Supersolid-like solitons in a spin-orbit-coupled spin-2 condensate

We study supersolid-like crystalline structures emerging in the stationary states of a quasi-two-dimensional spin-orbit (SO)-coupled spin-2 condensate in the ferromagnetic, cyclic, and antiferromagnetic phases by solving a mean-field model. Interplay of different strengths of SO coupling and interatomic interactions gives rise to a variety of nontrivial density patterns in the emergent solutions. For small SO-coupling strengths γ (γ≈0.5), the ground state is an axisymmetric multiring soliton for polar, cyclic, and weakly ferromagnetic interactions, whereas for stronger ferromagnetic interactions a circularly asymmetric soliton emerges as the ground state. Depending on the values of interaction parameters, with an increase in SO-coupling strength, a stripe phase may also emerge as the ground state for polar and cyclic interactions. For intermediate values of SO-coupling strength (γ≈1), in addition to these solitons, one could have a quasidegenerate triangular-lattice soliton in all magnetic phases. On further increasing the SO-coupling strength (γ⪆4), a square-lattice and a superstripe soliton emerge as quasidegenerate states. The emergence of all these solitons can be inferred from a study of solutions of the single-particle Hamiltonian.