A novel exact solution to transmission problem of electron wave in a nonlinear Kronig-Penney superlattice

TL;DR

This paper derives a novel exact solution for electron wave transmission in a nonlinear Kronig-Penney superlattice, revealing new quantum coherence effects and enabling precise control of electron transmission by tuning system parameters.

Contribution

It introduces a simple nonlinear map connecting transmission coefficients with system parameters, providing a new analytical approach to nonlinear electron transport problems.

Findings

Exact solution reveals quantum coherence effects in transmission.

Multiple transmission regimes including zero and total transmission.

Method applicable to various nonlinear and linear discrete systems.

Abstract

Nonlinear Kronig-Penney model has been frequently employed to study transmission problem of electron wave in a nonlinear electrified chain or in a doped semiconductor superlattice. Here from an integral equation we derive a novel exact solution of the problem, which contains a simple nonlinear map connecting transmission coefficient with system parameters. Consequently, we suggest a scheme for manipulating electronic distribution and transmission by adjusting the system parameters. A new effect of quantum coherence is evidenced in the strict expression of transmission coefficient by which for some different system parameters we obtain the similar aperiodic distributions and arbitrary transmission coefficients including the approximate zero transmission and total transmission, and the multiple transmissions. The method based on the concise exact solution can be applied directly to some nonlinear cold atomic systems and a lot of linear Kronig-Penney systems, and also can be extended to investigate electron transport in different discrete nonlinear systems.