Vortex studies in superconducting Ba(Fe0.93Co0.07)2As2
M. R. Eskildsen, L. Ya. Vinnikov, T. D. Blasius, I. S. Veshchunov, T. M. Artemova, J. M. Densmore, C. D. Dewhurst, N. Ni, A. Kreyssig, S. L. Bud'ko, P. C. Canfield, A. I. Goldman
We present small-angle neutron scattering (SANS) and Bitter decoration studies of the superconducting vortices in Ba(Fe$_{0.93}$Co$_{0.07}$)$_2$As$_2$}. A highly disordered vortex configuration is observed at all measured fields, and is attributed to strong pinning. This conclusion is supported by the absence of a Meissner rim in decoration images obtained close to the sample edge. The field dependence of the magnitude of the SANS scattering vector indicates vortex lattice domains of (distorted) hexagonal symmetry, consistent with the decoration images which show primarily 6-fold coordinated vortex domains. An analysis of the scattered intensity shows that this decreases much more rapidly than expected from estimates of the upper critical field, consistent with the large degree of disorder.
Small-angle neutron scattering on high quality single crystalline Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ reveals the transition from a low--field vortex solid phase with orientational order to a vortex polycrystal at high magnetic field. The vortex order-disorder transition is correlated with the second-peak feature in isothermal hysteresis loops, and is interpreted in terms of the generation of supplementary vortex solid dislocations. The sharp drop of the structure factor above the second peak field is explained by the dynamics of freezing of the vortex ensemble in the high field phase.
We investigate the superconducting behaviour of Bi doped Pb. Pure lead shows type-I behaviour entering an intermediate state in a magnetic field. High dopings of Bi ($>$3%) lead to type-II behaviour showing a mixed state, where the magnetic field penetrates the superconductor in the form of a flux lattice. At intermediate doping, the sample shows both type-I and type-II behaviour depending on the temperature. This arises because the Ginzburg-Landau parameter $κ$ passes through its critical value of $1/\sqrt{2}$ with temperature.
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 …
The vortex matter in bulk type-II superconductors serves as a prototype system for studying the random pinning problem in condensed matter physics. Since the vortex lattice is embedded in an atomic lattice, small angle neutron scattering (SANS) is the only technique that allows for direct structural studies. In traditional SANS methods, the scattering intensity is a measure of the structure factor averaged over the entire sample. Recent studies in vortex physics have shown that it is highly desirable to develop a SANS technique which is capable of resolving the spatial inhomogeneities in the b…
Solving numerically the 3D non linear Ginzburg-Landau (GL) equations, we study equilibrium and nonequilibrium phase transitions between different superconducting states of mesoscopic disks which are thinner than the coherence length and the penetration depth. We have found a smooth transition from a multi-vortex superconducting state to a giant vortex state with increasing both the disk thickness and the magnetic field. A vortex phase diagram is obtained which shows, as function of the magnetic field, a re-entrant behavior between the multi-vortex and the giant vortex state.
Nb/Cu superconducting superlattices have been fabricated by dc magnetron sputtering. This system shows a vortex glass transition with critical exponents similar to high temperatures superconductors exponents. The transition dymensionality is governed by the superconducting coupling regime. The vortex glass transition shows a pure two dimensional behavior in decoupled superlattices and a quasi-two dimensional behavior in the superlattice coupling regime.
We consider a type-II superconducting thin film in contact with a Néel skyrmion. The skyrmion induces spontaneous currents in the superconducting layer, which under the right condition generate a superconducting vortex in the absence of an external magnetic field. We compute the magnetic field and current distributions in the superconducting layer in the presence of Néel skyrmion.
The vortex structure in superconducting stripe states is studied according to the Bogoliubov-de Gennes theory on the two-dimensional Hubbard model with nearest-neighbor sites pairing interaction. The vortex is trapped at the outside region of the stripe line, where the superconductivity is weak. The superconducting coherence length along the stripe direction becomes long. There are no eminent low-energy electronic states even near the vortex core. These characters resemble the Josephson vortex in layered superconductors under a parallel field.
Within the non-linear Ginzburg-Landau (GL) theory, we investigate the vortex structure in a superconducting thin film with a ferromagnetic disk on top of it. Antivortices are stabilized in shells around a central core of vortices (or a giant-vortex) with size-magnetization controlled ``magic numbers''. An equilibrium vortex phase diagram is constructed. The transition between the different vortex phases occurs through the creation of a vortex-antivortex pair under the magnetic disk edge.
We numerically show that a vortex pinning occurs in superconducting quasicrystal without impurities and defects. This vortex pinning is intrinsic since the superconducting order parameter in quasicrystal is always inhomogeneous due to the lack of the translational symmetry. We propose that experiments influenced by vortex pinning effects can detect the atomic-scale inhomogeneous superconducting order parameter in quasicrystals. We develop a numerical method to solve the Bogoliubov-de Gennes equations and gap equations in large systems, which is based on the localized-Krylov subspace and a spar…
A thermodynamically stable vortex-antivortex pattern has been revealed in mesoscopic type I superconducting triangles, contrary to type II superconductors where similar patterns are unstable. The stable vortex-antivortex "molecule" appears due to the interplay between two factors: a repulsive vortex-antivortex interaction in type I superconductors and the vortex confinement in the triangle.
A controlled local enhancement of superconductivity yields unexpected modifications in the vortex dynamics. This local enhancement has been achieved by designing an array of superconducting Nb nanostructures embedded in a V superconducting film. The most remarkable findings are: i) vanishing of the main commensurability effect between the vortex lattice and the array unit cell, ii) hysteretic behavior in the vortex dynamics, iii) broadening of the vortex liquid phase and iv) strong softening of the vortex lattice. These effects can be controlled and they can be quenched by reducing the Nb arra…
We report on the observation of the rearrangement of vortices in the ns time scale following a fast magnetic field variation due to selective local heating of a high Tc superconducting film. Detailed simulations describing the measured photoinduced voltage signals along the film lead to a better understanding of vortex dynamics in fast regimes, where mean vortex velocities reach 10000 m/s
The small size vortex-antivortex pairs proliferation in type II superconducting film is considered for the wide interval of temperatures below Tc. The corresponding contribution to free energy is calculated. It is shown that these fluctuations give the main contribution to the heat capacity of the film both at low temperatures and in the vicinity of transition.
The vortex electronic structure in the multiband superconductor NbSe2 is studied by means of Scanning Tunneling Spectroscopy (STS) using a superconducting tip. The use of a superconducting tip (Pb) as a probe provides an enhancement of the different features related to the DOS of NbSe2 in the tunneling conductance curves. This use allows the observation of rich patterns of electronic states in the conductance images around the vortex cores in a wide range of temperature, as well as the simultaneous acquisition of Josephson current images in the vortex state.
The vortex-state electrodynamics of s-wave superconductors has been studied by infrared spectroscopy. Far-infrared transmission and reflection spectra of superconducting NbTiN and NbN thin films were measured in a magnetic field perpendicular to the film surface, and the optical conductivity was extracted. The data show clear reduction of superconducting signature. We consider the vortex state as a two-component effective medium of normal cores embedded in a BCS superconductor. The spectral features are well explained by the Maxwell-Garnett theory. Our analysis supports the presence of magneti…
The transitions between the different vortex states of thin mesoscopic superconducting disks and rings are studied using the non-linear Ginzburg-Landau functional. They are saddle points of the free energy representing the energy barrier which has to be overcome for transition between the different vortex states. In small superconducting disks and rings the saddle point state between two giant vortex states, and in larger systems the saddle point state between a multivortex state and a giant vortex state and between two multivortex states is obtained. The shape and the height of the nucleation…
Strong pinning of superconducting flux quanta by a square array of 1 $μ$m-sized ferromagnetic dots in a magnetic-vortex state was visualized by low-temperature magnetic force microscopy (LT-MFM). A direct correlation of the superconducting flux lines with the positions of the dots was derived. The force that the MFM tip exerts on the individual vortex in the depinning process was used to estimate the spatial modulation of the pinning potential. It was found, that the superconducting vortices which are preferably located on top of the Py dots experience about 15 times stronger pinning forces as…
We analyze theoretically and experimentally vortex configurations in mesoscopic superconducting squares. Our theoretical approach is based on the analytical solution of the London equation using Green's-function method. The potential-energy landscape found for each vortex configuration is then used in Langevin-type molecular-dynamics simulations to obtain stable vortex configurations. Metastable states and transitions between them and the ground state are analyzed. We present our results of the first direct visualization of vortex patterns in micrometer-sized Nb squares, using the Bitter decor…
The electronic nematic phase is characterized as an ordered state of matter with rotational symmetry breaking, and has been well studied in the quantum Hall system and the high-$T_c$ superconductors, regardless of cuprate or pnictide family. The nematic state in high-$T_c$ systems often relates to the structural transition or electronic instability in the normal phase. Nevertheless, the electronic states below the superconducting transition temperature is still an open question. With high-resolution scanning tunneling microscope measurements, direct observation of vortex core in FeSe thin film…
The properties of vortices in superconducting thin films are revisited. The interaction between two Pearl vortices in an infinite film is approximated at all distances by a simple expression. The interaction of a vortex with a regular lattice of real or image vortices is given. The two spring constants are calculated that one vortex in the vortex lattice feels when the surrounding vortices are rigidly pinned or are free. The modification of these London results by the finite size of real films is obtained. In finite films, the interaction force between two vortices is not a central force but d…
We show that standard impurities, magnetic or nonmagnetic, weak or strong, can cause topological phase transitions inside the vortex cores of a conventional s-wave superconductor. Because of the nonzero angular momentum of Cooper pairs in the vortex cores, the vortex bound states in a two dimensional superconductor are sensitive to impurities in a way similar to the Yu-Shiba-Rusinov bound states induced by magnetic impurities. In three dimensional cases, the vortex bound states can be driven into topologically nontrivial phases by an impurity chain inside the vortex core. The system can host M…
Vortex dynamics in superconductors have received a great deal of attention from both fundamental and applied researchers over the past few decades. Because of its critical role in the energy relaxation process of type II superconductors, vortex dynamics have been deemed a key factor for the emerging superconducting devices, but the effect of irradiation on vortex dynamics remains unclear. With the support of electrical transport measurements under external magnetic fields and irradiation, photon effect on vortex dynamics in amorphous MoSi (a MoSi) superconducting thin films are investigated in…
The interaction between a straight vortex line in a superconducting film and a soft magnetic nanodisk in the magnetic vortex state in the presence of a magnetic field applied parallel to the film surfaces is studied theoretically. The superconductor is described by London theory and the nanodisk by the Landau-Lifshitz continuum theory of magnetism, using the approximation known as the rigid vortex model. Pinning of the vortex line by the nanodisk is found to result, predominantly, from the interaction between the vortex line and the changes in the nanodisk magnetization induced by the magnetic…
It is shown that coherent scatterings by an ordered vortex lattice are critically enhanced for quasi particles moving in cyclotron orbits on the Fermi surface through vortex core regions, thus generating significant quasi-periodic oscillating contributions to the SC free energy as a function of the inverse magnetic field. The mean frequency of the oscillation provides a fingerprint of the vortex lattice geometry. Vortex-lattice disorder, tends to suppress this oscillatory component.
The dependence of the vortex penetration and expulsion on the geometry of mesoscopic superconductors is reported. Hall magnetometry measurements were performed on a superconducting Al square and triangle. The stability of the vortex patterns imposed by the sample geometry is discussed. The field-temperature $H-T$ diagram has been reconstructed showing the transitions between states with different vorticity. We have found that the vortex penetration is only weakly affected by the vortex configuration inside the sample while the expulsion is strongly controlled by the stability of the vortex pat…
In a superconducting topological insulator, superconducting vortex line may trap 1-dimensional topological band with Majorana zero modes (MZMs) localized at its ends. In this work, we study the effect of hexagonal warping to the vortex phase transition. We carry out both analytical calculations based on a semiclassical formula and numerical calculations based on full quantum mechanics of Bogliubov de Gennes equation. We find that the hexagonal warping term enlarges the topological region of the vortex line as the chemical potential changes, and leads to the MZMs even in the absence of topologi…
The discrete shell structure of vortex matter strongly influences the flux dynamics in mesoscopic superconducting Corbino disks. While the dynamical behavior is well understood in large and in very small disks, in the intermediate-size regime it occurs to be much more complex and unusual, due to (in)commensurability between the vortex shells. We demonstrate unconventional vortex dynamics (inversion of shell velocities with respect to the gradient driving force) and angular melting (propagating from the boundary where the shear stress is minimum, towards the center) in mesoscopic Corbino disks.
Recently, Aji and Goldenfeldt [Phys. Rev. Lett. 87, 197003 (2001), cond-mat/0105622] put forward an explanation for the value of the dynamic critical exponent z observed in certain Monte Carlo simulations of the superconducting phase transition in zero magnetic field. In this Comment, we point out that their analysis is based on incorrect assumptions regarding the scaling dimension of the vortex density.
In submicron superconducting squares in a homogeneous magnetic field, Ginzburg-Landau theory may admit solutions of the vortex-antivortex type, conforming with the symmetry of the sample [Chibotaru et al., Nature 408, 833 (2000)]. Here we show that these fascinating, but never experimentally observed states, can be enforced by artificial fourfold pinning, with their diagnostic features enhanced by orders of magnitude. The second-order nucleation of vortex-antivortex molecules can be driven either by temperature or applied magnetic field, with stable asymmetric vortex-antivortex equilibria foun…
Vortex trapping is investigated in thin-film strips of superconducting material. We present a model for the critical field above which vortex trapping occurs in these strips. This model includes the pairing energy of vortex-antivortex pairs in addition to the energy of single vortices. Experimental verification of the model with a scanning SQUID microscope shows very good agreement between the model and experiments on YBa2Cu3O7-delta and Nb strips. Statistical analysis of the vortex distribution in the strips above the critical field has been performed and a comparison has been made between Nb…
We study the differential resistivity transition of two-dimensional superconducting arrays induced by an external driving current, in the presence of thermal fluctuations and a magnetic field corresponding to $f$ flux quantum per plaquette. Recent experiments have identified this transition as a dynamic vortex Mott insulator transition at vortex densities near rational values of $f$. The critical behavior is determined from a scaling analysis of the current-voltage relation near the transition, obtained by Monte Carlo simulations of a Josephson-junction array model in the vortex representation…
Effects of the strong Pauli-paramagnetic pair-breaking (PPB) on the vortex lattice in d-wave superconductors are theoretically studied by putting emphasis on consequences of the PPB-induced antiferromagnetic (AFM) ordering in the spatial modulation in the vortex lattice. It is shown that the PPB-induced AFM fluctuation in the superconducting state leads to an enhancement of the vortex lattice form factor which is a measure of spatial variations of the internal magnetic field and that the enhancement becomes more remarkable as an AFM instability is approached. It is also demonstrated that the P…
We report Small-Angle Neutron Scattering (SANS) measurements on the vortex lattice in a PbIn polycrystal in the presence of an applied current. Using the rocking curves as a probe of the distribution of current in the sample, we observe that vortex pinning is due to the surface roughness. This leads to a surface current that persists in the flux flow region. We show the influence of surface treatments on the distribution of this current.
Bogoliubov-de Gennes theory is used to investigate the effect of the size of a superconducting square on the vortex states in the quantum confinement regime. When the superconducting coherence length is comparable to the Fermi wavelength, the shape resonances of the superconducting order parameter have strong influence on the vortex configuration. Several unconventional vortex states, including asymmetric ones, giant multi-vortex combinations, and states comprising giant antivortex, were found as ground states and their stability was found to be very sensitive on the value of $k_Fξ_0$, the siz…
The interaction between a superconducting vortex or antivortex in a superconducting film and a magnetic dipole with in- or out-of-plane magnetization is investigated within the London approximation. The dependence of the interaction energy on the dipole-vortex distance and the film thickness is studied and analytical results are obtained in limiting cases. We show how the short range interaction with the magnetic dipole makes the co-existence of vortices and antivortices possible. Different configurations with vortices and antivortices are investigated.
In this paper we investigate the elastic properties of the vortex lattice for a superconducting film of finite thickness. We derive an analytic expression for the compression modulus. The shear modulus is evaluated numerically by using both the Pearl interaction potential, valid in the limit of very thin film, and a potential for films of arbitrary thickness. A comparative study of the shear moduli is carried out.
We perform current(I)-voltage(V) measurements on low resistance superconductor-normal-superconductor arrays in finite magnetic fields, focusing on the dilute vortex population regime. We observe significant deviations from predicted behavior, notably the absence of a differential resistance peak near the vortex de-pinning current, and a broad linear I-V region with an extrapolated I intercept equal to the de-pinning current. Comparing these results to an overdamped molecular vortex model, we find that this behavior can be explained by the presence of a history dependent dissipative force. This…
In the present work we study an anisotropic layered superconducting film of finite thickness. The film surfaces are considered parallel to the $bc$ face of the crystal. The vortex lines are oriented perpendicular to the film surfaces and parallel to the superconducting planes. We calculate the local field and the London free energy for this geometry. Our calculation is a generalization of previous works where the sample is taken as a semi-infinite superconductor. As an application of this theory we investigate the flux spreading at the superconducting surface.
The dense vortex matter structure and associated magnetization are calculated for type-II superconducting mesoscopic disks. The magnetization exhibits generically first-order phase transitions as the number of vortices changes by one and presents two well-defined regimes: A non-monotonous evolution of the magnitude of the magnetization jumps signals the presence of a vortex glass structure which is separated by a second-order phase transition at $H_{c2}$ from a condensed state of vortices (giant vortex) where the magnitude of the jumps changes monotonously. We compare our results with Hall mag…
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 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.
Motivated by recent NMR data suggesting the presence of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) vortex lattice in magnetic fields perpendicular to the superconducting plane in the heavy-fermion superconductor CeCoIn5, we examine here the stability of FFLO states in quasi two-dimensional (2D) superconductors under a perpendicular field. It is found that a 3D-like portion of Fermi surfaces peculiar to CeCoIn5 stabilizes a FFLO vortex state modulating along the field parallel to the c-axis and that the direction of modulation in a FFLO vortex lattice is related to the characters of the normal t…
We use a magnetic force microscope (MFM) to investigate single vortex pinning and penetration depth in NdFeAsO$_{1-x}$F$_x$, one of the highest-$T_c$ iron-based superconductors. In fields up to 20 Gauss, we observe a disordered vortex arrangement, implying that the pinning forces are stronger than the vortex-vortex interactions. We measure the typical force to depin a single vortex, $F_{\mathrm{depin}} \simeq 4.5$ pN, corresponding to a critical current up to $J_c \simeq 7 \times 10^5$ A/cm$^2$. Furthermore, our MFM measurements allow the first local and absolute determination of the supercond…
By using the full 3D generalized time dependent Ginzbug-Landau equation we study a long superconducting film of finite width and thickness under an applied transport current. We show that, for sufficiently large thickness, the vortices and the antivortices become curved before they annihilate each other. As they approach the center of the sample, their ends combine, producing a single closed vortex. We also determine the critical values of the thickness for which the closed vortex sets in for different values of the Ginzburg-Ladau parameter. Finally, we propose a model of how to detect a close…
The distinctive features of the electronic structure of vortex states in superconducting graphene are studied within the Bogolubov-de Gennes theory applied to excitations near the Dirac point. We suggest a scenario describing the subgap spectrum transformation which occurs with a change in the doping level. For an arbitrary vorticity and doping level we investigate the problem of existence of zero energy modes. The crossover to a Caroli - de Gennes - Matricon type of spectrum is studied.
I investigate the vortex lattice structure of the Ginzburg Landau free energy for a two component order parameter in the weak-coupling clean-limit when the field is along the high symmetry axis in a tetragonal crystal. It is shown that the vortex lattice phase diagram as a function of the Ginzburg Landau free energy parameters includes phases with a hexagonal, centered rectangular, rectangular, and square unit cells. It is also shown that the square vortex lattice has the largest region of stability. The field distribution of the square vortex lattice near $H_{c2}$ is determined and the applic…
The orientation and deformation of moving vortex lattices in the flux-flow state have been investigated in amorphous superconducting NbGe thin films. Employing a mode-locking technique, we detect how moving lattices deform and their orientation changes as a magnetic field is tilted from normal to the film surface. For high tilt angles the lattice orientation is aligned parallely with the tilt direction. Meanwhile for low tilt angles the lattice orientation depends on the vortex velocity and a velocity-induced reorientation occurs. The characteristic velocity for the reorientation varies remark…
The interaction between a superconducting vortex in a type II superconducting film (SC) and a ferromagnet (FM) with out-of-plane magnetization is investigated theoretically within the London approximation. The dependence of the interaction energy on the FM-vortex distance, film thickness and different geometries of the magnetic structures: disk, annulus(ring), square and triangle are calculated. Analytic expressions and vectorplots of the current induced in the SC due to the presence of the FM are presented. For a FM disk with a cavity, we show that different local minima for the vortex positi…
When an electron beam strikes a superconducting thin film near a pinned vortex, it locally increases the temperature-dependent London penetration depth and perturbs the circulating supercurrent, thereby distorting the vortex's magnetic field toward the heated spot. This phenomenon has been used to visualize vortices pinned in SQUIDs using low-temperature scanning electron microscopy. In this paper I develop a quantitative theory to calculate the displacement of the vortex-generated magnetic-flux distribution as a function of the distance of the beam spot from the vortex core. The results are c…
We show that a large contribution to the inertial mass of a moving superconducting vortex comes from transversal displacements of the crystal lattice. The corresponding part of the mass per unit length of the vortex line is $M_{l} = ({\rm m}_e^2c^{2}/64πα^{2}μλ_{L}^{4})\ln(λ_{L}/ξ)$ , where ${\rm m}_{e}$ is the the bare electron mass, $c$ is the speed of light, $α=e^{2}/{\hbar}c {\approx} 1/137$ is the fine structure constant, $μ$ is the shear modulus of the solid, $λ_{L}$ is the London penetration length and $ξ$ is the coherence length. In conventional superconductors, this mass can be compar…
Superconductor-ferromagnet heterostructures hosting vortices and skyrmions are new area of an interplay between superconductivity and magnetism. We study an interaction of a Neel-type skyrmion and a Pearl vortex in thin heterostructures due to stray fields. Surprisingly, we find that it can be energetically favorable for the Pearl vortex to be situated at some nonzero distance from the center of the Neel-type skyrmion. The presence of a vortex-antivortex pair is found to result in increase of the skyrmion radius. Our theory predicts that a spontaneous generation of a vortex-anti-vortex pair is…
There seems to be a one to one correspondence between the phases of atomic and molecular matter (AMOM) and vortex matter (VM) in superfluids and superconductors. Crystals, liquids and glasses have been experimentally observed in both AMOM and VM. Here, we propose a vortex quasi-crystal state which can be stabilized due to boundary and surface energy effects for samples of special shapes and sizes. For finite sized pentagonal samples, it is proposed that a phase transition between a vortex crystal and a vortex quasi-crystal occurs as a function of magnetic field and temperature as the sample si…
We have combined high resolution magneto-optical imaging with an ultra-fast heating/cooling technique to measure the movement of individual vortices in a superconducting film. The motion took place while the film was heated close to $T_c$, where pinning and viscous forces are relatively small. Under these conditions, vortices move due to the magnetic repulsion between them. We found that a finite vortex mass has to be included in the analysis in order to account for the experimental results. The extent of the motion is consistent with a vortex mass being 3 orders of magnitude smaller than the …
While the electrodynamic treatment of a superconducting thin film by Yeh et al. [Phys. Rev. B 48, 9861 (1993)] ostensibly has application for the "thin-film limit," their work is shown to employ bulk-like instead of thin-film electrodynamics, and as such obtains an ostensible violation of the first law of thermodynamics and a surface resistance independent of the resistivity. Other theoretical and experimental difficulties are briefly noted.
We present a scanning tunneling spectroscopy study on quasiparticle states in vortex cores in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$. The energy of the observed vortex core states shows an approximately linear scaling with the superconducting gap in the region just outside the core. This clearly distinguishes them from conventional localized core states, and is a signature of the mechanism responsible for their discrete appearance in high-temperature superconductors. The energy scaling of the vortex core states also suggests a common nature of vortex cores in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ and YBa$_2$Cu…
Sub-nanovolt resolution longitudinal and Hall voltages are measured in an ultra pure YBa2Cu3O7-d single crystal. The Hall anomaly and the first-order vortex-lattice melting transition are observed simultaneously. Changes in the dynamic behavior of the vortex solid and liquid are correlated with features of the Hall conductivity sxy. With the magnetic field oriented at an angle from the twin-boundaries, the Hall conductivity sharply decreases toward large negative values at the vortex-lattice melting transition.
We investigated experimentally the frequency dependence of a superconducting vortex ratchet effect by means of electrical transport measurements and modeled it theoretically using the time dependent Ginzburg-Landau formalism. We demonstrate that the high frequency vortex behavior can be described as a discrete motion of a particle in a periodic potential, i.e. the so called stepper motor behavior. Strikingly, in the more conventional low frequency response a transition takes place from an Abrikosov vortex rectifier to a phase slip line rectifier. This transition is characterized by a strong in…
Usually, the measurements of electronic and magnetic properties of superconducting samples are carried out under a constant temperature bath. On the other hand, thermal gradients induce local variation of the superconducting order parameter, and the vortex dynamics can present interesting behaviors. In this work, we solved the time-dependent Ginzburg-Landau equations simulating samples under two different thermal gradients, and considering two values of the Ginzburg-Landau parameter, \k{appa}. We find out that both parameters, i.e., \k{appa} and thermal gradients, play an important role on the…
We consider two possible mechanisms for single-vortex fluctuative entry/exit through the surface barrier in ultrathin superconducting disk-shaped nanoislands made of Pb and consisting of just few monoatomic layers, which can be fabricated using modern techniques. We estimate tunnelling probabilities and establish criteria for the crossover between these two mechanisms depending on magnetic field and system sizes. For the case of vortex entry, quantum tunnelling dominates on the major part of the temperature/flux phase diagram. For the case of vortex exit, thermal activation turns out to be mor…
