Regular solutions in Abelian gauge model

TL;DR

This paper numerically investigates regular solutions in the Abelian gauge model, discovering new flux tube configurations that are energetically favorable in certain magnetic field ranges, enhancing understanding of phase transitions in superconductors.

Contribution

It introduces new regular static solutions called type B and flux tubes in the Abelian gauge model, expanding the known solution set and their role in phase transitions.

Findings

Flux tubes are energetically preferred between Hc and Hc2.

Type B and flux tube solutions are crucial for understanding vortex to normal state transition.

New solutions possess finite Gibbs free energy, unlike pure vortices.

Abstract

The regular solutions for the Ginzburg-Landau (-Nielsen-Olesen) Abelian gauge model are studied numerically. We consider the static isolated cylindrically symmetric configurations. The well known (Abrikosov) vortices, which present a particular example of such solutions, play an important role in the theory of type II superconductors and in the models of structure formation in the early universe. We find new regular static isolated cylindrically symmetric solutions which we call the type B and the flux tube solutions. In contrast to the pure vortex configurations which have finite energy, the new regular solutions possess a finite Gibbs free energy. The flux tubes appear to be energetically the most preferable configurations in the interval of external magnetic fields between the thermodynamic critical value $H_{c}$ and the upper critical field $H_{c_2}$, while the pure vortex dominate only between the lower critical field $H_{c_1}$ and $H_{c}$. Our conclusion is thus that type B and flux tube solutions are important new elements necessary for the correct understanding of a transition from the vortex state to the completely normal state.