# Spontaneous Long-range Vortex-antivortex Pair in the Two-band 2D Superconductor

## TL;DR

This paper demonstrates the spontaneous formation of a stable long-range vortex-antivortex pair in a two-band 2D superconductor, driven by Josephson-coupling effects, using a Ginzburg-Landau model.

## Contribution

It reveals a new stable vortex-antivortex pairing phenomenon in two-band superconductors caused by Josephson-coupling, supported by numerical minimization of the Ginzburg-Landau model.

## Key findings

- Stable vortex-antivortex pairs with long-range order are observed.
- The total free energy depends linearly on the vortex-antivortex separation.
- Josephson-coupling induces this spontaneous pairing phenomenon.

## Abstract

The relaxation iterative method is used to minimize Ginzburg-Landau model for the two-band superconductor with Josephson-coupling. A stable spontaneous vortex-antivortex pair with long range order has been revealed. Our result appears due to the Josephson-coupling effect, which leads to a linearly-dependence of total free energy on the distance between vortex-antivortex pair, hence accounts for this phenomenon.