Relativistic superconductivity in the framework of scalar electrodynamics: The order state as a two-complex component field

In a recent study, we introduced a relativistic model of type-II superconductivity in the framework of scalar electrodynamics (SED). The model extended the principles of the nonrelativistic Ginzburg–Landau (GL) theory to explore the electromagnetic (EM) properties of superconductors in a relativistic context. Building on this work, we now propose a generalization of the model by considering a superconducting condensate field composed of two complex components. This extension allows us to address a specific problem analogous to a two-level quantum system, where we derive the supercurrents associated with the vortex’s ground state and first excited state. Additionally, we comment on existing extensions of the GL theory and their potential adaptation to relativistic scenarios, particularly relevant to neutron-stars cores, offering insights into the broader implications of our findings for the field of superconductivity.