Semi-vortex solitons and their excited states in spin-orbit-coupled binary bosonic condensates

It is known that two-dimensional two-component fundamental solitons of the semi-vortex (SV) type, with vorticities (s₊,s₋)=(0,1) in their components, are stable ground states (GSs) in the spin-orbit-coupled (SOC) binary Bose-Einstein condensate with the contact self-attraction acting in both components, in spite of the possibility of the critical collapse in the system. However, excited states(ESs) of the SV solitons, with the vorticity set (s₊,s₋)=( S₊,S₊+1) and S₊=1,2,3,..., are unstable in the same system. We construct ESs of SV solitons in the SOC system with opposite signs of the self-interaction in the two components. The main finding is stability of the ES-SV solitons, with the extra vorticity (at least) up to S₊=6. The threshold value of the norm for the onset of the critical collapse, Nₜₕᵣ, in these excited states is higher than the commonly known critical value, Nc≈ 5.85,associated with the single-component Townes solitons, Nₜₕᵣ increasing with the growth of S₊. A velocity interval for stable motion of the GS-SV solitons is found too. The results suggest a solution for the challenging problem of the creation of stable vortex solitons with high topological charges.