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 with a stochastic creep motion of flux bundles. NBN exists in the peak effect region, showing that long range temporal correlations are preserved in this regime.
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 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 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…
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.…
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…
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 an…
The superconductor niobium possesses a narrow, roughly half-filled energy band with Bloch functions which can be unitarily transformed into optimally localized spin-dependent Wannier functions belonging to a double-valued representation of the space group of Nb. The special symmetry of this "superconducting band" can be interpreted within a nonadiabatic extension of the Heisenberg model of magnetism. While the original Heisenberg model assumes that there is exactly one electron at each atom, the nonadiabatic model postulates that the Coulomb repulsion energy in narrow, partly filled energy ban…
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 …
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 …
We report on the observation of dendritic flux avalanches in a large Niobium single crystal. In contrast to avalanches observed in thin films, they appear only in a very narrow temperature interval of about a tenth of a Kelvin near the critical temperature of Nb. At a fixed temperature, we find two sets of dendritic structures, which differ by the magnetic field required for their formation and by the maximum distance the dendrites penetrate into the sample. The effect is caused by dendritic flux penetration into thin superconducting surface layers formed in the single crystal close to the cri…
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 …
The phase difference between the banks of an edge-type planar Josephson junction crossing the narrow thin-film strip depends on wether or not vortices are present in the junction banks. For a vortex close to the junction this effect has been seen by Golod, Rydh, and Krasnov, \prl {\bf 104}, 227003 (2010), who showed that the vortex may turn the junction into $π$-type. It is shown here that even if the vortex is far away from the junction, it still changes the 0-junction to $π$-junction when situated close to the strip edges. Within the approximation used, the latter effect is independent of th…
We study vortex current distributions in narrow thin-film superconducting strips. If one defines the vortex core ``boundary" as a curve where the current reaches the depairing value, intriguing features emerge. Our conclusions based on the London approach have only qualitative relevance since the approach breaks down near the core. Still, the main observation which might be useful is that the core size near the strip edges is smaller than in the rest of the strip. If so, the Bardeen-Stephen flux-flow resistivity should be reduced near the edges. Moreover, at elevated temperatures, when the dep…
We calculate the critical magnetic fields for vortex expulsion for an infinitely long superconducting strip, using the Ginzburg-Landau formalism. Two critical fields can be defined associated with the disappearance of either the energetic stability or metastability of vortices in the center of the strip for decreasing magnetic fields. We compare the theoretical predictions for the critical fields in the London formalism with ours and with recently published experimental results. As expected, for narrow strips our results reproduce better the experimental findings.
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…
Superconducting and normal state properties of sputtered Niobium nanofilms have been systematically investigated, as a function of film thickness in a d=9-90 nm range, on different substrates. The width of the superconducting-to-normal transition for all films remained in few tens of mK, thus remarkably narrow, confirming their high quality. We found that the superconducting critical current density exhibits a pronounced maximum, three times larger than its bulk value, for film thickness around 25 nm, marking the 3D-to-2D crossover. The extracted magnetic penetration depth shows a sizeable enh…
In framework of Ginzburg-Landau model it is shown that narrow superconducting film with width w ~ 3-8 ξ(T) (ξ(T) is a temperature dependent coherence length) exhibits unusual transport properties. In the absence of bulk pinning its critical current Ic nonmonotonically depends on perpendicular magnetic field H and has one minima (dip) and one maxima (peak) at some magnetic fields. At currents I << Ic(H) the finite magnetoresistance R(H) of such a samples due to thermo-activated vortex hopping via edge barriers also shows both local maxima(peak) and minima(dip) nearly at the same magnetic fields…
We experimentally study effect of single circular hole on the critical current $I_c$ of narrow superconducting strip with width $W$ much smaller than Pearl penetration depth $Λ$. We found nonmonotonous dependence of $I_c$ on the location of a hole across the strip and a weak dependence of $I_c$ on radius of hole has been found in case of hole with $ξ\ll R \ll W$ ($ξ$ is a superconducting coherence length) which is placed in the center of strip. The observed effects are caused by competition of two mechanisms of destruction of superconductivity - the entrance of vortex via edge of the strip and…
A vortex crossing a thin-film superconducting strip from one edge to the other, perpendicular to the bias current, is the dominant mechanism of dissipation for films of thickness d on the order of the coherence length XI; and of width w much narrower than the Pearl length LAMBDA >> w >> XI. At high bias currents, I* < I < Ic, the heat released by the crossing of a single vortex suffices to create a belt-like normal-state region across the strip, resulting in a detectable voltage pulse. Here Ic is the critical current at which the energy barrier vanishes for a single vortex crossing. The belt f…
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…
It is shown that a vortex trapped in one of the banks of a planar edge-type Josephson junction in a narrow thin-film superconducting strip can change drastically the field dependence of the junction critical current $I_c(H)$. When the vortex is trapped at certain positions in the strip middle, the pattern $I_c(H)$ has zero at $H=0$ instead of the traditional maximum of '0-type' junctions. The number of these positions is equal to the number of vortices trapped at the same location. When the junction-vortex separation exceeds approximately $2W$, $I_c(H)$ is no longer sensitive to the vortex pre…
We have fabricated ultrafast dark count-free soft X-ray single-photon detectors (X-SNSPDs) from TaN with various conduction path widths, and we compare their properties with corresponding data from a Nb X-SNSPD. The TaN X-SNSPDs offer an improved detector performance regarding device detection efficiency, latching and pulse amplitudes. Wide conduction paths allow for a certain energy-resolving capability in contrast to narrow TaN conduction paths. However, wide paths also limit the detection efficiency at low temperatures, which can be explained within a hot-spot model.
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）
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…
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…
Motivated by the on-going rotating cryostat experiments in ISSP, Univ. of Tokyo, we explore the textures and vortices in superfluid 3He-A phase confined in narrow cylinders, whose radii are R=50mum and 115mum. The calculations are based on the Ginzburg-Landau (GL) framework, which fully takes into account the orbital (l-vector) and spin (d-vector) degrees of freedom for chiral p-wave pairing superfluid. The GL free energy functional is solved numerically by using best known GL parameters appropriate for the actual experimental situations at P=3.2MPa and H=21.6mT. We identify the ground state l…
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 a new nonlocal effect in vortex matter, where an electric current confined to a small region of a long and sufficiently narrow superconducting wire causes vortex flow at distances hundreds of inter-vortex separations away. The observed remote traffic of vortices is attributed to a very efficient transfer of a local strain through the one-dimensional vortex lattice, even in the presence of disorder. We also observe mesoscopic fluctuations in the nonlocal vortex flow, which arise due to "traffic jams" when vortex arrangements do not match a local geometry of a superconducting channel.
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…
Using numerical simulations we investigate the transverse depinning of moving vortex lattices interacting with random disorder. We observe a finite transverse depinning barrier for vortex lattices that are driven with high longitudinal drives, when the vortex lattice is defect free and moving in correlated 1D channels. The transverse barrier is reduced as the longitudinal drive is decreased and defects appear in the vortex lattice, and the barrier disappears in the plastic flow regime. At the transverse depinning transition, the vortex lattice moves in a staircase pattern with a clear transver…
The results of experimental investigations of the critical currents and certain nonequilibrium phenomena in thin Sn films of different width w are analyzed. Usually, thin superconducting films are divided into two groups: narrow channels w<lambda and wide films w>lambda. A wide transitional region where the condition w>lambda holds with a large margin and at the same time cannot be explained from the standpoint of the theory of the appearance of a vortex state has been found. This shows that the generally accepted criterion w \sim lambda for dividing films into wide and narrow does not work. T…
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）
We studied the conduction noise spectrum in the vortex state of a high-temperature superconductor, Bi2Sr2CaCu2Oy, subject to a uniform driving force. Two characteristic features, a broadband noise (BBN) and a narrow-band noise (NBN), were observed in the vortex-solid phase. The origin of the large BBN was determined to be plastic motion of the vortices, whereas the NBN was found to originate from the washboard modulation of the translational velocity of the driven vortices. We believe this to be the first observation of
We use large-scale parallel simulations to compute the motion of superconducting magnetic vortices during avalanches triggered by small field increases. We find that experimentally observable voltage bursts correspond to pulsing vortex movement along branched channels or winding chains, and relate vortex flow images to features of statistical distributions. As pin density is increased, a crossover occurs from interstitial motion in narrow easy-flow winding channels with typical avalanche sizes, to pin-to-pin motion in broad channels, characterized by a very broad distribution of sizes. Our res…
Observation of individual vortex penetration in a coplanar superconducting resonator
The University of Tokyo（东京大学）；University of Connecticut（康涅狄格大学）；University of Arizona（亚利桑那大学）；Institute of Science Tokyo（东京科学大学）；National Institute for Materials Science（物质材料研究机构）
Sufficiently thin films of type-I superconductor in a perpendicular magnetic field exhibit a triangular vortex lattice, while thick films develop an intermediate state. To elucidate what happens between these two regimes, precise numerical calculations have been made within Ginzburg-Landau theory at $κ=0.5$ and 0.25 for a variety of vortex lattice structures with one flux quantum per unit cell. The phase diagram in the space of mean induction and film thickness includes a narrow wedge in which a square lattice is stable, surrounded by the domain of stability of the triangular lattice at thinne…
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…
Recent experiments on the Iron-based superconductor FeSe in a high magnetic field have suggested the presence of both the fluctuation-induced vortex liquid regime and a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) vortex lattice. To get a general picture on the magnetic phase diagram in type II superconductors with strong superconducting (SC) fluctuation and strong paramagnetic pair-breaking (PPB) such as FeSe, the vortex lattice melting curve Hm(T) is theoretically investigated in the situations where a FFLO state is expected to occur. In general, the PPB tends to narrow the vortex liquid regime i…
To investigate in-phase structures (rectangular lattice) of Josephson vortex lattice (JVL) in intrinsic Josephson junctions (IJJs) of Bi2Sr2CaCu2O8+d, we fabricated IJJs with various lateral sizes down to a size of non-linear core of Josephson vortex using focused-ion-beam etching and measured flux flow resistance (RFF) with in-plane magnetic fields (H). We have found that above a size-independent critical field, the critical current shows Fraunhofer pattern in narrow-length IJJs (0.29-2.77 mm), and then the RFF~H oscillates with H0 period. Most strikingly, such oscillations become pulse-like …
The controlled motion of objects through narrow channels is important in many fields. We have fabricated asymmetric weak-pinning channels in a superconducting thin-film strip for controlling the dynamics of vortices. The lack of pinning allows the vortices to move through the channels with the dominant interaction determined by the shape of the channel walls. We present measurements of vortex dynamics in the channels and compare these with similar measurements on a set of uniform-width channels. While the uniform-width channels exhibit a symmetric response for both directions through the chann…
The theory of current transport in a narrow superconducting channel accounting for thermal fluctuations is revisited. The value of voltage appearing in the sample is found as the function of temperature (close to transition temperature $T-T_{\mathrm{c}}$ $\ll T_{\mathrm{c}}$) and bias current $J<J_{\mathrm{c}}$ ( $J_{\mathrm{c}}$ is a value of critical current calculated in the framework of the BCS approximation, neglecting thermal fluctuations). It is shown that the careful analysis of vortex crossing of the stripe results in considerable increase of the activation energy.
In this work we report the influence of intrinsic superconducting parameters on the vortex dynamics in an overdoped Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ (x=0.14) single crystal. We find a superconducting critical temperature of 13.5 K, magnetic penetration depth $λ_{ab}$(0) = 660 $\pm$ 50 nm, coherence length $ξ_{ab}$(0) = 5 nm, and the upper critical field anisotropy $γ_{T\rightarrow Tc}$ $\approx$ 3.7. In fact, the Ginzburg-Landau model may explain the angular dependent $H_{c2}$ for this anisotropic three-dimensional superconductor. The vortex phase diagram, in comparison with the optimally doped …
