Lecture notes on superconductivity a work in progress. Such a vortex comprises a thin nonsuperconducting core around which an. Soft superconductors are those which can tolerate impurities without affecting the superconducting properties. Onsager reasoned that quantisation of vorticity is a direct. What is a superconductor, discovery of superconductivity, meissner effect, type i superconductors, type ii superconductors, theory of superconductivity, tunneling and the josephson effect, hightemperature supercondutors and applications of superconductors. Rayleigh instability of confined vortex droplets in. Ginzburglandau equations, type ii superconductivity, vortices, pinning sites 2010 msc. Reviews of topical problems related content vortices in type. Some superconductors type ii superconductors do not exhibit a complete expulsion of flux if an external field is larger than a critical field. This article is concerned with the mechanisms by which type ii superconductors can carry currents.
We restrict our attention to materials where a the landauginzburg parameter x x4 is much larger than unity, b the field h. Since in this thesis we are interested mainly in the dynamics of vortices and. Materials science division, argonne national laboratory. The equilibrium properties of the vortex lattice are described and the generalized driving force in gradients of temperature and field is derived using irreversible thermodynamics. We do so with the aid of langevin molecular dynamics simulations of a coarsegrained elastic line model of flux vortices in the extreme london limit.
Pinning forces in superconductors from periodic ferromagnetic. Pdf the fluxpinning landscape in typeii superconductors determines the response of the flux line lattice to changing magnetic fields. The phenomena of vortexlattice melting, flux creep, and other fluctuation effects on the vortex lattice are significant theoretically as examples of emergent order in complex systems and have a. Introduction since about 1962 it has become universally recognized that there exists a whole new class of superconductors, type i1 superconductors. In the mixed state, even if the magnetic field is no longer expelled and diamagnetism does not exist, the electric resistance remains equal to zero. Superconductivity is the set of physical properties observed in certain materials, wherein electrical resistance vanishes and from which magnetic flux fields are expelled. Imaging flux vortices in type ii superconductors with a. Vortices in a 200nmthick ybco film imaged by scanning squid microscopy 1 in superconductivity, a type ii superconductor is a superconductor which exhibits an intermediate phase of mixed ordinary and superconducting properties at intermediate temperature and fields above the superconducting phases. Ginzburg i most hight t c superconductors are type ii. A superconductor can be type i, meaning it has a single critical field, above which all superconductivity is lost and below which the magnetic field is completely expelled from the superconductor. Effect of dimensionality on the vortex dynamics in a type.
If, it is a type i superconductor if, it is a type ii superconductor in all of my simulation, 5, and therefore i deal only with type ii super conductors 1 2 1 2 information from. Onnes np 19 2 electrical resistivity drops to zero if temperature becomes suf. Thus, in orderfora type ii superconductor to have zero resistivity whenvortices are present, one must prevent all the vortices from moving. In an isotropic type ii superconductor in a moderate magnetic. May 26, 2018 let me answer this in a simpler manner. Introduction the dynamics of magnetic vortices in type ii superconductors at temperatures close to the critical temperature can be modelled by the time dependent. When a magnetic field is applied to a type ii superconductor, it penetrates the sample in localized tubes of magnetic flux associated with quantized current vortices.
Department of mathematics, pennsylvania state university, university park, pa 16802, usa. Sep 10, 2018 when a weak magnetic field is applied to a type ii superconductor, it repels perfectly. These low lying states will play a major role in the discussion of transport and relaxation phenomena in type ii superconductors at low temperatures. This article is concerned with the mechanisms by which type ii super conductors can carry currents. The nature of vortices in extreme type ii superconductors has been an ever growing. This partial penetration is in the form of a regular array of normal conducting regions shown as the dark regions in figure 7. Flux vortices and transport currents in type ii superconductors. The aim was to isolate and investigate only the dimensional effects on vortex. Quantized vortices in bec and superconductors qiang du. We numerically investigate the dynamical properties of driven magnetic flux vortices in disordered typeii superconductors for a variety of temperatures, types of disorder and sample thicknesses. The methods of formal asymptotics are used to examine the behaviour of a system of curvilinear vortices in a type ii superconductor as the thickness of the vortex cores tends to zero.
In type ii superconductors there is a low critical. This behavior is different from type ii superconductors which exhibit two critical magnetic fields. We present a generalized variational model of an isolated vortex, valid in the anisotropic case when the external magnetic field is along one of the symmetry directions. Vortices in anisotropic typeii superconductors springerlink. The vortices in a typeii superconductor are quasi onedimensional objects. Inhomogeneities retard the motion of the vortex lattice. Certainly levitation occurs when using type i superconductors but in a type ii, the levitation is particular stable and robust. The main topic of interest here however, is the magnetic properties of type ii superconductors, whose magnetization curve is depicted in fig. Vorticity and magnetic shielding in a typeii superconductor. The flux flow dynamics in type ii superconductors are simulated based on the timedependent ginzburglandau equation with a new integration scheme. Using the focused beam of a helium ion microscope, we have fabricated periodic patterns of dense pinning centers with spacings as small as 70. Magnetic lattices and vortices in the copper superconductors. Dynamics of vortex fronts in type ii superconductors. The basis of abrikosovs model of the vortex state is the.
The properties of abrikosov vortices, like the energy of interaction for a slab and a. Vortex properties from resistive transport measurements on. On the left are the level curves of the magnitude of the order parameter. Systems of anisotropic, interacting constituents generally exhibit liquid crystalline phases. There are many criteria by which superconductors are classified. In physics, a quantum vortex represents a quantized flux circulation of some physical quantity. Quantization of magnetic flux magnetic flux is quantized, the quantum of. The system is characterized by the vortex and pin numbers n v,n p, the vortex and pin interaction ranges r v,r p, and the amplitude of the pin potentiala p. As presented in their original form, the above results pertain almost exclusively to type i superconductors. The answer lies in the properties of type ii superconductors for. For intermediate elds and temperatures, we have the mixed vortex state. Applied superconductivity lecture notes pdf 35p this note covers the following topics.
Vortex lattice in a twodimensional type ii superconductor. Onset of resistance i ideal type ii superconductor where vortices are free to move develops resistance. Oscillations of a single abrikosov vortex in hard typeii. In previous chapters, we observed that the free energy of an interface between normal and superconducting regions was negative.
A local analysis near each vortex core gives an equation of motion governing the. T and by the complete repulsion of magnetic flux, even if a magnetic field is applied before a superconductor is cooled below the critical temperature t c meissner and ochsenfeld 1933. Thevortices then appear as singularities in the field equation and are analagous to line. Because of the lnr behaviour of interaction energy of vortices, a twodimensional superfluid sample can exhibit a kosterlitzthouless type transition whereas a strictlyd 2 superconductors should not have any. Motion of vortices in typeii superconductors eprints soton. Pdf time dependent ginzburglandau equation is solved for type ii superconductors numerically, and the dynamics of entering vortices. When there is a magnetic field, a highly divided structure is therefore energetically favoured, in which normal and superconducting phases coexist 442, in such a. In this case they allow the applied field to partly penetrate the material, the magnetization of the specimen depends on its magnetic history in a complicated way. It is found that the pinning force of the magnetic dot with 50 nm thickness reaches 3. Vortices can also be observed in superfluids or in boseeinstein condensates, which are two similar forms of superconductivity for liquids and gases. We numerically calculate the interaction between ferromagnetic dots and vortices in type ii super conductors under various conditions. Quantized vortices is a wellknow signature of super. The vortices are then expected to move back out of the sample as the. Many years ago, i was a student and i was very surprised when i got to know the great experiments by dr.
Vortices in typeii superconductor arise when the magnetic field starts to penetrate the materials in the form of quantized flux. Vortices in superconductors the superconducting state of some material is characterized by a vanishing dc resistivity. Unlike an ordinary metallic conductor, whose resistance decreases gradually as its temperature is lowered even down to near absolute zero, a superconductor has a. Vortices in type ii superconductors andreas windisch. Selforganization of vortices in typeii superconductors. General thermodynamic concepts first and second law entropy gibbs free energy and coenergy 4.
The vortices then appear as singularities in the field equation and are analagous to line vortices in inviscid hydrodynamics. Manipulation of individual vortices in typeii super conductors can now be achieved with a variety of methods, including local magnetic elds1, magnetic force microscopes mfms25, mechanical forces6, scanning tunneling tips7, and optically8. The existence of quantum vortices was first predicted by lars onsager in 1949 in connection with superfluid helium. A type i superconductor keeps out the whole magnetic eld until a critical applied eld h c reached. Type ii superconductors show two critical magnetic field values, one at the onset of a mixed superconducting and normal state and one where superconductivity ceases. I published my derivation in the russian journal doklady akademii nauk sssr in 1954 4. Important fundamental and technological questions concerning magnetic properties and phase transitions in such small, bounded systems need to be considered. Pdf motion of vortices in type ii superconductors researchgate. The interaction energy of two parallel slowly moving vortices differs from the static case by a small term. In a type ii superconductor, however, the interfacial energy becomes negative above hc1 and, as abrikosov 9 first showed, flux penetrates type ii superconductors along many cylindrical channels, called flux vortices, each containing the smallest amount of magnetic flux consistent with the quantum. We discuss the effects of the field anisotropy on the core and magnetic pinning of individual vortices. Pdf the methods of formal asymptotics are used to examine the behavior of a system curvilinear vortices in a type ii superconductor as the thickness.
The vortex lattice of the typeii superconductor nb studied by small. Effects of sample geometry on the dynamics and con. Observation of carolide gennesmatricon vortex states in yba 2cu 3o 7 christophe berthod,1 ivan maggioaprile,1 jens bruer,1 andreas erb,2 and christoph renner1, 1department of quantum matter physics, university of geneva, 24 quai ernestansermet, 1211 geneva, switzerland. These vortices are increasing in number, placing themselves in networks of vortices that can be observed by means of appropriate techniques. Free superconductivity books download ebooks online textbooks. Bound fermion states on a vortex line in a type ii. Abrikosov vortices occur generically in the ginzburglandau theory of superconductivity, and can be explicitly demonstrated as solutions to that theory in a general mathematical setting, viz. We study the nonequilibrium relaxation properties of ux lines in the presence of. If it is increased, the system becomes unstable and begins to introduce vortices to decrease its energy. Pdf pinning forces in superconductors from periodic. The fluxpinning landscape in typeii superconductors determines the response of the flux line lattice to changing magnetic fields. A periodic vortex structure arises in typeii super conductors in sufficiently strong magnetic fields.
Introduction to superconduct ivity second edition, by michael tinkham. Superconductive magnets achieving magnetic field of about 20 tesla use wire from niobium alloys, and operate at temperature of 4 k cooled by liquid helium. In a clean superconductor they arrange in a hexagonal lattice, while by addition of periodic artificial pinning centers many other arrangements can be realized. The dynamics of magnetic vortices plays a key role in understanding the magnetization process of typeii. Type i superconductor al, nb type ii superconductor nb, most magnet materials massachusetts institute of technology 6. In certain anisotropic cases, the vortices acquire elongated cross sections and interactions. Type ii materials are used for superconductive magnets. On the theory of vortices in typeii superconductors. The model is based on a ginzburglandau gl free energy functional whose coef. In most cases quantum vortices are a type of topological defect exhibited in superfluids and superconductors. Motion of vortices in type ii superconductors siam. A type ii superconductor will only keep the whole magnetic eld out until a rst critical eld h c1 is reached.
Electrodynamics of inhomogeneous typeii superconductors. Vortex states and flux pinning stable levitation of a permanent magnet above a small and flat superconductor only occurs for type ii superconductors. Transport current in the mixed state 181 references 185 1. In erni 2 b 2 c, the magnetic penetration depth, also exhibits a soft vortex type behaviour below b o. Vortex avalanches in superconductors department of physics. In this laboratory work we will study the vortex lattice vl of a typeii supercon. We study a model for the pinning of vortices in a twodimensional, inhomogeneous, typeii superconductor in its mixed state. The ability to carry nondissipative electric currents in strong magnetic fields is one of the fundamental features of type ii superconductors crucial for many applications 1, 2,3,4,5,6,7,8,9,10. Critical current trends in type ii superconductors with pinning. Pdf 1mb avalanche dynamics is found in many phenomena spanning from earthquakes to the evolution of species. Flux vortices in superconductors can be imaged using transmission electron microscopy because the electron beam is deflected by the magnetic flux associated. Pdf vortex dynamics in type ii superconductors researchgate. The core structure of magnetic vortices in typeii superconductors.
In superconductivity, an abrikosov vortex also called a fluxon is a vortex of supercurrent in a type ii superconductor theoretically predicted by alexei abrikosov in 1957. We utilize an elastic line model to simulate magnetic ux lines in disordered typeii super conductors by performing langevin molecular dynamics simulations. Flow dynamics of quantum vortices in typeii superconductors. Any material exhibiting these properties is a superconductor. Vortex liquid crystals in anisotropic type ii superconductors. Dynamics of driven vortices in disordered typeii superconductors harshwardhan chaturvedi abstract we numerically investigate the dynamical properties of driven magnetic ux vortices in disordered typeii superconductors for a variety of temperatures, types of disorder and sample thicknesses.
It is possible for the vortices to be moved over certain distances1,2,6, entangled9, and. Interaction between moving abrikosov vortices in type ii superconductors. A journal of theoretical experimental and applied physics. Pdf ideal gas of vortices in typeii superconductors. The first, lower critical field occurs when magnetic flux vortices penetrate the material but the material remains superconducting outside of these microscopic vortices. Interaction between moving abrikosov vortices in typeii. This dependence is consistent with the mean field theory of soft vortices. The selfenergy of a moving vortex is shown do decrease with increasing velocity. We show that the apex angle of the rhombic cell of yni 2 b 2 c decreases as a function of increasing magnetic field up to a certain constant field, b o.
Most studies into vortex glass behaviour involve measurement or simulation of macroscopic quantities such as transport. It can be also found in vortex matter when a type ii superconductor is externally driven, for example, by increasing the magnetic field. Probing dynamics and pinning of single vortices in. Lasslike distributions of vortices in type ii super conductors have been a subject of intense interest in recent years 1, 2, in both the twodimensional thin. When the vortex density becomes too large, the entire material becomes non. An overview is given of the new theories and experiments on the phase diagram of type ii superconductors, which in recent years have progressed from the abrikosov mean field theory to the vortex. Pinning of flux vortices in type ii superconductors. The methods of formal matched asymptotics are used to examine the motion of a curvilinear vortex in an inhomogeneous type ii superconducting material in the limit as the vortex core radius tends to zero. Model for vortex pinning in a twodimensional inhomogeneous d. Currentinduced organization of vortex motion in typeii.
Type i superconductors are not suitable because of low bc. Earlier we said that for type ii, there is partial penetration of the magnetic field. Flux vortex dynamics in typeii superconductors iopscience. It is the nature of superconductors to exclude magnetic fields meissner effect so long as the applied field does not exceed their critical magnetic field. This actually does happenat lowenoughtemperatures because the vortices getpinned to imperfections in the materials. Introduction if a typeii superconductor is placed in a sufficiently strong magneti fieldc superconductin, g vortices or vortex filaments are produced in it. Above that eld a type i superconductor is no longer in its superconductiong state. Flux expulsion from a superconductor in the meissner state. Pdf flux vortex dynamics in typeii superconductors researchgate. Magnetic fields penetrate a type ii superconductor as magnetic flux quanta, called vortices. The equations for free and forced oscillations of a single elastic vortex line are analyzed taking into account different forces affecting its. Pdf optimized perturbation theory in the vortex liquid. Pdf equilibrium magnetic properties of the mixed state in typeii superconductors were measured with high purity bulk and film niobium samples in.
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