Theory of the in-plane photoelectric effect in quasi-one-dimensional electron systems

The in-plane photoelectric (IPPE) effect is a recently discovered [Sci. Adv. \textbf{8}, eabi8398 (2022)] quantum phenomenon which enables efficient detection of terahertz (THz) radiation in semiconductor structures with a two-dimensional (2D) electron gas. Here we develop a theory of the IPPE effect in quasi-one-dimensional electron systems in which the width of the 2D conducting channel is so small that the transverse quantization energy is larger than the thermal energy. We calculate the THz photoresponse of such a system, as a function of the THz frequency, control gate voltages, and geometrical parameters of the detector. We show that the transverse quantization of the electron motion manifests itself in oscillating gate-voltage dependences of the photocurrent, if the THz photon energy is less than the one-dimensional quantization energy. Results of the theory are applicable to any semiconductor systems with 2D electron gases, including III-V structures, silicon-based field effect transistors, and the novel 2D layered, graphene-related materials.