We study theoretically the effects of heating on the magnetic flux moving in superconductors with a periodic array of pinning sites (PAPS). The voltage-current characteristic (VI-curve) of superconductors with a PAPS includes a region with negative differential resistivity (NDR) of S-type (i.e., S-shaped VI-curve), while the heating of the superconductor by moving flux lines produces NDR of N-type (i.e., with an N-shaped VI-curve). We analyze the instability of the uniform flux flow corresponding to different parts of the VI-curve with NDR. Especially, we focus on the appearance of the filamentary instability that corresponds to an S-type NDR, which is extremely unusual for superconductors. We argue that the simultaneous existence of NDR of both N- and S-type gives rise to the appearance of self-organized two-dimensional dynamical structures in the flux flow mode. We study the effect of the pinning site positional disorder on the NDR and show that moderate disorder does not change the predicted results, while strong disorder completely suppresses the S-type NDR.
We examine vortex dynamics and pinning in layered superconductors using three-dimensional molecular dyanmics simulations of magnetically interacting pancake vortices. Our model treats the magnetic interactions of the pancakes exactly, with longe-range logarithmic interactions both within and between planes. At the matching field the vortices are aligned with the pinning array. As a function of tilt angle for the pinning arrays a series of commensuration effects occur, seen as peaks in the critical current, due to pancakes finding a favorable alignment.
Sharp increase of pinning force was observed at the 3D-2D phase transition in strongly anisotropic high temperature superconductors of the BiPbSrCaCuO system.
Enhancement of flux pinning by magnetic nanoparticles embedded into the bulk of type-2 superconductor is studied both theoretically and experimentally. Magnetic part of the pinning force associated with the interaction between a spherical magnetic inclusion and an Abrikosov vortex was calculated in the London approximation. Calculations are supported by the experimental results obtained on sonochemically modified MgB2 superconductor with embedded magnetic Fe2O3 nanoparticles and compared to MgB2 with nonmagnetic Mo2O5 pinning centers of similar concentration and particle size distribution. It …
This paper reports the observation of hysteresis in the vortex pinning in a superconductor / ferromagnetic epitaxial nanocomposite consisting of fcc Gd particles incorporated in a Nb matrix. We show that this hysteretic pinning is associated with magnetic reversal losses in the Gd particles and is fundamentally different in origin to pinning interactions previously observed for ferromagnetic particles or other microstructural features.
We investigate the dynamics of magnetic vortices in type II superconductors with normal state pinning sites using the Ginzburg-Landau equations. Simulation results demonstrate hopping of vortices between pinning sites, influenced by external magnetic fields and external currents. The system is highly nonlinear and the vortices show complex nonlinear dynamical behaviour.
Pinning and creep determine the current--voltage characteristic of a type II superconductor and thereby its potential for technological applications. The recent development of strong pinning theory provides us with a tool to assess a superconductor's electric properties in a quantitative way. Motivated by the observation of typical excess-current characteristics and field-scaling of critical currents, here, we analyze current--voltage characteristics measured on 2H-NbSe$_2$ and $a$-MoGe type II superconductors within the setting provided by strong pinning theory. The experimentally observed sh…
The elementary vortex pinning potential is studied in unconventional superconductors within the framework of the quasiclassical theory of superconductivity. Numerical results are presented for d-, anisotropic s-, and isotropic s-wave superconductors to show explicitly that in unconventional superconductors the vortex pinning potential is determined mainly by the loss of the condensation energy in bulk due to the presence of the pinning center, i.e., by the breakdown of the Anderson's theorem. It is found that the vortex pinning energy in the d-wave pairing case is 4 -- 13 times larger than tho…
Measurements of the high-frequency complex resistivity in superconductors are a tool often used to obtain the vortex parameters, such as the vortex viscosity, the pinning constant and the depinning frequency. In anisotropic superconductors, the extraction of these quantities from the measurements faces new difficulties due to the tensor nature of the electromagnetic problem. The problem is specifically intricate when the magnetic field is tilted with respect to the crystallographic axes. Partial solutions exist in the free-flux-flow (no pinning) and Campbell (pinning dominated) regimes. In thi…
Vortex pinning in a type-II superconducting Pb film covering a Co/Pt multilayer with perpendicular magnetic anisotropy is investigated. Different stable magnetic domain patterns like band and bubble domains can be created in the Co/Pt multilayer, clearly influencing the vortex pinning in the superconducting Pb layer. Most effective pinning is observed for the bubble domain state. We demonstrate that the pinning properties of the superconductor/ferromagnet bilayer can be controlled by tuning the size, density and magnetization direction of the bubbles.
The elementary vortex pinning potential is studied in a chiral p-wave superconductor with a pairing d=z(k_x + i k_y) on the basis of the quasiclassical theory of superconductivity. An analytical investigation and numerical results are presented to show that the vortex pinning potential is dependent on whether the vorticity and chirality are parallel or antiparallel. Mutual cancellation of the vorticity and chirality around a vortex is physically crucial to the effect of the pinning center inside the vortex core.
We predict a novel buckling instability in the critical state of thin type-II superconductors with strong pinning. This elastic instability appears in high perpendicular magnetic fields and may cause an almost periodic series of flux jumps visible in the magnetization curve. As an illustration we apply the obtained criteria to a long rectangular strip.
We study magnetic flux interacting with arrays of pinning sites (APS) placed on vertices of hyperbolic tesselations (HT). We show that, due to the gradient in the density of pinning sites, HT APS are capable of trapping vortices for a broad range of applied magnetic fluxes. Thus, the penetration of magnetic field in HT APS is essentially different from the usual scenario predicted by the Bean model. We demonstrate that, due to the enhanced asymmetry of the surface barrier for vortex entry and exit, this HT APS could be used as a "capacitor" to store magnetic flux.
Magnetic hysteresis loops (MHLs) have been comparatively measured on both textured and single crystalline Sc5Ir4Si10 superconductors. Critical current densities and flux pinning forces are calculated from MHLs by Bean model. Three kinds of peaks of the flux pinning force are found at low fields near zero, intermediated fields, and high fields near the upper critical field, respectively. The characters and origins of these peaks are studied in detail.
The dynamics of vortices in a type-II superconductor with defects are studied by solving the time-dependent Ginzburg-Landau equations in two and three dimensions. We show that vortex flux tubes are trapped by volume defects up to a critical current density where they begin to jump between pinning sites along static flow channels. We study the dependence of the critical current on the pinning distribution and find for random distributions a maximum critical current equal to a few percent of the depairing current at a pinning density three times larger than the vortex line density. Whereas for a…
An exact analytical solution is given for the critical state problem in long thin superconductor strips in a perpendicular magnetic field, when the critical current density j_c(B) depends on the local induction B according to a simple three-parameter model. This model describes both isotropic superconductors with this j_c(B) dependence, but also superconductors with anisotropic pinning described by a dependence j_c(theta) where theta is the tilt angle of the flux lines away from the normal to the specimen plane.
By measuring the dynamic and traditional magnetization relaxations we investigate the vortex dynamics of the newly discovered superconductor SmFeAsO_0.9F_0.1 with Tc = 55K. It is found that the relaxation rate is rather large reflecting a small characteristic pinning energy. Moreover it shows a weak temperature dependence in wide temperature region, which resembles the behavior of the cuprate superconductors. Combining with the resistive data under different magnetic fields, a vortex phase diagram is obtained. Our results strongly suggest that the model of collective vortex pinning applies to …
The magnetic field dependent critical current density $j_c(B)$ of a MgB$_2$ bulk sample has been obtained by means of magnetization hysteresis measurements. The $j_c(B)$ curves at different temperatures demonstrate a crossover from single vortex pinning to small-bundle vortex pinning, when the field is larger than the crossover field $B_{sb}$. The temperature dependence of the crossover field $B_{sb}(T)$ is in agreement with a model of randomly distributed weak pinning centers via the spatial fluctuations of the transition temperature ($δT_c$-pinning), while pinning due to the mean free path f…
The magnetic response of type-II superconductors can be irreversible due to two different reasons: vortex pinning and barriers for flux penetration. Even without bulk pinning and in absence of a microscopic Bean-Lingston surface barrier for vortex penetration, superconductors of nonellipsoidal shape can exhibit a large geometric barrier for flux penetration. This edge barrier and the resulting irreversible magnetization loops and flux-density profiles are computed from continuum electrodynamics for superconductor strips and disks with constant thickness, both without and with bulk pinning. Exp…
We study the pinning of vortices in thin film superconductors by magnetic dots in the London approximation. A single dot is in general able to pin multiple field-induced vortices, up to a saturation number n_s, which can be much larger than one. However, the magnetic field of the dot also creates intrinsic vortices and anti-vortices, which must be accounted for. In a ferromagnetic dot array, the intrinsic anti-vortices are pinned only interstitially. Much stronger pinning effect is expected of an antiferromagnetic dot array. Possible realizations of various magnetic configurations are discusse…
The field dependence of flux pinning potential, U0, for under-doped, optimally doped and over-doped Ba(Fe,Co)2As2 single crystals has been investigated. U0 is determined using the Thermally Activated Flux Flow (TAFF) model, for both H || ab and H || c configurations. The observed power law dependencies of U0 versus H suggest that for fields upto 12 T for H || ab and 7 T for H || c, individual flux pinning, and for fields beyond 7 T for H || c, collective pinning becomes operative. A comparison of U0 for the Ba(Fe,Co)2As2 system with some other superconductors is presented
As a function of applied field, we find a rich variety of ordered and partially-ordered vortex lattice configurations in systems with square or triangular arrays of pinning sites. We present formulas that predict the matching fields at which commensurate vortex configurations occur and the vortex lattice orientation with respect to the pinning lattice. Our results are in excellent agreement with recent imaging experiments on square pinning arrays [K. Harada et al., Science 274, 1167 (1996)].
The vortex-lattice melting line in three-dimensional type-II superconductors with pinning is derived by equating the free energies of the vortex system in the solid and liquid phases. We account for the elastic and pinning energies and the entropy change that originates from the disappearance of the phonon shear modes in the liquid. The pinning is assumed to be caused by point defects and to be not too strong so that the melting line lies inside the so-called bundle-pinning region. We show that the derived equation for the melting line is equivalent to some Lindemann criterion, which however d…
A simulation study using the time-dependent Ginzburg-Landau theory is performed for the vortex state in two-component superconductors, such as PrOs_4_Sb_12_. We investigate the flux flow and the pinning of the vortex sheet structure. We find domain wall that traps half flux-quantum vortices and moves with the flux flow. In the pinning case, we observe an emitting process of a conventional vortex from the vortex sheet by combining a pair of half flux-quantum vortices.
Measuring the $ac$ magnetic response of a type II superconductor provides valuable information on the pinning landscape (pinscape) of the material. We use strong pinning theory to derive a microscopic expression for the Campbell length $λ_{\rm \scriptscriptstyle C}$, the penetration depth of the $ac$ signal. We show that $λ_{\rm \scriptscriptstyle C}$ is determined by the jump in the pinning force, in contrast to the critical current $j_c$ which involves the jump in pinning energy. We demonstrate that the Campbell lengths generically differ for zero-field-cooled and field-cooled samples and pr…
New model of the pinning potential barrier in multi-layered HTc superconductors has been presented, basing on geometrical approach to the capturing interaction of pancake type vortices with nano-scale defects. Using this model the transport current flow phenomena in these materials, especially current-voltage characteristics and critical current density, have been considered. Details of theoretical analysis are given, including derivation of basic mathematical equations describing the potential barrier in the function of transport current density and initial position of captured pancake vortex…
Charge doping of iron-pnictide superconductors leads to collective pinning of flux vortices, whereas isovalent doping does not. Moreover, flux pinning in the charge-doped compounds is consistently described by the mean-free path fluctuations introduced by the dopant atoms, allowing for the extraction of the elastic quasiparticle scattering rate. The absence of scattering by dopant atoms in isovalently doped BaFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ is consistent with the observation of a linear temperature dependence of the low-temperature penetration depth in this material.
We report on the vortex dynamics of a single crystal of the non-centrosymmetric heavy-fermion superconductor CePt$_{3}$Si. Decays of the remnant magnetization display a clean logarithmic time dependence with rates that follow the temperature dependence expected from the Kim-Anderson theory. The creep rates are lower than observed in any other centrosymmetric superconductor and are not caused by high critical currents. On the contrary, the critical current in CePt$_{3}$Si is considerably lower than in other superconductors with strong vortex pinning indicating that an alternative impediment on …
To understand the anisotropy of flux pinning and critical current density in technological superconductors, the scaling law for the anisotropy of single-vortex collective pinning in uniaxial superconductors is extended to flux-bundle collective pinning in biaxial superconductors. The scaling results show that in a system of random uncorrected point defects, the critical current density is described by a unified function with the magnetic field of the scaled isotropic superconductor. The obtained angular dependence of the critical current density depicts the main features of experimental observ…
We performed ac-susceptibility measurements to explore the vortex dynamics and the flux pinning properties of superconducting Pb films with an array of micro-holes (antidots) and non-fully perforated holes (blind holes). A lower ac-shielding together with a smaller extension of the linear regime for the lattice of blind holes indicates that these centers provide a weaker pinning potential than antidots. Moreover, we found that the maximum number of flux quanta trapped by a pinning site, i.e. the saturation number ns, is lower for the blind hole array.
We present results from extensive simulations of driven vortex lattices interacting with periodic arrays of pinning sites. Changing an applied driving force produces a rich variety of novel dynamical plastic flow phases which are very distinct from those observed in systems with random pinning arrays. Signatures of the transition between these different dynamical phases include sudden jumps in the current-voltage curves as well as marked changes in the vortex trajectories and the vortex lattice order. Several dynamical phase diagrams are obtained as a function of commensurability, pinning stre…
The vortex liquid-to-glass transition has been studied in Ba0.72K0.28Fe2As2, Ba0.9Co0.1Fe2As2, and Ba(Fe0.45Ni0.05)2As2 single crystal with superconducting transition temperature, Tc = 31.7, 17.3, and 18 K, respectively, by magnetoresistance measurements. For temperatures below Tc, the resistivity curves were measured in magnetic fields within the range of 0 \leq B \leq 13 T, and the pinning potential was scaled according to a modified model for vortex liquid resistivity. Good scaling of the resistivity ρ(B, T) and the effective pinning energy U0(B,T) was obtained with the critical exponents s…
We report the magnetic-field dependence of the irreversible magnetization of the recently discovered binary superconductor MgB$_{2}$. For the temperature region of $T< 0.9T_c$, the contribution of the bulk pinning to the magnetization overwhelms that of the surface pinning. This was evident from the fact that the magnetization curves, $M(H)$, were well described by the critical-state model without considering the surface pinning effect. It was also found that the $M(H)$ curves at various temperatures scaled when the field and the magnetization were normalized by the characteristic scaling fact…
The effect of a periodic pinning array on the vortex state in a 2D superconductor at low temperatures is studied within the framework of the Ginzburg-Landau approach. It is shown that attractive interaction of vortex cores to a commensurate pin lattice stabilizes vortex solid phases with long range positional order against violent shear fluctuations. Exploiting a simple analytical method, based on the Landau orbitals description, we derive a rather detailed picture of the low temperatures vortex state phase diagram. It is predicted that for sufficiently clean samples application of an artifici…
The flux pinning mechanism of NdO0.82F0.18FeAs superconductor made under high pressure, with a critical temperature, Tc, of 51 K, has been investigated in detail in this work. The field dependence of the magnetization and the temperature dependence of the magnetoresistivity were measured in fields up to 13 T. The field dependence of the critical current density, Jc(B), was analyzed within the collective pinning model. A crossover field, Bsb, from the single vortex to the small vortex bundle pinning regime was observed. The temperature dependence of Bsb(T) is in good agreement with the delta-l …
The pinning of quantized flux lines, or vortices, in the mixed state is used to quantify the effect of impurities in iron-based superconductors (IBS). Disorder at two length scales is relevant in these materials. Strong flux pinning resulting from nm-scale heterogeneity of the superconducting properties leads to the very disordered vortex ensembles observed in the IBS, and to the pronounced maximum in the critical current density jc at low magnetic fields. Disorder at the atomic scale, most likely induced by the dopant atoms, leads to "weak collective pinning" and a magnetic field-independent …
The field-angular dependence and anisotropy of the critical current density in iron-based superconductors is evaluated using a phenomenological approach featuring distinct anisotropy factors for the penetration depth and the coherence length. Both the weak collective pinning limit, and the strong pinning limit relevant for iron-based superconductors at low magnetic fields are considered. It is found that in the more anisotropic materials, such as SmFeAsO and NdFeAsO, the field-angular dependence is completely dominated by the coherence-length (upper-critical field) anisotropy, thereby explaini…
We examine vortex pinning and dynamics in thin-film superconductors interacting with square and rectangular pinning arrays for varied vortex densities including densities significantly larger than the pinning density. For both square and rectangular pinning arrays, the critical depinning force shows maxima at only certain integer matching fields where the vortices can form highly ordered arrays. For rectangular arrays the depinning force and commensurability effects are anisotropic with a much lower depinning threshold for vortex motion in the easy flow directions. We find evidence for a cross…
We use local and global magnetometry measurements to study the influence of magnetic domain width w on the domain-induced vortex pinning in superconducting/ferromagnetic bilayers, built of a Nb film and a ferromagnetic Co/Pt multilayer with perpendicular magnetic anisotropy, with an insulating layer to eliminate proximity effect. The quasi-periodic domain patterns with different and systematically adjustable width w, as acquired by a special demagnetization procedure, exert tunable vortex pinning on a superconducting layer. The largest enhancement of vortex pinning, by a factor of more than 10…
Using numerical simulations we show that novel transport phenomena can occur for vortices moving in periodic pinning arrays when two external perpendicular ac drives are applied. In particular, we find a ratchet effect where the vortices can have a net dc drift even in the absence of a dc drive. This ratchet effect can occur for ac drives which create orbits that break one or more reflection symmetries.
The three-dimensional frustrated anisotropic XY model with point disorder is studied with both Monte Carlo simulations and resistively-shunted-junction dynamics to model the dynamics of a type-II superconductor with quenched point pinning in a magnetic field and a weak applied current. Both the collective pinning and the depinning of the Bragg glass is examined. We find a critical current I_c that separates a creep region with unmeasurable low voltage from a region with a voltage V \sim I-I_c, and also identify the mechanism behind this behavior. It is further found to be possible to collapse …
We performed systematic AC susceptibility and magnetic moment measurements to investigate the vortex dynamics and pinning in the $EuRbFe_4As_4$ single crystal as a function of temperature, frequency, and DC magnetic field. The vortex solid-liquid line was determined and it fits well with $H(T_p)=H_0(1-t_p)^β$ using $β$=1.74-1.91, for $H\parallel ab$. It indicates a rather high pinning strength of the vortex system. The activation energy $U_0$ was determined from thermally activated flux creep theory and reached 6700 K at low fields, suggesting strong vortex pinning. A field dependence of $U_0(…
The intrinsic pinning in high-temperature superconductor with long range antiferromagnetic order of rare-earth ions confined to the isolating planes is described. The interaction of antiferromagnetic and superconducting subsystems in the mixed state may lead to the creation of spin-flop domain along the vortex core. It is shown that the behavior of several physical quantities such as magnetization, activation energy, current-voltage characteristic and flux creep changes when the direction of the external field changes in the basal a-b plane. It is also shown that the decay of the trapped flux …
We report a detailed study of isofield magnetic relaxation and isothermal magnetization measurements with $H$$\parallel$c on an underdoped Ba$_{0.75}$K$_{0.25}$Fe$_2$As$_2$ pnictide single crystal, with superconducting transition temperature $T_c$ = 28 K. The second magnetization peak (SMP) has been observed at temperatures below $T_c$/2 and vanished at higher temperatures. The observed behaviour of the SMP has been studied by measuring the magnetic field dependence of relaxation rate, $R(H)$ and by performing the Maley's analysis. The results suggest that the crossover from collective to plas…
By doping MgB_2 superconductor with SiC nano-particles, we have successfully introduced pinning sites directly into the crystal lattice of MgB_2 grains (intra-grain pinning). It became possible due to the combination of counter-balanced Si and C co-substitution for B, leading to a large number of intra-granular dislocations and the dispersed nano-size impurities induced by the substitution. The magnetic field dependence of the critical current density was significantly improved in a wide temperature range, whereas the transition temperature in the sample MgB_2(SiC)_x having x = 0.34, the highe…
We study vortex states and dynamics in 2D superconductors with periodic pinning at fractional sub-matching fields using numerical simulations. For square pinning arrays we show that ordered states form at 1/1, 1/2, and 1/4 filling fractions while only partially ordered states form at other filling fractions, such as 1/3 and 1/5, in agreement with recent imaging experiments. For triangular pinning arrays we observe matching effects at filling fractions of 1/1, 6/7, 2/3, 1/3, 1/4, 1/6, and 1/7. For both square and triangular pinning arrays we also find that, for certian sub-matching fillings, vo…
Vortices driven with both a transverse and a longitudinal AC drive which are out of phase are shown to exhibit a novel commensuration-incommensuration effect when interacting with periodic substrates. For different AC driving parameters, the motion of the vortices forms commensurate orbits with the periodicity of the pinning array. When the commensurate orbits are present, there is a finite DC critical depinning threshold, while for the incommensurate phases the vortices are delocalized and the DC depinning threshold is absent.
We discuss and propose a complete data treatment, in close contact to typical microwave experimental data, in order to derive vortex parameters, such as pinning constant and viscous drag coefficient (also referred to as ``vortex viscosity''), in a way as model-independent as possible. We show that many of the accepted models for the complex resistivity can be described by a single, very general analytical expression. Using typical measurements of real and imaginary resistivity as a function of the applied field, we show that, even for single-frequency measurements, it is always possible to obt…
Type-II superconductors owe their magnetic and transport properties to vortex pinning, the immobilization of flux quanta through material inhomogeneities or defects. Characterizing the potential energy landscape for vortices, the pinning landscape (or short, pinscape), is of great technological importance. Besides measurement of the critical current density $j_c$ and of creep rates $S$, the $ac$ magnetic response provides valuable information on the pinscape which is different from that obtained through $j_c$ or $S$, with the Campbell penetration depth $λ_{\rm \scriptscriptstyle C}$ defining a…
The interaction of (quasi)particles with a periodic potential arises in various domains of science and engineering, such as solid-state physics, chemical physics, and communication theory. An attractive test ground to investigate this interaction is represented by superconductors with artificial pinning sites, where magnetic flux quanta (Abrikosov vortices) interact with the pinning potential $U(r) = U(r + R)$ induced by a nanostructure. At a combination of microwave and dc currents, fluxons act as mobile probes of $U(r)$: The ac component shakes the fluxons in the vicinity of their equilibriu…
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 H…
Using numerical simulations, we show that a novel spontaneous transverse response can appear when a longitudinal drive is applied to type-II superconductors with honeycomb pinning arrays in a magnetic field near certain filling fractions. This response is generated by dynamical symmetry breaking that occurs at fields away from commensurability. We find a coherent strongly amplified transverse switching effect when an additional transverse ac current is applied. The transverse ac drive can also be used to control switching in the longitudinal velocity response. We discuss how these effects coul…
It has been shown that graphene doping is sufficient to lead to an improvement in the critical current density - field performance (Jc(B)), with little change in the transition temperature in MgB2. At 3.7 at% graphene doping of MgB2 an optimal enhancement in Jc(B) was reached by a factor of 30 at 5 K and 10 T, compared to the un-doped sample. The results suggested that effective carbon substitutions by grapheme, 2D nature of grapheme and the strain effect induced by difference thermal coefficient between single grapheme sheet and MgB2 superconductor may play an important role in flux pinning e…
The vortex hopping motion in a type-II superconductor determines the current-carrying ability and consequently the application fields of the superconductor. However, it is not clear how the vortices hop between the different pinning regions in the superconductor. Here we proposed that there should be magnetic \textit{flux exchange} between two contacting pinning regions. A system of differential equations was constructed to describe the flux exchange phenomenon. The qualitative analysis methods were used. The approximate numerical solutions and approximate analytical solutions of the system we…
We consider magnetic flux moving in superconductors with periodic pinning arrays. We show that sample heating by moving vortices produces negative differential resistivity (NDR) of both N and S type (i.e., N- and S-shaped) in the voltage-current characteristic (VI curve). The uniform flux flow state is unstable in the NDR region of the VI curve. Domain structures appear during the NDR part of the VI curve of an N type, while a filamentary instability is observed for the NDR of an S type. The simultaneous existence of the NDR of both types gives rise to the appearance of striking self-organized…
We explore the effects of sample dimensionality on vortex pinning in a type-II, low-$T_C$, s-wave superconductor, NbN, in the presence of a perpendicular magnetic field, $H$. We find significant differences in the phase diagrams in the magnetic field--temperature plane between 3-dimensional (3D) and 2-dimensional (2D) NbN films. The differences are most striking close to the normal-superconductor phase transition. We establish that these variances have their origin in the differing pinning properties in two different dimensions. We obtain the pinning strength quantitatively in both the dimensi…
New results of the investigations critical current problems in the high temperature oxide superconductors are presented, basing on an analysis of the flux pinning on nano-sized centers. New model of the interaction pancake vortices with the nano-sized centers is proposed, while comparison of obtained results with others pinning forces approaches presented. The energy balance approach is applied, which leads to the appearance of the potential barrier determining the pancake vortices movement in the flux creep process. Various initial positions of the captured vortex have been analyzed, while va…
We discuss the elementary vortex pinning in type-II superconductors in connection with the Anderson's theorem for nonmagnetic impurities. We address the following two issues. One is an enhancement of the vortex pinning energy in the unconventional superconductors. This enhancement comes from the pair-breaking effect of a nonmagnetic defect as the pinning center far away from the vortex core (i.e., the pair-breaking effect due to the non-applicability of the Anderson's theorem in the unconventional superconductors). The other is an effect of the chirality on the vortex pinning energy in a chira…
We have studied flux-pinning effects of MgB$_2$ superconductor by doping (Fe, Ti) particles of which radius is 163 nm on average. 5 wt.\% (Fe, Ti) doped MgB$_2$ among the specimens showed the best field dependence of magnetization and 25 wt.\% one did the worst at 5 K . The difference of field dependence of magnetization of the two increased as temperature increased. Here we show experimental results of (Fe, Ti) particle-doped MgB$_2$ according to dopant level and the causes of the behaviors. Flux-pinning effect of volume defects-doped superconductor was modeled in ideal state. During the stud…
