Type I superconductors

The Ginzburg-Landau theory for the CFL phase has been derived in Refs. [10, 16-19], The authors of Ref. [19] have taken into account the rotated electromagnetism and the rotation of the star. They conclude that ordinary quantized magnetic vortices are unstable in the CFL phase, but the rotational vortices are topologically stable. They have not considered boundary problems and concluded that the CFL condensate in an external magnetic held behaves like a type I superconductor. 

The magnetic field induced by the current cancels the magnetic field induced in the superconductor by the magnet. This is the origin of the perfect diamagnetism of Type I superconductors. 

Levitation in Type I superconductors is, however, a rather ephemeral effect. The absence of restraints on the lateral motion of the magnet eventually result in the magnet falling at the side of the superconductor. 

Tcr cuprates), whose superconductivity depends on subtle, phonon-free coupling between electrons. It is interesting that the highest known temperature Type-I superconductor, MgB2, shows a much larger isotope effect than does mercury (TCr (MgnB2) = 39.2 K, TCr (Mg10B2) = 40.2 K). 

In addition to a critical temperature and critical field, all superconductors have a critical current density, Jc, above which they will no longer superconduct. This limitation has important consequences. A logical application of superconductors is as current-carrying media. However, there is a limit, often a low one, to how much current they can carry before losing their superconducting capabilities. The relationship between Jc, He, and Te for a Type II superconductor is shown in Figure 6.32. Notice that the Hc-Tc portion of this plot has already been presented in Figure 6.10 for a Type I superconductor. 

Liquid crystals have found widespread application in optical display devices as well as in detection of temperature uniformity and impurities. These properties are related to the orientational order of molecules in the temperature region between and the melting point. The possible applications of ferroelectric liquid crystals are promising. Superconductors (type II) can be used to create high magnetic fields at low power the ability of type I superconductors to trap magnetic flux within the domains of the normal material may also have applications. 

Figure 6.9 Properties of superconductors (a) resistivity-temperature curve for a pure (solid) and an impure (broken) superconductor (b) magnetization as a function of external field for type I superconductor (c) magnetization curve for a type II superconductor.

Conductor-Superconductor Transition When some metals or compounds are cooled below a certain temperature, their electrical resistance drops abruptly to zero. This temperature is referred to as the superconducting transition temperature. These materials are classified into two categories, type I or type II superconductors, depending upon how a bulk sample behaves in an external magnetic field. In the absence of an external magnetic field, the (superconductor + normal) transition is continuous in both types of superconductors. When a magnetic field is applied, the transition becomes first order in type I superconductors, but remains continuous in the type II superconductors. 

Figure 13.16 Magnetization verses applied magnetic field for (a) a type I superconductor and (b) a type II superconductor. For the type I superconductor, the magnetic flux does not penetrate the sample below 9 Cc where the sample is a superconductor. Above rMc, the sample is a normal conductor. For the type II superconductor, the magnetic field starts to penetrate the sample at 3Cc, 1, a magnetic field less than rXc, the thermodynamic critical field. Superconductivity remains in the so-called vortex state between 9 c and Ci2 until WCt2 is attained. At this magnetic field, complete penetration occurs, and the sample becomes a normal conductor.

Figure 13.17 (a) Typical graph of critical magnetic field 3Cc as a function of temperature for a type I superconductor. Magnetic fields greater than 3tc suppress the superconducting transition, (b) Critical magnetic fields for several type I superconductors. 

Soft metallic elements such as Al, In, Pb, Hg, Sn, Zn, Tl, Ga, Cd, V and Nb are type I superconductors. Alloys and chemical compounds such as Nb3Sn, V3Ga, and lZa3In, and some transition elements, are type II superconductors. Type II substances generally have a higher Tc than do type I superconductors. The recently discovered transition metal oxide superconductors have generated intense interest because they are type II superconductors with very high transition temperatures. Table 13.1 summarizes Tc for selected superconductors. 

Figure 13.18s illustrates the behavior of the entropy and heat capacity respectively of aluminum (a type I superconductor) in the vicinity of its (continuous) superconducting transition. Referring back to Figure 13.1, we... 

If a Type I superconductor such as lead is placed in a small magnetic field (e.g. a few mT) and cooled, then at 7[. the magnetic field is expelled from the interior of the specimen. This is the Meissner effect, which is fundamental to the superconducting state it is not simply characteristic of a material which happens to be a (fictitious) perfect conductor. The total absence of an electric field in a... 

Fig. 4.53 The induced magnetic moment (nQM) as a function of applied field for (a) a Type I superconductor and (b) a Type II superconductor.

Below Tc the applied magnetic field can be increased up to a critical value Bc, when the superconductor changes to the normal state. This behaviour is characteristic of a Type I superconductor. 

Because useful currents carried by a Type I superconductor generate magnetic fields it follows that there are also critical current densities Jc, corresponding to the critical applied magnetic fields. In a Type II superconductor the... 

When an applied current, called a transport current, is caused to flow through a superconductor it induces magnetic fields near it. For a Type I superconductor, this current flows in a surface layer of thickness k, where k is the penetration depth, corresponding to an area A = 27rRk. The current I = AJ is given by... 

The levitation demonstration works only with Type II superconductors because the magnetic field lines that do enter the superconductor resist sideways motion and allow the balance of magnetic repulsion and gravitation to float the magnet above the superconductor. With Type I superconductors, the magnetic field lines cannot enter the superconductor at all and, because there is no resistance to sideways motion, the magnet will not remain stationary over the superconductor. 

Superconductivity [1.35]. Timgsten is a Type I superconductor with a transition temperature of 0.0154 0.0005 K. The critical magnetic field strength -> 0) is 1.15 0.03Oe. (91.5 A-m ). Impurities only show a minor influence on the transition... 

Bardeen (along with Leon Neil Cooper and John Robert Schrieffer) won a second Nobel Prize in 1972 for their jointly developed theory of superconductivity, usually called (using the last initials of the three scientists) the BCS theory. In essence, BCS theory explains the phenomenon of superconductivity in Type I superconductors—metals, such as mercury, lead, and niobium. 

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