Superconducting temperature dependence

Uranium metal is weaMy paramagnetic, with a magnetic susceptibility of 1.740 X 10 A/g at 20°C, and 1.804 x 10 A/g (A = 10 emu) at 350°C (51). Uranium is a relatively poor electrical conductor. Superconductivity has been observed in a-uranium, with the value of the superconducting temperature, being pressure-dependent. This was shown to be a result of the fact that there are actually three transformations within a-uranium (37,52). 

Metals and semiconductors are electronic conductors in which an electric current is carried by delocalized electrons. A metallic conductor is an electronic conductor in which the electrical conductivity decreases as the temperature is raised. A semiconductor is an electronic conductor in which the electrical conductivity increases as the temperature is raised. In most cases, a metallic conductor has a much higher electrical conductivity than a semiconductor, but it is the temperature dependence of the conductivity that distinguishes the two types of conductors. An insulator does not conduct electricity. A superconductor is a solid that has zero resistance to an electric current. Some metals become superconductors at very low temperatures, at about 20 K or less, and some compounds also show superconductivity (see Box 5.2). High-temperature superconductors have enormous technological potential because they offer the prospect of more efficient power transmission and the generation of high magnetic fields for use in transport systems (Fig. 3.42). 

TES are based on the steep temperature dependence of the resistance of superconducting metallic films. The useful temperature range is very narrow. These thermometers which may have a very low intrinsic noise, are fabricated by a vacuum deposition process at very low pressure and are patterned either by photolithography technique (see e.g. ref. [21]) or by micromechanical machining (see e.g. ref. [22]). The dimensionless parameter a = T/R-dR/dT defines the DC quality of a sensor. TES with a as high as 1000 have been built [23],... 

The temperature dependence of the pairing gap for the homogeneous, LOFF and DFS superconducting phases shows the phenomenon of reentrance the superconducting state is revived at finite temperatures. There exist two critical temperatures corresponding to phase transitions from the normal to the superconducting state and back as the temperature is increased from zero to finite values. 

S5 — Sjv)r—o = yT- The behaviour of y in the superconducting state is different from that of the normal state y is a linear function of temperature in the normal state but its temperature dependence is exponential in the superconducting state. The superconducting transition at zero magnetic field is a second-order phase transition since there is discontinuity in specific heat but no latent heat change. 

Fig. 38. (a) Resistivity vs. temperature measured at different magnetic fields H on a polycrystalline HoNi2B2C sample. Tc is the superconducting transition temperature at H = 0. A near-reentrant behaviour occurs around a temperature Tn. (b) Temperature dependence of the specific heat Cp of a HoNi2B2C single crystal (2 mm x 3 mm x 0.1 mm in size), measured at zero magnetic fiekL Above the main peak of Cp(T) at Tn. two additional features appear (marked by arrows). Samples prepared by I. Freudenberger. 

Fig. 47. (a) Temperature dependence of the specific heat C as aC/T-vs.-T2 plot for TmNi2B2C. The maximum at 7"c indicates the transition to superconductivity and the low-temperature upturn is related to magnetic ordering. The solid line is calculated taking into account contributions from phonons and crystal field levels (b) specific heat of TmNi2B2C at low temperatures with a maximum at Tn (after Movshovich et al. 1994). 

The list of materials which displayed such type of behaviour contains amorphous Mo Gei j, [1] and Moa,Sii a [2] films, amorphous InOx films [3, 4], ultrathin films of Be [5], crystalline films of Nd2-a Cea Cu04+y [6, 7]. Two typical examples of such sets of curves relevant to different limits are presented in Figs. 1 and 2. In Nd2-a Cea Cu04+ / (Fig. 1) the growth of the resistance with decreasing temperature on the non-superconducting side of the field-induced transition was below ten percent so that it reminded more a metal with quantum corrections to its conductivity than an insulator. In amorphous InO (Fig. 2), typical for insulator exponential temperature dependence of the resistance resulted in almost tenfold increase of the resistance. 

Summary. On the basis of phenomenological Ginzburg-Landau approach we investigate the problem of order parameter nucleation in a ferromagnetic superconductor and hybrid superconductor - ferromagnetic (S/F) systems with a domain structure in an applied external magnetic field H. We study the interplay between the superconductivity localized at the domain walls and between the domain walls and show that such interplay determines a peculiar nonlinear temperature dependence of the upper critical field. For hybrid S/F systems we also study the possible oscillatory behavior of the critical temperature TC(H) similar to the Little-Parks effect. 

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