# Two-dimensional solitons and quantum droplets supported by competing self- and cross-interactions in spin-orbit-coupled condensates

## TL;DR

This paper investigates the formation and stability of two-dimensional solitons and quantum droplets in spin-orbit-coupled Bose-Einstein condensates with competing interactions, revealing new stable states and the effects of spin-orbit coupling.

## Contribution

It introduces the first study of quantum droplets in spin-orbit-coupled BECs, analyzing their stability, properties, and the impact of different spin-orbit coupling types.

## Key findings

- Stable 2D solitons of mixed-mode and semi-vortex types identified.
- Quantum droplets can be stabilized by Lee-Huang-Yang corrections, avoiding collapse.
- Spin-orbit coupling influences the shape and stability of quantum droplets.

## Abstract

We study two-dimensional (2D) matter-wave solitons in spinor Bose-Einstein condensates (BECs) under the action of the spin-orbit coupling (SOC) and opposite signs of the self- and cross-interactions. Stable 2D two-component solitons of the mixed-mode (MM) type are found if the cross-interaction between the components is attractive, while the self-interaction is repulsive in each component. Stable solitons of the semi-vortex type are formed in the opposite case, under the action of competing self-attraction and cross-repulsion. The solitons exist with the total norm taking values below a collapse threshold. Further, in the case of the repulsive self-interaction and inter-component attraction, stable 2D self-trapped modes, which may be considered as quantum droplets (QDs), are created if the beyond-mean-field Lee-Huang-Yang (LHY) terms are added to the self-repulsion in the underlying system of coupled Gross-Pitaevskii equations. Stable QDs of the MM type, of a large size with an anisotropic density profile, exist with arbitrarily large values of the norm, as the LHY terms eliminate the collapse. The effect of the SOC term on characteristics of the QDs is systematically studied. We also address the existence and stability of QDs in the case of SOC with mixed Rashba and Dresselhaus terms, which makes the density profile of the QD more isotropic. Thus, QDs in the spin-orbit-coupled binary BEC are for the first time studied in the present work.