Half-vortex soliton lattices in spin–orbit-coupled Bose–Einstein condensates with a quasi-flat band

Periodic potentials with flat bands in their spectra support strongly localized nonlinear excitations. Although a perfectly flat band cannot exist in a continuous systems, a spin–orbit–coupled Bose–Einstein condensate loaded in a Zeeman lattice can realize the quasi-flat lowest band with an extremely narrow bandwidth. In such a quasi-flat band, half-vortex solitons become confined within a single lattice cell, enabling the formation of arrays of coupled half-vortex solitons arranged of various spatial geometries. In this work, we study the existence and stability of these lattices within the framework of the two-component Gross–Pitaevskii equation. We demonstrate that, near the quasi-flat band, half-vortex solitons and their arrays can be excited with a nearly negligible number of atoms and are constrained by their local symmetries, which are isomorphic to a dihedral group of order 8. This allows observation of the respective field patterns in the nearly linear regime where they exhibit enhanced stability. The constructed lattices may have diverse geometric profiles, and in particular create a composite super-half-vortex soliton with nonlinear symmetry breaking. • A two-dimensional Zeeman lattice with a quasi-flat is obtained. • Half-vortex solitons with a negligible threshold energy are found; they can be observed in a quasi-linear regime. • Stable half-vortex soliton lattices of different shapes, as well as super-half-vortex solitons are obtained.