Superconducting Plate in Transverse Magnetic Field: New State

TL;DR

This paper introduces a new superconducting state in thin plates under transverse magnetic fields near the critical value, characterized by a Laughlin-like wave function and energetically favorable over the Abrikosov vortex state.

Contribution

It proposes a novel superconducting state modeled after fractional quantum Hall states, extending understanding of superconductivity near critical magnetic fields.

Findings

New state is energetically more favorable than Abrikosov vortex state.

The new state's energy scales linearly with (1 - H/Hc2).

Existence interval of the new state is larger in dirty specimens.

Abstract

A model to describe Cooper pairs near the transition point (on temperature and magnetic field), when the distance between them is big compared to their sizes, is proposed. A superconducting plate whose thickness is less than the pair size in the transverse magnetic field near the critical value $H_{c2}$ is considered as an application of the model. A new state that is energetically more favourable than that of Abrikosov vortex state within an interval near the transition point was obtained. The system's wave function in this state looks like that of Laughlin's having been used in fractional quantum Hall effect (naturally, in our case - for Cooper pairs as Bose-particles) and it corresponds to homogeneous incompressible liquid. The state energy is proportional to the first power of value $(1 - H/H_{c2})$, unlike the vortex state energy having this value squared. The interval of the new state existence is greater for dirty specimens.