Composite localized modes in discretized spin-orbit-coupled Bose-Einstein condensates

We introduce a discrete model for binary spin-orbit-coupled Bose-Einstein condensates trapped in a deep one-dimensional optical lattice. Two different types of the couplings are considered, with spatial derivatives acting inside each species, or between the species. The discrete system with inter-site couplings dominated by the spin-orbit coupling (SOC), while the usual hopping is negligible, emulates condensates composed of extremely heavy atoms, as well as those with opposite signs of the effective atomic masses in the two components. Stable localized composite states of miscible and immiscible types are constructed. The effect of the SOC on the immiscibility-miscibility transition in the localized complexes, which emulates the phase transition between insulating and conducting states in semiconductors, is studied.