Emerging complexity in the self-dual theory of superconductivity

Abstract

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. The existence of configurations of qualitatively distinct morphology is attributed to the system frustration induced by the multi-scale interactions. 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 profiles observed in superconductors between the two conventional superconductivity types, I and II.