Towards relativistic type-II superconductivity: A scalar electrodynamics approach

This work advances our 2D scalar electrodynamics (SED) model, a relativistic analogue of type-II superconductivity, by implementing a cylindrical coordinate representation. This adaptation addresses the importance of cylindrical symmetry in describing 2D systems, especially those featuring Dirac fermion bound states in magnetic fields. Focusing on a specific example, we explore the relativistic limit, significant in astrophysical environments like neutron-star cores, where magnetic fields reach critical levels. Along the lines of the Ginzburg-Landau theory we postulate the structure the proton vortex-supercurrent, and connect it with the SED current. From this connection we analytically determine the squared modulus of the relativistic order parameter state which is to be proportional to the local density of Cooper pairs in the superconducting condensate. This study could contribute to the theoretical understanding of superconductivity in strong electromagnetic fields within the SED framework, with potential applications to neutron star physics.