On the Abrikosov transition in disordered superconducting films

TL;DR

This paper models the phase transition in disordered superconducting films near the upper critical field as a zero-dimensional replica spin-glass transition, revealing a smoother magnetic response and potential paramagnetic Meissner effect.

Contribution

It introduces a replica model describing the second-order glassy superconducting transition in disordered films, linking it to the SK spin-glass model.

Findings

Magnetic moment dependence on field is smoother than in clean cases.

Transition part of magnetic moment is paramagnetic, indicating a paramagnetic Meissner effect.

Close to transition, the total magnetic moment remains diamagnetic.

Abstract

We consider a disordered superconducting film in the magnetic field close to the upper critical field. Assuming that the phase transition to the glassy superconducting state exists and it is of the second order we show that it is exactly described by a zero-dimensional replica model having a form of one describing the phase transition in the SK (Sherrington-Kirkpatrick) spin-glass model. The dependence of the magnetic moment on the external magnetic field is shown to be more smooth than the Abrikosov mean field result for the clean case. While the total magnetic moment of the film close to the phase transition is diamagnetic, the part of it emerging due to the phase transition is paramagnetic, this shows tendency to the paramagnetic Meissner effect.