Two-dimensional Josephson vortex lattice and anomalously slow decay of the Fraunhofer oscillations in a ballistic SNS junction with a warped Fermi surface

TL;DR

This paper investigates how the shape of the Fermi surface affects the decay of Fraunhofer oscillations in a 2D ballistic SNS Josephson junction, revealing a slow decay and vortex lattice formation for warped Fermi surfaces.

Contribution

It demonstrates that Fermi surface warping leads to a slower decay of critical current oscillations and the emergence of a vortex lattice, contrasting with the circular Fermi surface case.

Findings

Amplitude decay slows to 1/√Φ for warped Fermi surfaces.

A 2D vortex-antivortex lattice forms in the normal region.

Circular Fermi surfaces do not exhibit the vortex lattice.

Abstract

$ $The critical current of a Josephson junction is an oscillatory function of the enclosed magnetic flux $\Phi$, because of quantum interference modulated with periodicity $h/2e$. We calculate these Fraunhofer oscillations in a two-dimensional (2D) ballistic superconductor--normal-metal--superconductor (SNS) junction. For a Fermi circle the amplitude of the oscillations decays as $1/\Phi$ or faster. If the Fermi circle is strongly warped, as it is on a square lattice near the band center, we find that the amplitude decays slower $\propto 1/\sqrt\Phi$ when the magnetic length $l_m=\sqrt{\hbar/eB}$ drops below the separation $L$ of the NS interfaces. The crossover to the slow decay of the critical current is accompanied by the appearance of a 2D array of current vortices and antivortices in the normal region, which form a bipartite rectangular lattice with lattice constant $\simeq l_m^2/L$. The 2D lattice vanishes for a circular Fermi surface, when only the usual single row of Josephson vortices remains.