Seltrapping in flat band lattices with nonlinear disorder

Danilo Rivas,Mario I Molina

doi:10.1038/s41598-020-62079-8

Abstract

We study the transport properties of an initially localized excitation in several flat band lattices, in the presence of nonlinear (Kerr) disorder. In the weak nonlinearity regime, the dynamics is controlled by the degeneracy of the bands leading to a linear form of selftrapping. In the strong nonlinearity regime, the dynamics of the excitations depends strongly on the local environment around the initial excitation site that leads to a highly fluctuating selfrapping profile. For a binary nonlinear disorder, it is shown that the spreading of the flat band fundamental mode, is completely inhibited for a finite fraction of all cases. This fraction corresponds to the fraction of times the same value of (random) nonlinearity is assigned to all sites of the fundamental mode.

Highlights

We study the transport properties of an initially localized excitation in several flat band lattices, in the presence of nonlinear (Kerr) disorder
The phenomenon of selftrapping of excitations in nonlinear lattices has been an active research field for many years, from the time it was realized that some solutions of the coupled electron-phonon problem in biomolecules, featured stable, propagating localized excitations, termed discrete solitons
Its existence can be argued based on the local character of the DNLS (Eq 1): Starting with a nonlinear lattice and assuming that a localized excitation exists, say of size d, the nonlinearity is only appreciable near the soliton position, and the rest of the lattice can be taken as linear, to a first approximation

Summary

OPEN Seltrapping in flat band lattices with nonlinear disorder

We study the transport properties of an initially localized excitation in several flat band lattices, in the presence of nonlinear (Kerr) disorder. There remains finer details like the minimum value of the nonlinearity parameter for trapping to occur Another mechanism for generating localized modes, this time in linear systems, has gained recent interest: Flat bands. In an optical context they are interesting since they allow the long-distance propagation without distortion of shapes based on combinations of these flat modes These states rely on a precise geometrical interference condition, and have been studied and observed in optical and photonic lattices[28,29,30,31,32], graphene[33,34], superconductors[35,36], fractional quantum Hall systems[37,38,39], and exciton-polariton condensates[40,41]. The transport properties are affected by the existence of flat bands and we will show that there are conditions under which nonlinear disorder does not affect the system transport

The Model

Uniform Nonlinearity

Conclusions

Additional information