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.
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.
Using a self-devised numerical approach, we developed a powerful tool to investigate vortex properties and interactions in mean-field theories for superconductors and superfluids, based on fixing the vortex phase distribution in the energy minimization process. The method was applied to (i) multi-component Bose-Einstein condensates (BECs) and (ii) superconductors with single- or multi-component superconducting condensates. In these systems, vortex-vortex interaction and other key vortex features are analytically described only in specific regimes, that do not account for a large part of vortex behavior observed experimentally. In multi-component BECs, for example, the vortex-vortex interaction is only known for inter-vortex distances much greater than the healing length, i.e. far from the vortex core. Under our approach, by assuming multi-vortex structures, within Gross-Pitaevskii theory, we report the vortex-vortex interaction in the full range of distances, capturing the mechanism behind unusual vortex conformations previously reported in literature, such as bound clusters with two or three vortices. Usually, these clusters emerge from a competition between intra- and inter-component vortex interaction, but we demonstrate they can also emerge from the phase-frustration between the components. In superconductors, the description of vortex-vortex interaction is usually restricted to bulk or very thin films, and most of the key vortex features, such as the spatial magnetic field and current density profiles, are known only in the limit of London theory, i.e. for coherence length negligible as compared to magnetic field penetration depth and other system dimensions. The parametric range outside this limit is actually relevant to many materials. We fill that gap by applying our method to Ginzburg-Landau theory. The vortex structure is investigated for single- and two-gap bulk superconductors, outside the London regime. This enables us to extend analytical expressions describing the condensate and magnetic profiles around the vortex available in literature by numerical calculations and suitable fitting functions. We expand our approach to account for films with finite thickness, to connect our findings to both bulk and Pearl’s description by adjusting the sample thickness. This also allowed us to describe how vortex configurations change for samples with intermediate thickness, where we observe the effective magnetic response of the superconductor changing between the textbook type-1 and type-2 behaviors, in a nontrivial manner, governed by the non-monotonic vortex interaction. As a result of a detailed analysis, we propose new critical parameters to define the crossover between different regimes and establish their relation with the superconducting critical fields.
Josephson vortices play an essential role in superconducting quantum electronics devices. Often seen as purely conceptual topological objects, 2π-phase singularities, their observation and manipulation are challenging. Here we show that in Superconductor-Normal metal-Superconductor lateral junctions Josephson vortices have a peculiar magnetic fingerprint that we reveal in Magnetic Force Microscopy (MFM) experiments. Based on this discovery, we demonstrate the possibility of the Josephson vortex generation and manipulation by the magnetic tip of a MFM, thus paving a way for the remote inspection and control of individual nano-components of superconducting quantum circuits.
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.
In 1964 V. L. Ginzburg predicted that new superconducting phases could appear in ultrathin films deposited on insulating surfaces. In 2010 superconductivity below 2K was discovered in some crystalline atomic monolayers of Pb grown on atomically clean Si(111) [1,2]. In crystalline monolayers of Pb on Si(111) the superconducting condensate is an intrinsic Josephson network formed by superconducting terraces coupled by Josephson links at individual atomic steps [1]. The detailed atomic arrangement at each step decides the strength of the Josephson coupling. In a magnetic field, the superconducting vortex phase contains different kinds of vortices, ranging from Abrikosov to Josephson limits. Amorphous monolayers of Pb are non-superconducting correlated metals. Playing with geometry of in-situ grown samples enables realizing lateral SNS junctions, reveal and study Josephson proximity vortices inside their N-parts [2].When individual magnetic impurities are added, the Cooper pairs are diffused forming so-called Yu, Shiba and Rusinov (YSR) bound states. While in three-dimensional superconductors these states rapidly decay around impurities on atomic scale, superconductors with two-dimensional electronic structure such as Pb-monolayers on Si(111) or 2H-NbSe2 host YSR bound states with spatial extents orders of magnitude larger [3]. These long-range magnetic states could be used to produce new topological phases in hybrid systems such as arrays or clusters of magnetic atoms and molecules coupled through the 2D-superconducting medium.In this talk we describe a series of recent experiments which mapped superconductivity, vortices and YSR states in Pb/Si(111) and 2H-NbSe2 by scanning tunneling microscopy and spectroscopy at ultralow temperatures.[1] Ch. Brun, et al. Nature Phys. 10, 444 (2014)[2] D. Roditchev, et al. Nature Phys. 11, 332 (2015)[3] G. Ménard, et al. Nature Phys. 11, 1013 (2015)
We demonstrate a method for manipulating small ensembles of vortices in multiply connected superconducting structures. A micron-size magnetic particle attached to the tip of a silicon cantilever is used to locally apply magnetic flux through the superconducting structure. By scanning the tip over the surface of the device and by utilizing the dynamical coupling between the vortices and the cantilever, a high-resolution spatial map of the different vortex configurations is obtained. Moving the tip to a particular location in the map stabilizes a distinct multivortex configuration. Thus, the scanning of the tip over a particular trajectory in space permits nontrivial operations to be performed, such as braiding of individual vortices within a larger vortex ensemble-a key capability required by many proposals for topological quantum computing.
Superconductivity is an electronic state of matter arising from the existence of a common wave function with a coherent phase extending on a truly macroscopic scale. One major manifestation of this striking quantum phenomenon is the dissipationless transport of electrical current, an asset deserving particular attention in the present times where the efficient energy distribution has become of utmost importance. Unfortunately, the motion of quantum units of magnetic flux (so-called vortices or fluxons), which is an unavoidable side-effect found in superconductors in the presence of transport currents and magnetic fields, severely limits the conditions to preserve dissipationless transport. This poses a challenge for achieving the functionalization of superconducting materials and threatens their spectrum of applications. It is widely known that any inhomogeneities (either material imperfections, or ones made artificially), which locally suppress superconductivity on the scale comparable to the core of the vortex, can pin the vortex and delay the onset of the vortex motion to higher applied currents. In recent years a substantial effort has been made to minimize the effects of current-induced vortex motion by tailoring arrays of artificial pinning centers. Besides improving the critical parameters of the superconducting state, a pinning matrix can be used for the manipulation of vortex matter, thus directly affecting the vortex dynamics, such as rectification of vortex motion under an ac drive (vortex diode) by introducing asymmetric pinning landscapes. In the literature one can find that the realization of the anchoring of the vortices can be based on nanostructured arrays of perforations, chemically grown defects, permanent nanomagnets, or even pinning sites produced by heavy ion bombardment. All of those realizations are based on a permanent imprint on the superconductor, without any possibility for subsequent modifications in the distribution and strength of the pinning. The principal objective of this thesis is to investigate the dynamical behavior of vortex matter under an entirely new kind of pinning landscape consisting of spatial and temporal modulation of the superconducting condensate. A particular case of spatial modulation is considered in a constricted structure where current lensing can cause extremely high vortex velocities. Subsequently, a time-dependent thermal potential introduced to the superconducting condensate will cause stroboscopic resonances during the vortex motion - a phenomenon that cannot be observed in the systems with static pinning imprints. Finally, a study of electronic gating is presented, where the local properties of superconductor, such as mean free path, or electronic band structure in general, can be influenced electronically. This is a completely unexplored interdisciplinary research topic, which will eventually allow one to manipulate individual vortices in superconducting materials by means of spatially confined and temporally controlled thermal and electromagnetic excitations. Furthermore, such techniques can provide one fundamental insight in different states of the vortex matter with respect to variation of the transport current, highly relevant for understanding the resistive state of superconducting materials and their applications.