Nonlinear localized flatband modes with spin-orbit coupling

TL;DR

This paper explores stable nonlinear localized modes, including compact localized states and discrete solitons, in a spinor wave system with spin-orbit coupling on a flatband network, revealing their existence, stability, and tunability.

Contribution

It demonstrates the coexistence and stability of CLSs and DSs in a nonlinear spinor system with SOC, providing exact analytical solutions and insights into their spectral properties.

Findings

CLS and DS families are stable near the flatband and within the minigap.

SOC opens a minigap and preserves CLSs at the flatband frequency.

Stable localized modes exist deep inside the semi-infinite gap.

Abstract

We report the coexistence and properties of stable compact localized states (CLSs) and discrete solitons (DSs) for nonlinear spinor waves on a flatband network with spin-orbit coupling (SOC). The system can be implemented by means of a binary Bose-Einstein condensate loaded in the corresponding optical lattice. In the linear limit, the SOC opens a minigap between flat and dispersive bands in the system's bandgap structure, and preserves the existence of CLSs at the flatband frequency, simultaneously lowering their symmetry. Adding onsite cubic nonlinearity, the CLSs persist and remain available in an exact analytical form, with frequencies which are smoothly tuned into the minigap. Inside of the minigap, the CLS and DS families are stable in narrow areas adjacent to the FB. Deep inside the semi-infinite gap, both the CLSs and DSs are stable too.