Emerging complexity in the self-dual theory of superconductivity

To describe the way complexity emerges in seemingly simple systems of nature, requires one to attend to two principal questions: how complex patterns appear spontaneously and why a single system can accommodate their inexhaustible variety. It is commonly assumed the pattern formation phenomenon is related to the competition of several types of interactions with disparate length scales. These multi-scale interactions also lead to frustration within the system, resulting in the existence of a manifold of configurations-patterns with qualitatively distinct morphologies. This work explores an alternative approach through a mechanism that leads to a wide range of intricate and topologically non-trivial patterns. The mechanism is described by the self-dual Ginzburg-Landau theory and, possibly, other Maxwell-Higgs models. It gives rise to unique spatial flux and condensate spatial profiles observed in superconductors between the two conventional superconductivity types I and II.