  Self-organized regular patterns are ubiquitous in nature, and one of their
most celebrated manifestations is the Abrikosov vortex lattice: under an
applied magnetic field, the homogeneous superconductivity becomes unstable and
cast itself into a regular texture of the "normal" filaments, called Abrikosov
vortices, immersed into a superconducting matrix. Its prediction and the
experimental discovery became a breakthrough in our understanding of
superconductivity and founded a new direction in physics. Here we show that the
interplay between the superconducting order parameter and elastic fields, which
are intimately connected to the very existence of the superconductivity itself,
can result in a novel superconducting state dual to the Abrikosov state: a
regular texture of superconducting islands. The fact that both patterns emerge
within the framework of the Ginzburg-Landau description of superconductivity
indicates that the formation of regular structures may be a generic feature of
any phase transition. Emergence of superconducting island arrays is not
specific to the effect of the elastic forces, but can be caused by any inherent
mechanism generating long-range non-local interactions in the Ginzburg-Landau
functional, for example, by the Coulomb forces. In particular, our findings
suggest the formation of a superconducting island textures as a scenario for a
superconductor-to-insulator transition in thin films.
