Nonlinearity effect on 1D periodic and disordered lattices

TL;DR

This paper investigates how nonlinear interactions influence the transmission and localization properties of 1D periodic and disordered lattices using the Kronig-Penney model, revealing critical nonlinear effects on electronic states.

Contribution

It provides new insights into the nonlinear effects on localization and transmission in 1D lattices, highlighting differences between ordered and disordered systems.

Findings

Nonlinearity can localize or delocalize states depending on its sign and strength.

A critical nonlinearity strength leads to complete localization of states.

Transmission decay follows a power law near the band edge, with exponents depending on potential type.

Abstract

The Kronig-Penney model is used to Study the effect of nonlinear interaction on the transmissive properties of both ordered and disordered chains. In the ordered case, the nonlinearity can either localize or delocalize the electronic states depending on both its sign and strength but there is a critical strength above which all the states are localized. In the disordered case, however, we found that the transmission decays as $T\sim L^{-\gamma}$ around the band edge of the corresponding periodic system. The exponent $\gamma$ is independent of the strength of the nonlinearity in the case of disordered barrier potentials, while it varies with the strength for mixed potentials.