Saddle point states in 2D superconducting film biased near the depairing current

TL;DR

This paper investigates the structure and energy of saddle point states in 2D superconducting films near the depairing current, revealing a transition from vortex to nucleus states and the impact of current concentration on fluctuation effects.

Contribution

It provides a detailed analysis of saddle point states in 2D superconducting films near the depairing current, including the transition from vortex to nucleus states and the role of current concentration.

Findings

Vortex saddle point states do not exist near the depairing current and transition to nucleus states.

Core energy of vortices becomes significant for currents above 0.6 times the depairing current.

Current concentration near bends reduces saddle point energy, enhancing fluctuation effects.

Abstract

The structure and energy of saddle point (SP) states in 2D superconducting film of finite width $w$ with transport current $I$ are found in the framework of Ginzburg-Landau model. We show that very near depairing current $I_{dep}$ the SP state with a vortex does not exist and it transforms to 2D nucleus state, which is a finite region with partially suppressed order parameter. It is also shown that for slightly lower currents the contribution of the vortex core energy is important for SP state with a vortex and it cannot be neglected for $I\gtrsim 0.6 I_{dep}$. It is demonstrated that in the film with local current concentration near the bend the energy of SP state may be much smaller than one in the straight film and it favors the effect of fluctuations in such a samples.