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

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 $l_m=\sqrt{\hslash /eB}$ 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.

12 pages, 14 figures; V2: added three appendices, including data on the superconducting order parameter and density of states

References in corpus (7)

• Anomalous Josephson effect induced by spin-orbit interaction and Zeeman effect in semiconductor nanowires
• Edge-mode Superconductivity in a Two Dimensional Topological Insulator
• Mechanics of Individual, Isolated Vortices in a Cuprate Superconductor
• Magnetic Interference Patterns and Vortices in Diffusive SNS junctions
• Proximity Induced Vortices and Long-Range Triplet Supercurrents in Ferromagnetic Josephson Junctions and Spin Valves
• Magnetic field oscillations of the critical current in long ballistic graphene Josephson junctions
• Edge effects in the magnetic interference pattern of a ballistic SNS junction

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• Theory of scanning gate microscopy imaging of the supercurrent distribution in a planar Josephson junction
• Anomalous quantum interference effects in graphene SNS junctions due to strain-induced gauge fields
• Vortex spin-valve on a topological insulator
• Spin relaxation, Josephson effect and Yu-Shiba-Rusinov states in superconducting bilayer graphene
• Local density of states in clean two-dimensional superconductor--normal metal--superconductor heterostructures
• Hybrid kernel polynomial method
• Enhanced Andreev Reflection in Flat-Band Systems: Wave Packet Dynamics, DC Transport and the Josephson Effect