Using the time-dependent Ginzburg-Landau equation with the complex relaxation time and the Maxwell equation, we systematically examine transverse motion of vortex dynamics in the presence of pinning disorders. Consequently, in a plastic flow phase in which moving and pinned vortices coexist, we find that the Hall voltage generally changes its sign. The origin of the sign change is ascribed to a fact that moving vortices are strongly drifted by circular current of pinned vortices and the enforced transverse moving direction becomes opposite to that by transport current. This suggests that the Hall sign change is a behavior common in all disordered type-II superconductors.
Measurements of the Hall effect and the resistivity in twinned YBa2Cu3O7-delta thin films in magnetic fields B oriented parallel to the crystallographic c-axis and to the twin boundaries reveal a double sign reversal of the Hall coefficient for B below 1 T. In high transport current densities, or with B tilted off the twin boundaries by 5 degrees, the second sign reversal vanishes. The power-law scaling of the Hall conductivity to the longitudinal conductivity in the mixed state is strongly modified in the regime of the second sign reversal. Our observations are interpreted as strong, disorder…
Explicit current-dependent expressions for anisotropic longitudinal and transverse nonlinear magnetoresistivities are represented and analyzed on the basis of a Fokker-Planck approach for two-dimensional single-vortex dynamics in a washboard pinning potential in the presence of point-like disorder. Graphical analysis of the resistive responses is presented both in the current-angle coordinates and in the rotating current scheme. The model describes nonlinear anisotropy effects caused by the competition of point-like (isotropic) and anisotropic pinning. Nonlinear guiding effects are discussed a…
The transverse (Hall) voltage in thin films of the high-temperature superconductor YBa$_{2}$Cu$_{3}$O$_{7-δ}$ with an artificial periodic pinning array is investigated. Columnar defect regions along the crystallographic $c$ axis, in which superconductivity is suppressed, are created by irradiation with He$^+$ ions through a silicon stencil mask. The commensurate arrangement of magnetic flux quanta with the artificial defect lattice is confirmed by maxima of the critical current and minima of the resistance, respectively. The magnetic field dependence of the transverse voltage reveals a commens…
The effect of the Hall force on the pinning of vortices in type II superconductors is considered. A field theoretic formulation of the pinning problem allows a non-perturbative treatment of the influence of quenched disorder. A self-consistent theory is constructed using the diagrammatic functional method for the effective action, and an expression for the pinning force for independent vortices as well as vortex lattices is obtained. We find that the pinning force for a single vortex is suppressed by the Hall force at low temperatures while it is increased at high temperatures. The effect of t…
The Langevin equation for a two-dimensional (2D) nonlinear guided vortex motion in a tilted cosine pinning potential in the presence of an ac is exactly solved in terms of a matrix continued fraction at arbitrary value of the Hall effect. The influence of an ac of arbitrary amplitude and frequency on the dc and ac magnetoresistivity tensors is analyzed. The ac density and frequency dependence of the overall shape and the number and position of the Shapiro-like steps on the anisotropic current-voltage characteristics are considered. The influence of a subcritical or overcritical dc on the time-…
We find universal scaling relations of the pinning effect on the Hall resistivity $ρ_{xy}$ and Hall angle $θ_{H}$. Considering the extended power law form of $ρ_{xx}$ and the microscopic analysis of $σ_{xy}$, we obtain unified $ρ_{xy}$ equations for superconductors with and without double sign reversal. These equations reasonably explain the striking universality in doping dependence found by Nagoaka et al., which contradicts the prediction of the time dependent Ginzburg-Landau equation based on s-wave coupling theory [PRL {\bf{80}},3594 (1998)]. A full comparison of experiment with prediction…
The interplay between vortex guiding and the Hall effect in superconducting Nb films with periodically arranged nanogrooves is studied via four-probe measurements in standard and Hall configurations and accompanying theoretical modeling. The nanogrooves are milled by focused ion beam and induce a symmetric pinning potential of the washboard type. The resistivity tensor of the films is determined in the limit of small current densities at temperatures close to the critical temperature for the fundamental matching configuration of the vortex lattice with respect to the pinning nanolandscape. The…
We show that the longitudinal current-voltage characteristics of superconductors in mixed state have the general form of extended power law. Isotherms simulated from this nonlinear equation fit the experimental I-V data of Strachan et al. [ Phys. Rev. Lett. {\bf 87}, 067007 (2001)]. We determine the average pinning force in the flux creep and strong pinning regime and discuss both the puzzling scaling behavior $ρ_{xy}\proptoρ_{xx}^β$ and a recently found new scaling relationship of nonlinear Hall resistivity $ρ_{xy}(T)$.
The anomalous Hall effect for type-II superconductors is investigated by random walk theorem. It is shown that the origin of Hall anomaly is induced by the thermally activated vortex bundle flow (TAVBF) over the directional-dependent energy barrier formed by the Magus force, random collective pinning force, and strong pinning force inside the vortex bundles. The directional-dependent potential barrier of the vortex bundles renormalizes the Hall and longitudinal resistivities strongly. Under the framework of present theory, it is also shown that the Hall anomaly is universal for type-II superco…
Thermally activated flux flow (TAFF) and flux flow Hall effect (FFHE) of Fe(Te,S) single crystal in the mixed state are studied in magnetic fields up to 35 T. Thermally activated energy (TAE) is analyzed using conventional Arrhenius relation and modified TAFF theory which is closer to experimental results. The results indicate that there is a crossover from single-vortex pinning region to collective creep pinning region with increasing magnetic field. The temperature dependence of TAE is different for H//ab and H//c. On the other hand, the analysis of FFHE in the mixed state indicates that the…
The mixed-state Hall effect was examined in a Ba(Fe1-xCox)2As2 epitaxial film with a high critical current density. The transverse resistivity ρxy and the longitudinal resistivity ρxx follow power law scaling ρxy = Aρxxβ. In the temperature-sweep with a fixed field (T sweep), all of the β values are independent of magnetic field up to 9 T, and are lower than 2.0 (around 1.8). In contrast, the β values in the magnetic-field sweep with a fixed temperature (H sweep) change from 1.8 to 2.0 as the temperature increases from 13 to 16 K even in the T/H region that overlaps with the T sweep measuremen…
High-resolution scanning Hall probe microscopy has been used to image vortex configurations in very large periodic arrays of artificial pinning sites. Strong matching effects are seen at fields where either one or two vortices can sit at a site; with three vortices per site, however, no clear matching is observed. Matching effects have been also been observed at several fractional multiples of the matching field, including 1/5, 1/4, 1/3, 1/2, and 3/4. These fractional values are characterized by striking domain structure and grain boundaries.
We study the vortex structure in a Pb film deposited on top of a periodic array of ferromagnetic square microrings by combining two high resolution imaging techniques: Bitter decoration and scanning Hall probe microscopy (SHPM). The periodicity and strength of the magnetic pinning potential generated by the square microrings are controlled by the magnetic history of the template. When the square rings are in the magnetized dipolar state, known as the onion state, the strong stray field generated at the domain walls prevents the decoration of vortices. SHPM images show that the stray field gene…
A direct visualization of the flux distribution in a Pb film covering a five-fold Penrose array of Co dots is obtained by mapping the local field distribution with a scanning Hall probe microscope. We demonstrate that stable vortex configurations can be found for fields H~0.8H_1, H_1 and 1.6H_1, where H_1 corresponds to one flux quantum per pinning site. The vortex pattern at 0.8H_1 corresponds to one vacancy in one of the vertices of the thin tiles whereas at 1.6H_1 the vortex structure can be associated with one interstitial vortex inside each thick tile. Strikingly, for H=1.6H_1 interstitia…
The longitudinal resistivity (rho_{xx}) and transverse resistivity (rho_{xy}) of MgB2 thin films in the mixed state were studied in detail. We found that the temperature dependencies of rho_{xx} and ρ_{xy} at a fixed magnetic field (H) satisfy the scaling law of $ρ_{xy}=Aρ_{xx}^β$, where the exponent beta varies around 2.0 for different fields. In the low field region (below 1T), beta maintains a constant value of 2.0 due to the weak pinning strength of the vortices, mainly from the superfluid of the pi band. When H>1T, beta drops abruptly to its lowest value at about 2T because of the prolife…
The anomalous Hall effect in type-II conventional and high-Tc superconductors is investigated based on the proposed novel theory of the thermally activated motion of vortex bundles over a directional-dependent energy barrier. Our calculations demonstrate clearly that anomalous Hall effect is induced by the competition between the Magnus force and the random collective pinning force of the vortex bundle. The Hall as well as the longitudinal resistivity for constant temperature and constant applied magnetic field of type-II superconducting films and bulk materials are calculated. The reentry phe…
From a very simple description of vortices and pinning centers and without using any electrodynamical assumptions, we obtain nonlinear density profiles of vortices in type-II dirty superconductors that result from raising or lowering an external magnetic field. The results confirm a modified Bean model description of these systems, and in particular, follow the Kim empirical form that relates the current inside the material to the local magnetic field. We also obtain realistic magnetization hysteresis loops and examine the discrete evolution of the density profiles in our systems. This evoluti…
Magnetoresistivity and Hall effect measured in magnetic fields up to B=9T (B||c, J||ab) in electron-doped $Nd_{2-x}$Ce_{x}Cu$O_{4+δ} single crystal films with x = 0.14; 0.15; 0.18 and different oxygen content (δ) were studied in a temperature range of 0.4-4.2 K. The resistivity and Hall coefficient behaviors in the mixed state are discussed in the framework of flux-flow model with the inclusion of the back-flow of vortices owing to the pinning forces.
Current - voltage characteristics in magnetic field for layered superconductor with intrinsic pinning of Josephson vortices
M.N. Mikheev Institute of Metal Physics, Ural Branch, Russian Academy of Sciences（俄罗斯科学院乌拉尔分校 M.N. 米凯耶夫金属物理研究所）；National Research Nuclear University MEPhI（国立核研究大学莫斯科工程物理学院）
Measurements of the Hall effect and the resistivity on precisely-patterned YBCO thin films in magnetic fields B from 0.5 to 6 T oriented parallel to the sample crystallographic c axis reveal a sign reversal of the Hall coefficient for B <= 3 T. The data are compared to the full, quantitative expressions based on the renormalized fluctuation model for the Hall conductivity. The model offers a satisfactory understanding of the experimental results, for moderate fields and temperatures near the critical region, provided that the inhomogeneity of the critical temperature distribution is also taken…
We report the growth and characterization of single crystals of iron chalcogenide superconductor FeCr$_{0.02}$Se. There is an enhancement of the superconducting transition temperature (T$_{\rm c}$) as compared to the T$_{\rm c}$ of the single crystals of the parent compound Fe$_{1+x}$Se by about 25%. The superconducting parameters such as the critical fields, coherence length, penetration depth and the Ginzburg-Landau parameter have been estimated for these single crystals. Analysis of the critical current data suggests a fluctuation in electronic mean free path induced ($δl$) pinning mechanis…
The anomalous Hall effect for type-II conventional and high-Tc superconductors is studied based upon the theory of thermally activated motion of vortex bundles jumping over the directional-dependent energy barrier. It is shown that the Hall anomaly is universal for type-II conventional and high-Tc superconductors as well as for superconducting bulk materials and thin films, provided certain conditions are satisfied. We find that the directional-dependent potential barrier of the vortex bundles renormalizes the Hall and longitudinal resistivities, and Hall anomaly for superconductors is induced…
We investigated the nature of the quasi-particle state in the vortex core by means of the flux-flow Hall effect measurements at 15.8 GHz. We measured the flux-flow Hall effect in cuprate superconductors, Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{y}$ and YBa$_{2}$Cu$_{3}$O$_{y}$ single crystals, whose equilibrium $B$-$T$ phase diagrams were different. As a result, we found that the Hall angle is independent of the magnetic field, and reaches an order of unity at low temperatures in BSCCO. However, in YBCO, the angle increases with increasing magnetic field even at low temperatures. We understood that this …
Thanks to the 9 contacts deposited on the surface of a high quality YBCO twinned single crystal, we investigate both vortex guided motion along twins and the mixed state Hall effect. Firstly, we clearly identify the vortex phase transition and show that, when the magnetic field is along the twin boundaries (within about 2 degrees), the vortex solid is a Bose glass. Secondly, the effects of twins on the vortex dynamics are studied by measuring the direction and magnitude of the total electric field while rotating the current in the ab plane. We observe a partially guided vortex motion along the…
The magnetic-field dependencies of the longitudinal and Hall resistance of the electron-doped compounds Nd$_{2-x}$Ce$_x$CuO$_{4+δ}$ in underdoped region with $x$=0.14 and with varying degrees of disorder ($δ$) were investigated. It was established experimentally that the correlation between the longitudinal electrical resistivity and the Hall resistivity can be analyzed on the basis of scaling relationships: $ρ_{xy}$($B$)$\sim$ $ρ^β_{xx}$($B$). For the totality of the investigated single-crystal films of Nd$_{2-x}$Ce$_x$CuO$_{4+δ}$/SrTiO$_3$ the universal value $β$=1.5 $\pm$0.4 is found. The o…
The transport properties of La$_{1.89}$Ce$_{0.11}$CuO$_{4}$(LCCO) and La$_{1.89}$Ce$_{0.11}$(Cu$_{0.99}$Co$_{0.01}$)O$_{4}$ (LCCO:Co) superconducting thin films are investigated. When the external field $\bf H$ is applied along the crystallographic c-axis, a double sign reversal of the Hall voltage in the mixed state of LCCO:Co thin films is observed whereas a single sign reversal is detected in LCCO. A double sign reversal of the Hall signal in LCCO can be recovered if the magnetic field is tilted away from the plane of the film. We find that the transition from one to two of the Hall sign re…
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…
The tunneling rate t_v of a vortex between two pinning sites (of strength V separated by d) is computed using the Bogoliubov expansion of vortex wavefunctions overlap. For BCS vortices, tunneling is suppressed beyond a few Fermi wavelengths. For Bose condensates, t_v = V exp(- pi n_s d^2/2), where n_s is the boson density. The analogy between vortex hopping in a superconducting film and 2D electrons in a perpendicular magnetic field is exploited. We derive the variable range hopping temperature, below which vortex tunneling contributes to magneto-resistance. Using the 'Quantum Hall Insulator' …
Miniature Hall-probe arrays were used to measure the critical current densities for the three main directions of vortex motion in the stoichiometric LiFeAs superconductor. These correspond to vortices oriented along the c-axis moving parallel to the ab-plane, and to vortices in the ab-plane moving perpendicular to, and within the plane, respectively. The measurements were carried out in the low-field regime of strong vortex pinning, in which the critical current anisotropy is solely determined by the coherence length anisotropy parameter, ε_ξ. This allows extraction of ε_ξ at magnetic fields f…
The Hall effect in LuNi_2B_2C and YNi_2B_2C borocarbides has been investigated in normal and superconducting mixed states. The Hall resistivity rho_{xy} for both compounds is negative in the normal as well as in the mixed state and has no sign reversal below T_c typical for high-T_c superconductors. In the mixed state the behavior of both systems is quite similar. The scaling relation rho_{xy}\simρ_{xx}^β(ρ_{xx} is the longitudinal resistivity) was found with β=2.0 and 2.1 for annealed Lu- and Y-based compounds, respectively. The scaling exponent βdecreases with increasing degree of disorder a…
A scaling relation of vortex-induced rectification effects in a superconducting thin-film heterostructure
Osaka University（大阪大学）；Institute for Open and Transdisciplinary Research Initiatives, Osaka University（大阪大学开放跨学科研究倡议研究所）；Institute for Materials Research, Tohoku University（东北大学材料科学研究所）
We describe and analyze in detail our recent theoretical proposal for the realization and manipulation of anyons in a weakly interacting system consisting of a two-dimensional electron gas in the integer quantum Hall regime adjacent to a type-II superconducting film with an artificial array of pinning sites. The anyon is realized in response to a defect in the pinned vortex lattice and carries a charge \pm e/2 and a statistical angle pi/4. We establish this result, both analytically and numerically, in three complementary approaches: (i) a continuum model of two-dimensional electrons in the vo…
