The morphology of the superconducting flux line lattice (FLL) of Nb comprises gradual variations with various lock-in transitions and symmetry breaking rotations. We report a comprehensive small-angle neutron scattering study of the FLL in an ultra-pure single crystal of Nb as a function of the orientation of the applied magnetic field. We attribute the general morphology of the FLL and its orientation to three dominant mechanisms. First, non-local contributions, second, the transition between open and closed Fermi surface sheets and, third, the intermediate mixed state between the Meissner and the Shubnikov phase.
Superconducting vortex lattices, glasses and liquids attract great interest as model systems of crystallization and as a source of microscopic information of the nature of superconductivity. We report for the first time direct microscopic measurements of the vortex lattice tilt modulus c44 in ultra-pure niobium using time-resolved small angle neutron scattering. Besides a general trend to faster vortex lattice dynamics for increasing temperatures we observe a dramatic changeover of the relaxation process associated with the non-trivial vortex lattice morphology in the intermediate mixed state.…
We investigated the Abrikosov vortex lattice (VL) of a pure Niobium single crystal with the muon spin rotation (μSR) technique. Analysis of the μSR data in the framework of the BCS-Gor'kov theory allowed us to determine microscopic parameters and the limitations of the theory. With decreasing temperature the field variation around the vortex cores deviates substantially from the predictions of the Ginzburg-Landau theory and adopts a pronounced conical shape. This is evidence of partial diffraction of Cooper pairs on the VL predicted by Delrieu for clean superconductors.
We report measurements of voltage noise due to vortex motion in Niobium, a conventional low-Tc superconductor. A coherent oscillation leading to narrow band noise (NBN) is evidenced. Its characteristic frequency is a linear function of the overcritical transport current in the flux-flow regime, and hence scales as the main velocity of the vortex flow. The associated length scale is not the intervortex distance but the width of the sample, indicating temporal coherence at a large scale. NBN is also observed in the non linear part of the V(I) at the onset of depinning, in apparent disagreement w…
We have investigated the intermediate mixed state of a superconducting niobium sample by Very Small Angle Neutron Scattering.We show that this state is stabilized through a sequence where a regular vortex lattice appears, which then coexists with vortex clusters before vanishing at low temperature. Vortices in clusters have a constant periodicity regardless of the applied field, exhibit a temperature dependence close to the one of the penetration depth. The clusters disappear in the high temperature limit. All the results agree with an explanation in terms of vortex attraction due non local ef…
In 1993 Tang proposed [1] that vortex avalanches should produce a self organized critical state in superconductors, but conclusive evidence for this has heretofore been lacking. In the present paper, we report extensive micro-Hall probe data from the vortex dynamics in superconducting niobium, where a broad distribution of avalanche sizes scaling as a power-law for more than two decades is found. The measurements are combined with magneto-optical imaging, and show that over a widely varying magnetic landscape the scaling behaviour does not change, hence establishing that the dynamics of superc…
In the intermediate mixed state (IMS) of type-II/1 superconductors, vortex lattice (VL) and Meissner state domains coexist due to a partially attractive vortex interaction. Using a neutron-based multiscale approach combined with magnetization measurements, we study the continuous decomposition of a homogeneous VL into increasingly dense domains in the IMS in bulk niobium samples of varying purity. We find a universal temperature dependence of the vortex spacing, closely related to the London penetration depth and independent of the external magnetic field. The rearrangement of vortices occurs …
The field distribution in the vortex lattice of a pure niobium single crystal with an external field applied along a three-fold axis has been investigated by the transverse-field muon-spin-rotation (TF-$μ$SR) technique over a wide range of temperatures and fields. The experimental data have been analyzed with the Delrieu's solution for the form factor supplemented by phenomenological formulas for the parameters. This has enabled us to experimentally establish the temperatures and fields for the Delrieu's, Ginzburg-Landau's, and Klein's regions of the vortex lattice. Using the numerical solutio…
Recent experiments [I.V. Grigorieva et al., Phys. Rev. Lett. 96, 077005 (2006)] on visualization of vortices using the Bitter decoration technique revealed vortex shells in mesoscopic superconducting Nb disks containing up to L=40 vortices. Some of the found configurations did not agree with those predicted theoretically. We show here that this discrepancy can be traced back to the larger disks with radii R ~ 1 to 2.5μm, i.e., R ~ 50-100ξ(0) used in the experiment, while in previous theoretical studies vortex states with vorticity L < 40 were analyzed for smaller disks with R ~ 5-20ξ(0). The p…
We describe an experimental protocol to characterize magnetic field dependent microwave losses in superconducting niobium microstrip resonators. Our approach provides a unified view that covers two well-known magnetic field dependent loss mechanisms: quasiparticle generation and vortex motion. We find that quasiparticle generation is the dominant loss mechanism for parallel magnetic fields. For perpendicular fields, the dominant loss mechanism is vortex motion or switches from quasiparticle generation to vortex motion, depending on cooling procedures. In particular, we introduce a plot of the …
The experimental investigation of the $I_c(B)$--$T_c(B)$ phase boundary of superconducting niobium films with large area quasihexagonal hole arrays is reported. The hole arrays were patterned with microsphere photolithography. We investigate the perforated niobium films by means of electrical directed current transport measurements close to the transition temperature $T_c$ in perpendicularly applied magnetic fields. We find pronounced modulations of the critcal current with applied magnetic field, which we interpret as a consequence of commensurable states between the Abrikosov vortex lattice …
Microscopic structure of the vortex cores in granular niobium: A coherent quantum puzzle
LPEM, UMR-8213, ESPCI Paris, PSL, CNRS, Sorbonne University（巴黎高等物理化工学院）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；HSE University（俄罗斯国立高等经济大学）；Lobachevsky State University of Nizhny Novgorod（下诺夫哥罗德罗巴切夫斯基州立大学）；Institute for Physics of Microstructures RAS（俄罗斯科学院微结构物理研究所）；Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University（莫斯科国立大学索别尔茨因核物理研究所）；Institut des Nanosciences de Paris, UMR-7588, Sorbonne University, CNRS（巴黎纳米科学研究所）
Analogous to the various states of condensed matter exhibiting crystalline, amorphous, liquid and spatially inhomogeneous phases, such structures are likewise observed in superconducting vortex matter.
We report on a combined structural and electronic analysis of niobium ultrathin films (from 2 to 10 nm) deposited in ultra-high vacuum on atomically flat R-plane sapphire wafers. A textured polycrystalline morphology is observed for the thinnest films showing that hetero-epitaxy is not achieved under a thickness of 3.3nm, which almost coincides with the first measurement of a superconducting state. The superconducting critical temperature rise takes place on a very narrow thickness range, of the order of a single monolayer (ML). The thinnest superconducting sample (3 nm/9ML) has an offset crit…
We experimentally investigate the vortex induced energy losses in niobium coplanar waveguide resonators with and without quasihexagonal arrays of nanoholes (antidots), where large-area antidot patterns have been fabricated using self-assembling microsphere lithography. We perform transmission spectroscopy experiments around 6.25 and 12.5 GHz in magnetic field cooling and zero field cooling procedures with perpendicular magnetic fields up to B=27 mT at a temperature T=4.2 K. We find that the introduction of antidot arrays into resonators reduces vortex induced losses by more than one order of m…
The transport critical current of a Niobium (Nb) thick film has been measured for a large range of magnetic field. Its value and variation are quantitatively described in the framework of the pinning of vortices due to boundary conditions at the rough surface, with a contact angle well explained by the spectral analysis of the surface roughness. Increasing the surface roughness using a Focused Ion Beam results also in an increase of the superficial critical current.
The state of the vortex lattice extremely close to the superconducting to normal transition in an applied magnetic field is investigated in high purity niobium. We observe that thermal fluctuations of the order parameter broaden the superconducting to normal transition into a crossover but no sign of a first order vortex lattice melting transition is detected in measurements of the heat capacity or the small angle neutron scattering (SANS) intensity. Direct observation of the vortices via SANS always finds a well ordered vortex lattice. The fluctuation broadening is considered in terms of the …
In magnetic fields applied within the angular range of the surface superconductivity state a magnetically anisotropic layered medium is created in structurally isotropic, sufficiently thick niobium films. Surface (Kulik) vortices residing in the superconducting sheaths on both main film surfaces in tilted fields are shown to undergo a decoupling transition from a coherent to an independent behavior, similar to the behavior observed for Giaever transformer. At the transition a feature in pinning properties is measured, which implies different pinning for the lattice of surface vortices coherent…
Superconducting films in perpendicular magnetic field are found to rectify alternating currents. The effect has been observed both in plain and nanostructured superconducting films (niobium and lead). The rectified voltage appears both along and transverse to alternating current and strongly depends on the magnetic field. Rectification phenomena is based on the property of superconductors to have permanent circulating currents in magnetic field (vortices) and to develop electric fields at high enough currents. In contrast to previous findings, at higher current frequencies no asymmetric pinnin…
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 …
Here we report a novel nitridation technique for transforming niobium into hexagonal Nb2N which appears to be superconducting below 1K. The nitridation is achieved by high temperature annealing of Nb films grown on Si3N4/Si (100) substrate under high vacuum. The structural characterization directs the formation of a majority Nb2N phase while the morphology shows granular nature of the films. The temperature dependent resistance measurements reveal a wide metal-to-superconductor transition featuring two distinct transition regions. The region close to the normal state varies strongly with the f…
In this paper, we describe the vortex dynamics under high-amplitude microwave drive and its effect on the surface resistance of superconductors. The vortex surface resistance is calculated with a Montecarlo approach, where the vortex motion equation is solved for a collection of vortex flux lines each oscillating within a random pinning landscape. This approach is capable of providing a detailed description of the microscopic vortex dynamics and in turn important insights into the microwave field amplitude dependence of the vortex surface resistance. The numerical simulations are compared agai…
The superconducting transition region in a Nb disk showing the paramagnetic Meissner effect (PME) has been investigated in detail. From the field-cooled magnetization behavior, two well-defined temperatures can be associated with the appearance of the PME: T_1 (< T_c) indicates the characteristic temperature where the paramagnetic moment first appears and a lower temperature T_p (< T_1) defines the temperature where the positive moment no longer increases. During the subsequent warming, the paramagnetic moment begins to decrease at T_p and then vanishes at T_1 with the magnitude of the magneti…
We report measurements and analysis of the voltage noise due the to vortex motion, performed in superconducting Niobium micro-bridges. Noise in such small systems exhibits important changes from the behavior commonly reported in macroscopic samples. In the low biasing current regime, the voltage fluctuations are shown to deviate substantially from the Gaussian behavior which is systematically observed at higher currents in the so called flux-flow regime. The responsibility of the spatial inhomogeneities of the critical current in this deviation from Gaussian behavior is emphasized. We also rep…
We report on critical currents and voltage noise measurements in Niobium strips in the superconducting state, in the presence of a bulk vortex lattice ($B < B_{C2}$) and in the surface superconducting state ($B_{c2}< B < B_{C3}$). For homogeneous surfaces, the correlation length of the current fluctuations can be associated with the electromagnetic skin depth of vortex superficial instabilities. The modification of the surface state by means of low energy irradiation induces a strong modification of the critical current and of the noise. The appearance of a corner frequency in the spectral dom…
We report small-angle neutron scattering measurements of the vortex lattice (VL) structure in single crystals of the lightly underdoped cuprate superconductor YBa2Cu3O6.85. At 2 K, and for fields of up to 16 T applied parallel to the crystal c-axis, we observe a sequence of field-driven and first-order transitions between different VL structures. By rotating the field away from the c-axis, we observe each structure transition to shift to either higher or lower field dependent on whether the field is rotated towards the [100] or [010] direction. We use this latter observation to argue that the …
Vortex-driven superconducting diode effect in asymmetric multilayer heterostructures
Institute for Advanced Study in Physics, Zhejiang University（浙江大学物理高等研究院）；Zhejiang Key Laboratory of Micro-Nano Quantum Chips and Quantum Control, School of Physics, Zhejiang University（浙江大学物理学院微纳量子芯片与量子控制浙江省重点实验室）；International Quantum Academy, Shenzhen（深圳国际量子研究院）；Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学先进微结构协同创新中心）
Small-angle neutron scattering is used in combination with transport measurements to investigate the current-induced effects on the morphology of the intermediate mixed state domains in the intertype superconductor niobium. We report the robust self-organisation of the vortex lattice domains to elongated parallel stripes perpendicular to the applied current in a steady-state. The experimental results for the formation of the superstructure are supported by theoretical calculations, which highlight important details of the vortex matter evolution. The investigation demonstrates a mechanism of a…
Magnetic flux trapped during the cooldown of superconducting radio-frequency cavities through the transition temperature due to incomplete Meissner state is known to be a significant source of radio-frequency losses. The sensitivity of flux trapping depends on the distribution and the type of defects and impurities which pin vortices, as well as the cooldown dynamics when the cavity transitions from a normal to superconducting state. Here we present the results of measurements of the flux trapping sensitivity on 1.3 GHz elliptical cavities made from large-grain niobium with different purity fo…
In this work we study the effect of engineered disorder on the local magnetic response of proximity coupled superconducting island arrays by comparing scanning Superconducting Quantum Interference Device (SQUID) susceptibility measurements to a model in which we treat the system as a network of one-dimensional (1D) superconductor-normal metal-superconductor (SNS) Josephson junctions, each with a Josephson coupling energy $E_J$ determined by the junction length or distance between islands. We find that the disordered arrays exhibit a spatially inhomogeneous diamagnetic response which, for low l…
To identify the contributions of the multiband nature and the anisotropy of a microscopic electronic structure to a macroscopic vortex lattice morphology, we develop a method based on the Eilenberger theory near Hc2 combined with the first-principles band calculation to estimate the stable vortex lattice configuration. For a typical two-band superconductor MgB2, successive transitions of vortex lattice orientation that have been observed recently by small angle neutron scattering [Das, et al.: Phys. Rev. Lett. 108 (2012) 167001] are explained by the characteristic field-dependence of twoband s…
Small angle neutron scattering (SANS) is an historical technique to study the flux lines lattice (FLL) in a superconductor. Structural characteristics of the FLL can be revealed, providing fundamental information for the physics of vortex lattice. However, the spatial resolution is limited and all the correlation lengths of order are difficult to extract with precision. We show here that a time of flight technique reveals the Bragg peak of the FLL, and also its translational order with a better resolution. We discuss the implication of these results for pinning mechanisms in a Niobium sample.
Equidistant resonance jumps in superconducting coplanar resonators driven by Abrikosov vortices
Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Institute for Physics of Microstructures, Russian Academy of Sciences（俄罗斯科学院微结构物理研究所）；Dukhov Research Institute of Automatics (VNIIA)（杜霍夫自动仪器科学研究院）
The flux flow properties of epitaxial niobium films with different pinning strengths are investigated by dc electrical resistance measurements and mapped to results derived within the framework of a theoretical model. Investigated are the cases of weak random pinning in as-grown films, strong random pinning in Ga ion-irradiated films, and strong periodic pinning induced by a nanogroove array milled by focused ion beam. The generic feature of the current-voltage curves of the films consists in instability jumps to the normal state at some instability current density $j^\ast$ as the vortex latti…
Tuning Bound States of Symmetry-Breaking Vortices via Unidirectional Charge Density Wave in a Transition-Metal Dichalcogenide Superconductor
Beijing National Center for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Hefei National Laboratory（合肥国家实验室）
Superconductor/Ferromagnet (S/F) hybrid systems show interesting magneto-transport behaviors that result from the transfer of properties between both constituents. For instance, magnetic memory can be transferred from the F into the S through the pinning of superconducting vortices by the ferromagnetic textures. The ability to tailor this type of induced behavior is important to broaden its range of applications. Here we show that engineering the F magnetization reversal allows tuning the strength of the vortex pinning (and memory) effects, as well as the field range in which they appear. This…
The defect-rich morphology of YBa$_{2}$Cu$_{3}$O$_{7-δ}$ (YBCO) thin films leads to a glass-like arrangement of Abrikosov vortices which causes the resistance to disappear in vanishing current densities. This vortex glass consists of entangled vortex lines and is identified by a characteristic scaling of the voltage-current isotherms. Randomly distributed columnar defects stratify the vortex lines and lead to a Bose glass. Here, we report on the observation of an ordered Bose glass in a YBCO thin film with a hexagonal array of columnar defects with 30 nm spacings. The periodic pinning landscap…
Thin films of the high-temperature superconductor HgBa$_2$CaCu$_2$O$_{6+δ}$ have been prepared on SrTiO$_3$ substrates by pulsed-laser deposition of precursor films and subsequent annealing in mercury-vapor atmosphere. The microstructural properties of such films can vary considerably and have been analyzed by x-ray diffraction and atomic force microscopy. Whereas the resistivity is significantly enhanced in samples with coarse-grained structure, the Hall effect shows little variation. This disparity is discussed based on models for transport properties in granular materials. We find that, des…
Current-voltage measurements of type-II superconductors are described by a coarse-grained model of superconducting vortex dynamics. We find that the power spectra of the voltage fluctuations, and the noise power, are related to the large scale morphology of the plastic flux flow. At currents corresponding to the peak in differential resistance, the flux flow forms a braided river, the noise power is maximal, and the power spectra has a 1/f^α form with α\approx 1.8 over a wide frequency range. This agrees with recent experiments on NbSe_2. The observed variation of αwith applied current is a cr…
Microwave Signature of the Emerging Abrikosov Lattice Above $H_{c2}$
Xiamen University（厦门大学）；CNR-SPIN（意大利国家研究委员会自旋物理研究所）；Argonne National Laboratory（阿贡国家实验室）；Northern Illinois University（北伊利诺伊大学）；Istituto di Struttura della Materia of the National Research Council（意大利国家研究委员会物质结构研究所）
The fabrication of high-quality thin superconducting films is essential for single-photon detectors. Their device performance is crucially affected by their material parameters, thus requiring reliable and nondestructive characterization methods after the fabrication and patterning processes. Important material parameters to know are the resistivity, superconducting transition temperature, relaxation time of quasiparticles, and uniformity of patterned wires. In this work, we characterize micro-patterned thin NbN films by using transport measurements in magnetic fields. We show that from the in…
