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Imaging vortices in superconducting weakly coupled arrays

Mark Sheldon Wistrom

Published May 22, 2012• 0 citations
OpenAlex

Abstract

This thesis presents the direct observations of magnetic flux vortices in superconducting weakly coupled arrays. Real space images of vortices were obtained for various values of f, the fractional flux per unit cell in the array, and , the strength of the coupling between the islands of the superconducting array. Images and results were obtained for a single vortex in a triangular array, demonstrating the effect of changing , which increased the penetration depth of the magnetic field of the vortex in the sample. The ground state of a triangular array is measured and discussed as a function of f with emphasis for f = 1/4, 1/3 where there are several degenerate ground states corresponding to different vortex patterns. Annealing the arrays at a particular f is also discussed. In particular, for a square array at f = 1/2, the domain walls are the dominant defects, and they move through the sample as the temperature increases resulting in a single domain. The instrument used to perform the experiments, a Scanning SQUID Microscope (SSM), is discussed. The vortices in the superconducting arrays have weak magnetic fields that change over small length scales, requiring certain techniques for measurement. Also presented are the numerical calculations relating the magnetic field output from the SSM to the underlying phases of the array.

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Numerical studies of superfluids and superconductors

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•Jan 1, 2001•5 citations
This thesis presents the direct observations of magnetic flux vortices in superconducting weakly coupled arrays. Real space images of vortices were obtained for various values of f, the fractional flux per unit cell in the array, and , the strength of the coupling between the islands of the superconducting array. Images and results were obtained for a single vortex in a triangular array, demonstrating the effect of changing , which increased the penetration depth of the magnetic field of the vortex in the sample. The ground state of a triangular array is measured and discussed as a function of f with emphasis for f = 1/4, 1/3 where there are several degenerate ground states corresponding to different vortex patterns. Annealing the arrays at a particular f is also discussed. In particular, for a square array at f = 1/2, the domain walls are the dominant defects, and they move through the sample as the temperature increases resulting in a single domain. The instrument used to perform the experiments, a Scanning SQUID Microscope (SSM), is discussed. The vortices in the superconducting arrays have weak magnetic fields that change over small length scales, requiring certain techniques for measurement. Also presented are the numerical calculations relating the magnetic field output from the SSM to the underlying phases of the array.
Vortices and vortex lattices play a major role in determining the transport properties of type-II superconductors[1–3], and enable a platform to investigate exotic superconducting physics[4,5]. The study of vortex matter has generally focused on novel states in 2D films and structures, and has recently moved to investigating systems with constrained dimensions and smaller vortex numbers[6–11]. Vortices are responsible, for example, for some electrical transport regimes in superconducting films, as well as the Berezinkskii-Kosterlitz-Thouless phase transition in superconducting films[12]. Unconventional forms of superconductivity, such as the spin triplet pairing predicted in Sr2RuO4, or in topological insulators paired to s-wave superconductors, contain two condensates that may support two vortex lattices, and may display Majorana modes, signatures of which may have been seen in other superconducting systems[13–17]. The vortex-vortex interactions, or inter and intra-condensate couplings in multicondensate systems, are important parameters that characterize the behavior of the systems that display such phenomena[18–20]. In investigating these parameters, a technique that can both probe the energies in a system, as well as manipulate the vortices therein, has long been desired. In this work, we report on progress in determining the energy scales of vortex systems, as well as limited control over the vortex motion. Using a technique based on magnetic force microscopy, we can directly measure the resonant motion of vortices present in a superconducting lattice. We use a scanning magnetic tip to trap a small number of vortices in a superconducting Josephson junction array near the tip. By observing the resonant motion of the configuration of vortices, a map of the location of energy degeneracies between different stable configurations is generated. From this data, we use a simulation to extract the relative strengths of the characteristic energy scales for the system, including the vortex-magnetic field interaction, the vortex-vortex interaction strength, and the chemical potential for the vortices. The simulations for small numbers of vortices fits the data well for multiple field profiles and lattice spacings. The ability to tune the vortex number and configurations by changing the magnetic field profile from the tip, as well as the lattice parameters of the superconducting surface, are key portions of this technique. We demonstrate that the relative strengths of the chemical potential and vortex-vortex interactions can be tuned relative to the vortex-magnetic field energy by changing the lattice spacing of the array. We also show that by moving the tip farther from or closer to the surface, which changes the potential well from the tip, that the configurations of vortices can be modified. From the experiments, we show that this technique can be used to both extract the strengths of the relative energy scales in this system and other superconducting systems, as well as for manipulating the vortex configurations for quantum computation applications.
Various techniques have been applied to visualize superconducting vortices, providing clues to their electromagnetic response. Here, we present a wide-field, quantitative imaging of the stray field of the vortices in a superconducting thin film using perfectly aligned diamond quantum sensors. Our analysis, which mitigates the influence of the sensor inhomogeneities, visualizes the magnetic flux of single vortices in YBa2Cu3O7−δ with an accuracy of ±10%. The obtained vortex shape is consistent with the theoretical model, and penetration depth and its temperature dependence agree with previous studies, proving our technique's accuracy and broad applicability. This wide-field imaging, which in principle works even under extreme conditions, allows the characterization of various superconductors.
Understanding vortex matter in type-II superconductors is central to controlling dissipation and flux pinning in superconducting materials and devices. Here, we use cryogenic scanning nitrogen vacancy magnetometry (NVM) to image Abrikosov vortices in the cuprate superconductors BSCCO-2212 and YBCO under controlled field-cooled conditions. Measurements, which are performed using continuous-wave optically detected magnetic resonance (cw-ODMR) in a closed-cycle cryostat, yield quantitative magnetic-field maps with nanoscale spatial resolution. In BSCCO-2212 at 71 K, we resolve a well-ordered triangular vortex lattice, whose symmetry and spacing are confirmed through 2D Fourier analysis and are consistent with flux quantization. YBCO thin films imaged at 3 K exhibit a more disordered vortex arrangement reflecting stronger pinning, while maintaining quantitative agreement between measured vortex density and the applied magnetic field. These results render our cryogenic scanning NVM a reliable quantitative tool for real-space studies of vortices in high-TcT_cTc​ superconductors, in particular since such a remarkable magnetic resolution has been achieved within relatively short acquisition times of 2 to 4 h.
In order to investigate the vortex lattice melting transition in detail Bi2Sr2CaCu2O8+ δ Scanning Hall probe microscopy (SHPM), a novel scanned probe magnetic imaging method, has been developed for single crystals. Using an integrated scanning tunnelling microscope (STM) or atomic force microscope (AFM) tip, the topography of a material can be recorded in real-time, enabling correlation with magnetic images later on. The numerous advantages of SHPM over other methods include its almost complete non-invasiveness and its suitability across a wide range of temperatures and magnetic fields. (0.3-300 Kelvin(K) and 0-7 Tesla (T), respectively), and its capacity to offer magnetic induction's z-component in quantitative maps. Photographing vortices at low temperatures in type II superconductors is made possible by the method's strong signal-to-noise ratio and reasonably good spatial resolution (>100 nm). Making use of models that GaAs/AlGaAs diameters between “0.4 µm - 0.8 µm high-resolution scanning Semiconductor 2DEG Hall probe microscopy (SHPM) Two orthogonal forms of flux structure, named Josephson vortices and pancake vortices, respectively, are generated in the crossing lattices domain of these highly anisotropic superconductors under tilted magnetic fields, according to research using Hall probe devices. (JVs and PVs)”. We see clear evidence for the formation about vortex lattice structures from H=+2.5 Oersted (Oe) gradually disappear.
In this thesis we demonstrate the power of the Gross-Pitaevskii and the time-dependent Ginzburg-Landau equations by numerically solving them for various fundamental problems related to superfluidity and superconductivity. We start by studying the motion of a massive object through a quantum fluid modelled by the Gross-Pitaevskii equation. Below a critical velocity, the object does not exchange momentum or energy with the fluid. This is a manifestation of its superfluid nature. We discuss the effect of applying a constant force to the object and show that for small forces a vortex ring is created to which the object becomes attached. For a larger force the object detaches from the vortex ring and we observe periodic shedding of rings. All energy transfered to the system is contained within the vortex rings and the drag force on the object is due to the recoil of the vortex emission. If we exceed the speed of sound, there is an additional contribution to the drag from sound emission. To make a link to superconductivity, we then discuss vortex states in a rotating system. In the ground state, regular arrays of vortices are observed which, for systems containing many vortices, mimic solid-body rotation. In the second part of the thesis, we initially review solutions to the Ginzburg-Landau equations in an applied magnetic field. For superconducting disks we observe vortex arrays similar to those in rotating superfluids. Finally, we study an electrical current flow along a superconducting wire subject to an external magnetic field. We observe the motion of flux lines, and hence dissipation, due to the Lorentz force. We measure the V - I curve which is analogous to the drag force in a superfluid. With the introduction of impurities, flux lines become pinned which gives rise to an increased critical current. (author)