit coupling is unnecessary. Moreover, by analyzing terms contributing to the essential parameters in the lowest order, the appearance of the nonlinear Hall effect can be interpreted by the subsequent two processes: the orbital magneto-current effect and the linear anomalous Hall effect by the induced orbital magnetization. In this way, the present method provides a microscopic picture of responses. By combining with computational analysis, it stimulates further discoveries of anomalous responses by filling in a missing link among hidden degrees of freedom in a wide variety of materials.