Pseudo-Euler equations from nonlinear optics: plasmon-assisted photodetection beyond hydrodynamics

A great deal of theoretical and experimental efforts have been devoted in the last decades to the study of long-wavelength photodetection mechanisms in field-effect transistors hosting two-dimensional electron systems. A particularly interesting subclass of these mechanisms is intrinsic and based on the conversion of the incoming electromagnetic radiation into plasmons of a two-dimensional electron system, which resonantly enhance the photoresponse, and subsequent rectification via hydrodynamic nonlinearities. Here we show that such conversion and subsequent rectification occur well beyond the frequency regime in which hydrodynamic theory applies. We consider the nonlinear optical response of generic 2D electron systems and derive pseudo-Euler equations of motion for suitable collective variables. These are solved in one- and two-dimensional geometries for the case of graphene and the results are compared with those of hydrodynamic theory. Significant qualitative differences are found, which are amenable to experimental studies. Our theory expands the knowledge of the fundamental physics behind long-wavelength photodetection.