  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.
