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

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.

RevTex, 4 pages, epsf.sty to insert figures, to appear in Phys.Rev.B

References in corpus (1)

• Nonlinear feedback oscillations in resonant tunneling through double barriers

Cited by in corpus (8)

• Blow-up for the pointwise NLS in dimension two: absence of critical power
• Well-posedness of the Two-dimensional Nonlinear Schrödinger Equation with Concentrated Nonlinearity
• Stability of the standing waves of the concentrated NLSE in dimension two
• A general review on the NLS equation with point-concentrated nonlinearity
• The 1-D Dirac equation with concentrated nonlinearity
• Prescribed mass ground states for a doubly nonlinear Schrödinger equation in dimension one
• Well-posedness of the three-dimensional NLS equation with sphere-concentrated nonlinearity
• On the standing waves of the Schroedinger equation with concentrated nonlinearity