A simple model for simulating the current dynamics and the magnetic properties of superconductors is presented. Short simulation times are achieved by solving the differential form of Maxwell's equations inside the sample, whereas integration is only required at the surface to meet the exact boundary conditions. The procedure reveals the time and position dependence of the current density and the magnetic induction (B) making it very convenient to apply field dependent material parameters for the simulation of magnetization loops, relaxation measurements, etc. Two examples, which are important for standard magnetometry experiments, are discussed. Firstly, we prove that evaluating the critical current density (J_c) from experiment by applying Bean's model reveals almost the exact J_c(B) behavior, if the evaluation is corrected by a simple numerical expression. Secondly, we show that the superconducting volume fraction of a sample can be directly determined from magnetization loops by carefully comparing experiment and simulation in the field range, where the current loops are differently oriented within the sample.
We report on direct, real-space imaging of the stray magnetic field above a micro-scale disc of a thin film of the high-temperature superconductor YBa$_2$Cu$_3$O$_{7-δ}$ (YBCO) using scanning single spin magnetometry. Our experiments yield a direct measurement of the sample's local London penetration depth and allow for a quantitative reconstruction of the supercurrents flowing in the sample as a result of Meissner screening. These results show the potential of scanning single spin magnetometry for studies of the nanoscale magnetic properties of thin-film superconductors, which could be readil…
The lower critical magnetic field, $H_{c1}$, of superconductors is measured by using ensembles of NV-centers-in-diamond optical magnetometry. The technique is minimally invasive, and has sub-gauss field sensitivity and sub-$μ$m spatial resolution, which allow for accurate detection of the vector field at which the vortices start penetrating the sample from the corners. Aided by the revised calculations of the effective demagnetization factors of actual cuboid - shaped samples, $H_{c1}$ and the London penetration depth, $λ$, derived from $H_{c1}$ can be obtained. We apply this method to three w…
We present muon spin rotation and relaxation (muSR) measurements as well as demagnetising field corrected magnetisation measurements on polycrystalline samples of the noncentrosymmetric superconductor BeAu. From muSR measurements in a transverse field, we determine that BeAu is a type-I superconductor with Hc = 256 Oe, amending the previous understanding of the compound as a type-II superconductor. To account for demagnetising effects in magnetisation measurements, we produce an ellipsoidal sample, for which a demagnetisation factor can be calculated. After correcting for demagnetising effects…
We present two magnetometry-based methods suitable for assessing gradients in the critical temperature and hence the composition of multifilamentary superconductors: AC magnetometry and Scanning Hall Probe Microscopy. The novelty of the former technique lies in the iterative evaluation procedure we developed, whereas the strength of the latter is the direct visualization of the temperature dependent penetration of a magnetic field into the superconductor. Using the example of a PIT Nb3Sn wire, we demonstrate the application of these techniques, and compare the respective results to each other …
Non-invasive magnetic field sensing using optically - detected magnetic resonance of nitrogen-vacancy (NV) centers in diamond was used to study spatial distribution of the magnetic induction upon penetration and expulsion of weak magnetic fields in several representative superconductors. Vector magnetic fields were measured on the surface of conventional, Pb and Nb, and unconventional, LuNi$_2$B$_2$C, Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$, Ba(Fe$_{0.93}$Co$_{0.07}$)$_2$As$_2$, and CaKFe$_4$As$_4$, superconductors, with diffraction - limited spatial resolution using variable - temperature confocal sy…
We present magnetometry and muon spin rotation ($μ$SR) measurements of the superconducting dichalcogenide Ir$_{0.95}$Pt$_{0.05}$Te$_2$. From both sets of measurements we calculate the penetration depth and thence superfluid density as a function of temperature. The temperature dependence of the superfluid densities from both sets of data indicate fully gapped superconductivity that can be fit to a conventional s-wave model and yiel fitting parameters consistent with a BCS weak coupling superconductor. We therefore see no evidence for exotic superconductivity in Ir$_{0.95}$Pt$_{0.05}$Te$_2$.
A major challenge to the chiral $p$-wave hypothesis for the pairing symmetry of the unconventional superconductor Sr$_2$RuO$_4$ is the null result of sensitive scanning magnetometry experiments designed to detect the expected spontaneous charge currents. Motivated by junction tunneling conductance measurements which indicate the quenching of superconductivity at the surfaces of even high-purity samples, we examine the spontaneous currents in a chiral $p$-wave superconductor near a normal metal / superconductor interface using the lattice Bogoliubov-de Gennes equations and Ginzburg-Landau theor…
We propose nanoscale magnetometry via isolated single-spin qubits as a probe of superconductivity in two-dimensional materials. We characterize the magnetic field noise at the qubit location, arising from current and spin fluctuations in the sample and leading to measurable polarization decay of the qubit. We show that the noise due to transverse current fluctuations studied as a function of temperature and sample-probe distance can be used to extract useful information about the transition to a superconducting phase and the pairing symmetry of the superconductor. Surprisingly, at low temperat…
Miniaturization of superconducting quantum interference devices (SQUIDs) is of major importance for the development of sensitive scanning nanoscale magnetometry tools. The high sensitivity of nanoSQUIDs is restricted, however, to only particular periodic values of the applied magnetic field, making accurate measurements at intermediate values of the field impossible. We present a theoretical investigation of a multi-terminal, multi-junction SQUID (mSQUID) that lifts this limitation by providing electrical means for a continuous shift of the quantum interference pattern with respect to the appl…
In recent years diamond magnetometers based on the nitrogen-vacancy (NV) center have been of considerable interest for magnetometry applications at the nanoscale. An interesting application which is well suited for NV centers is the study of nanoscale magnetic phenomena in superconducting materials. We employ the magnetic sensitivity of NV centers in diamond to interrogate the magnetic properties of a thin-layer yttrium barium copper oxide (YBCO) superconductor. Using fluorescence-microscopy methods and samples integrated with an NV sensor on a microchip, we measure the temperature of phase tr…
We study magnetic field penetration into a thin film made of a superconducting niobium. Imaging of magnetic field is performed by optically detecting magnetic resonances of negatively charged nitrogen-vacancy defects inside a single crystal diamond, which is attached to the niobium film under study. The experimental results are compared with theoretical predictions based on the critical state model, and good agreement is obtained.
Understanding the mechanisms behind high-$T_{c}$ Type-II superconductors (SC) is still an open task in condensed matter physics. One way to gain further insight into the microscopic mechanisms leading to superconductivity is to study the magnetic properties of the SC in detail, for example by studying the properties of vortices and their dynamics. In this work we describe a new method of wide-field imaging magnetometry using nitrogen-vacancy (NV) centers in diamond to image vortices in an yttrium barium copper oxide (YBCO) thin film. We demonstrate quantitative determination of the magnetic fi…
Magnetic texture modulated superconductivity in superconductor/ferromagnet shells of semiconductor nanowires
Stanford University（斯坦福大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）；Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所）；Universidad de Chile（智利大学）；Danish Fundamental Metrology（丹麦基础计量）；Universidad de Santiago de Chile（圣地亚哥德智利大学）
An increase of the magnetic moment in superconductor/ferromagnet (S/F) bilayers V(40nm)/F [F$=$Fe(1,3nm), Co(3nm), Ni(3nm)] was observed using SQUID magnetometry upon cooling below the superconducting transition temperature Tc in magnetic fields of 10 Oe to 50 Oe applied parallel to the sample surface. A similar increase, often called the paramagnetic Meissner effect (PME), was observed before in various superconductors and superconductor/ferromagnet systems. To explain the PME effect in the presented S/F bilayers a model based on a row of vortices located at the S/F interface is proposed. Acc…
The standard interpretation of the phase diagram of type-II superconductors was developed in 1960s and has since been considered a well-established part of classical superconductivity. However, upon closer examination a number of fundamental issues arise that leads one to question this standard picture. To address these issues we studied equilibrium properties of niobium samples near and above the upper critical field Hc2 in parallel and perpendicular magnetic fields. The samples investigated were very high quality films and single crystal discs with the Ginzburg-Landau parameters 0.8 and 1.3,…
Heterostructures consisting of a cuprate superconductor YBa2Cu3O7x and a ruthenate/manganite (SrRuO3/La0.7Sr0.3MnO3) spin valve have been studied by SQUID magnetometry, ferromagnetic resonances and neutron reflectometry. It was shown that due to the influence of magnetic proximity effect a magnetic moment is induced in the superconducting part of heterostructure and at the same time the magnetic moment is suppressed in the ferromagnetic spin valve. The experimental value of magnetization induced in the superconductor has the same order of magnitude with the calculations based on the induced ma…
We study the electrodynamics of spin triplet superconductors including dipolar interactions, which give rise to an interplay between the collective spin dynamics of the condensate and orbital Meissner screening currents. Within this theory, we identify a class of spin waves that originate from the coupled dynamics of the spin-symmetry breaking triplet order parameter and the electromagnetic field. In particular, we study magnetostatic spin wave modes that are localized to the sample surface. We show that these surface modes can be excited and detected using experimental techniques such as micr…
We present a theory of magnetic response in a finite-size two-dimensional superconductors with Rashba spin-orbit coupling. The interplay between the latter and an in-plane Zeeman field leads on the one hand to an out-of-plane spin polarization which accumulates at the edges of the sample over the superconducting coherence length, and on the other hand, to circulating supercurrents decaying away from the edge over a macroscopic scale. In a long finite stripe of width W both, the spin polarization and the currents, contribute to the total magnetic moment induced at the stripe ends. These two con…
We have fabricated arrays of High-T$_c$ Superconducting Quantum Interference Devices (SQUIDs) with randomly distributed loop sizes as sensitive antennas for Radio-Frequency (RF) waves. These sub-wavelength size devices known as Superconducting Quantum Interference Filters (SQIFs) detect the magnetic component of the electromagnetic field. We use a scalable ion irradiation technique to pattern the circuits and engineer the Josephson junctions needed to make SQUIDs. Here we report on a 300 SQUIDs series array with loops area ranging from $6$ to $60\ μm^{2}$, folded in a meander line covering a $…
The magnetic properties attributed to the hydroxide layer of Li1-xFex(OH)Fe1-ySe have been elucidated by the study of superconducting and nonsuperconducting members of this family. Both ac magnetometry and muon spin relaxation measurements of nonsuperconductors find a magnetic state existing below approximately 10 K which exhibits slow relaxation of magnetization. This magnetic state is accompanied by a low-temperature heat capacity anomaly present in both superconducting and nonsuperconducting variants suggesting that the magnetism persists into the superconducting state. The estimated value …
We investigate Josephson junctions among conventional superconducting wires, in the presence of externally applied Zeeman fields and supercurrents. We demonstrate that the critical Josephson current and the current-phase relation of the junction depends on the relative orientation of the applied Zeeman fields and supercurrents. The controllability of the Josephson current relies on the stabilization of conventional superconductivity in high magnetic fields, due to the restoration of the opposite momentum opposite spin projection resonance at the Fermi level. We assert that our results can lead…
Current-Induced Superconductor-Insulator Transition in Granular High-T_c Superconductors
在这项工作中，我们报告了一个系统的研究电流对颗粒Y $_{1-x}$ Pr $_{x}$ Ba $_{2}$ Cu $_{3}$ O $_{7-δ}$样品的超导性能的影响，x接近临界Pr浓度以上的超导性消失。结果表明，在外加电流的驱动下，超导体-绝缘体发生了量子相变（SIT），电流诱导的SIT可以看作是磁场调谐的SIT的动力学对应物.
Equilibrium magnetic properties of the mixed state in type-II superconductors were measured with high purity bulk and film niobium samples in parallel and perpendicular magnetic fields using dc magnetometry and scanning Hall-probe microscopy. Equilibrium magnetization data for the perpendicular geometry were obtained for the first time. It was found that none of the existing theories is consistent with these new data. To address this problem, a theoretical model is developed and experimentally validated. The new model describes the mixed state in an averaged limit, i.e. %without detailing the …
We demonstrate the operation of low-noise nano superconducting quantum interference devices (SQUIDs) based on the high critical field and high critical temperature superconductor YBa$_2$Cu$_3$O$_7$ (YBCO) as ultra-sensitive magnetometers for single magnetic nanoparticles (MNPs). The nanoSQUIDs exploit the Josephson behavior of YBCO grain boundaries and have been patterned by focused ion beam milling. This allows to precisely define the lateral dimensions of the SQUIDs so as to achieve large magnetic coupling between the nanoloop and individual MNPs. By means of focused electron beam induced de…
To understand the anisotropy of flux pinning and critical current density in technological superconductors, the scaling law for the anisotropy of single-vortex collective pinning in uniaxial superconductors is extended to flux-bundle collective pinning in biaxial superconductors. The scaling results show that in a system of random uncorrected point defects, the critical current density is described by a unified function with the magnetic field of the scaled isotropic superconductor. The obtained angular dependence of the critical current density depicts the main features of experimental observ…
For many technological applications of superconductors the performance of a material is determined by the highest current it can carry losslessly - the critical current. In turn, the critical current can be controlled by adding non-superconducting defects in the superconductor matrix. Here we report on systematic comparison of different local and global optimization strategies to predict optimal structures of pinning centers leading to the highest possible critical currents. We demonstrate performance of these methods for a superconductor with randomly placed spherical, elliptical, and columna…
Here we describe a three-dimensional current mapping technology developed for a superconductor using an array of Hall sensors distributed around it. We demonstrate this in a prototype similar to a conventional resistive superconducting fault current limiter (SCFCL). By calibrating the Hall sensor voltage, we can directly measure the distribution of the currents in the superconductor and the shunt. Using pulsed measurements, we measure the fractions of current distributed between the superconductor and shunt resistor parallel combination when a fault-like condition is mimicked in the system. Us…
We report on the design and operation of a transport critical-current measurement option for superconductors based on the widely used Physical Property Measurement System from Quantum Design. The system is capable of supplying transport currents up to 30 A while maintaining a sample temperature of 2.0 +/- 0.1 K, and currents up to 200 A at higher sample temperatures.
The profile of a nonlinear stationary thermomagnetic wave in the resistive state of superconductors is studied at different transport currents. It is proved that the thermomagnetic wave has an oscillating profile at relatively high values of the transport current in the sample. A shock wave with a monotonic structure corresponds to comparatively weak transport currents. The wave propagation velocity and the wave front width in a superconductor are estimated.
Correlated electron systems, particularly iron-based superconductors, are extremely sensitive to strain, which inevitably occurs in the crystal growth process. Built-in strain of this type has been proposed as a possible explanation for experiments where nematic order has been observed at high temperatures corresponding to the nominally tetragonal phase of iron-based superconductors. Strain is assumed to produce linear defect structures, e.g. dislocations, which are quite similar to O vacancy chainlets in the underdoped cuprate superconductor YBCO. Here we investigate a simple microscopic mode…
We present a perspective on a new critical-current-by-design paradigm to tailor and enhance the current-carrying capacity of applied superconductors. Critical current by design is based on large-scale simulations of vortex matter pinning in high-temperature superconductors and has qualitative and quantitative predictive powers to elucidate vortex dynamics under realistic conditions and to propose vortex pinning defects that could enhance the critical current, particularly at high magnetic fields. The simulations are validated with controlled experiments and demonstrate a powerful tool for desi…
A method is proposed for estimating the length scale of currents circulating in superconductors. The estimated circulation radius is used to determine the critical current density on the basis of magnetic measurements. The obtained formulas are applicable to samples with negligibly small demagnetizing factors and to polycrystalline superconductors. The proposed method has been verified using experimental magnetization loops measured for polycrystalline YBa$_2$Cu$_3$O$_{7-d}$ and Bi$_{1.8}$Pb$_{0.3}$Sr$_{1.9}$Ca$_2$Cu$_3$O$_x$ superconductors.
In this work, we show that a giant spin current can be injected into a nodal topological superconductor, using a normal paramagnetic lead, through a large number of zero energy Majorana fermions at the superconductor edge. The giant spin current is caused by the selective equal spin Andreev reflections (SESAR) induced by Majorana fermions. In each SESAR event, a pair of electrons with certain spin polarization are injected into the nodal topological superconductor, even though the pairing in the bulk of the nodal superconductor is spin-singlet s-wave. We further explain the origin of the spin …
