Localization in a non-Hermitian flat band lattice with nonlinearity

In this article, we aim to report the competing role of non-Hermiticity and nonlinearity introduced in the flat band lattice. For this, we initially examine the dynamics of a nonHermitian single chain diamond network and show a pure imaginary flat band between the complex dispersive bands. The presence of a pure imaginary flat band leads to light propagation either with amplification or attenuation in a confined manner. With this information, we shift to exploiting the non-Hermitian dual chain diamond lattice which shows.. -symmetric nature in a particular situation. In the linear case, the model has two flat bands in its spectrum, whereas its nature depends on the system parameters. This gives rise to the distinct nature of localized light propagation in the system with controllable intensity. Interestingly, in the case of a pure real flat band with broad-site excitation, large-site stable oscillations appear in the system and exist for a long propagation distance. Finally, we study the dual chain lattice with on-site cubic nonlinearity which shows transient localized propagation for initially localized excitation and stationary kovaton like localization for broad-site excitation. Our results reveal the possibility of controlling transport dynamics in non-Hermitian systems with nonlinearity. Our system also acts as a candidate for optical applications, as in the long-distance diffraction-less transmission of information.

Automated summary

This article reports on the competition between non-Hermiticity and nonlinearity in flat band lattices. The presence of a pure imaginary flat band leads to confined light propagation with amplification or attenuation. The dual chain lattice exhibits distinct properties of localized light propagation, and the lattice with on-site cubic nonlinearity shows transient localized propagation and stationary localization. The results highlight the possibility of controlling transport dynamics in non-Hermitian systems with nonlinearity and suggest potential applications in diffraction-less transmission of information.