Coherent patterns and self-induced diffraction of electrons on a thin nonlinear layer

TL;DR

This paper investigates how electrons scatter on a thin nonlinear layer, revealing that self-induced patterns like solitons can cause diffraction and beam splitting, depending on the nonlinearity type and wave amplitude.

Contribution

It introduces the concept of a self-induced nonlinear quantum screen where electron wave patterns form spontaneously and influence diffraction.

Findings

Formation of soliton-shaped brightening or darkening on the layer.

Different diffraction patterns arise from attractive or repulsive nonlinearities.

Nonlinear effects include self-focusing, beam splitting, and suppression of reflection or transmission.

Abstract

Electron scattering on a thin layer where the potential depends self-consistently on the wave function has been studied. When the amplitude of the incident wave exceeds a certain threshold, a soliton-shaped brightening (darkening) appears on the layer causing diffraction of the wave. Thus the spontaneously formed transverse pattern can be viewed as a self-induced nonlinear quantum screen. Attractive or repulsive nonlinearities result in different phase shifts of the wave function on the screen, which give rise to quite different diffraction patterns. Among others, the nonlinearity can cause self-focusing of the incident wave into a ``beam'', splitting in two ``beams'', single or double traces with suppressed reflection or transmission, etc.