Superconducting vortex loops have so far avoided experimental detection despite being the focus of much theoretical work. We here propose a method of creating controllable vortex loops in the superconducting condensate arising in a normal metal through the proximity effect. We demonstrate both analytically and numerically that superconducting vortex loops emerge when the junction is pierced by a current-carrying insulated wire and give an analytical expression for their radii. The vortex loops can readily be tuned big enough to hit the sample surface, making them directly observable through scanning tunneling microscopy.
Introduction:Many key properties of physical systems are determined by topological defects such as dislocations in solids, domain walls in ferroics, vortices in superfluids, magnetic skyrmions in condensed matter systems and cosmic strings in quantum field theories. In superconductors, the topological entities are vortex lines of quantized magnetic flux. The topological nature of these vortices makes them stable, which is important for potential applications such as superconducting qubits [1-3], digital memory and long-range spin transport [4]. Vortices have non-superconducting cores and a phase winding of an integer multiple of 2π in the superconducting order parameter, leading to circulating supercurrents [5].The formation of superconducting vortex loops is topologically allowed, and has theoretically been predicted to form around strong magnetic inclusions inside the superconductor [6] or through vortex cutting and recombination [7,8]. However, no observation of vortex loops in superconducting systems has been found to date. One challenging aspect is that vortex loops are typically small in conventional superconductors and difficult to stabilize for an extended period of time [9]. Recently it has been shown that vortex loops can be formed in proximity systems by inserting physical barriers, around which the vortices can wrap [8].In this Letter, we present a way to create controllable vortices in mesoscopic proximity systems in a manner which makes them experimentally detectable through scanning tunneling microscopy. The system considered is a three-dimensional SNS junction pierced by a current-carrying wire which creates the inhomogeneous field responsible for the vortex loops. In planar SNS-junctions with uniform applied magnetic field, changing the superconducting phase difference between the two superconductors shifts the vortex lines in the vertical direction [10]. We here show that the corresponding effect on vortex loops in three dimensions is to change their size. Thus, these vortex loops are easily tunable. This makes it possible to make the vortices touch the surface, leaving distinct traces which are directly observable by scanning tunneling spectroscopy [11].Vortex loops in superconducting systems has previously been predicted using the phenomenological Ginzburg-Landau theory [6][7][8]. Here we use a fully microscopic framework known as quasiclassical theory and solve the Usadel equ...
