Superconducting temperature, equation

The BCS theory leads to the following equation for the critical temperature, Tc, for superconductivity ... 

At low temperatures, matter will undergo a transition to a color-superconducting state, with a different quasiparticle structure than presumed in our quasiparticle approach. Nonetheless, pairing affects the thermodynamic bulk properties only at the relative order of 0(A2/fi2), where the estimated gap A < 100 MeV is comfortably smaller than the chemical potential. Therefore, our equation of state is a reasonable approximation even at small temperatures (maybe except for the pressure where it becomes very small). 

For small asymmetries, the superconducting state is homogeneous and the order parameter preserves the space symmetries. For most of the systems of interest the number conservation should be implemented by solving equations for the gap function and the densities of species self-consistently. In such a scheme the physical quantities are single valued functions of the asymmetry and temperature, contrary to the double valued results obtained in the non-conserving schemes. 

Fig. 7.15 Conductivity cr (solid symbols) and superconductivity transition temperature Tc (open symbols) in Bi-Kr as functions of atomic bismuth concentration x The solid line is a fit to the equation a=const x (x—xc)v with xc=0.55 and v = 1.07. The dashed lines...

It would be interesting to carry out experiments on S/F structures with non-collinear magnetization in order to observe this new type of superconductivity. As follows from a semiquantitative analysis, the best conditions to observe the Josephson critical current caused by the TC are high interface transparency (small y ) and low temperatures. These conditions are a bit beyond our quantitative study. Nevertheless, all qualitative features predicted here (angle dependence, etc) should remain in a general case when one has to deal with the non-linear Usadel equation. 

Planar resonators - Equation (5.11) is not only valid for dielectric resonators. Any other type of electromagnetic resonator employing dielectric parts, like metal ceramic coaxial-type resonators (e.g. used as filters in mobile phones) and microstrip or coplanar resonators (used in microwave integrated circuits) have a Q-contribution due to dielectric losses. For the latter type of resonator the dielectric losses are negligible in comparison to metallic losses, unless high temperature superconducting metallization layers are applied. 

Figure 3. The superconductive transition temperature, Tc, as a function of distance, ctr, from the metal/insulator transition (ctr =0) for nine alloy systems. The data points are shown as solid circles, and the solid curves represent fits to equations 2. The fitting parameter, a, is given in parentheses for each system Nb3Sn (0.01), NbTi (0.69), VTi (1.5), TaTi (2.5), MoTi (6.), MoGe (15), ReMo (11), MoSi (17), and WSi (24.1).

The emergence of superconductivity in electronic systems close to a ferromagnetic instability has recently been studied by solving a linearized gap equation within the Eliashberg formalism [3-5], In both two- (2D) and three-dimensional (3D) systems, it was found that the superconducting transition temperature, Tlc (T stands for linearized) substantially decreases as the sys-... 

Following the widespread acceptance of the view that silicate perovskites may be major components of the lower mantle (see Jeanloz and Thompson, 1983), there have been a number of attempts to calculate the structure, elastic properties, and equations of state of these materials (Wolf and Jeanloz, 1985 Wolf and Bukowinski, 1985, 1987 Matsui et al., 1987 Hemley et al., 1987). A great deal of interest has also been generated in the crystal chemistry of perovskite-structure phases because of their high-temperature superconducting properties. 

We can now calculate the superconductive transition temperature through the approximate solution of the Eliashberg equation, given the intra-molccular deformation potentials These, and the vibrational frequencies, were calculated using the quahtum-chemical MNDO semi-empirical technique (IS). This method has been successfully used previously on a wide variety of... 

BCS theory, developed by John Bardeen, Leon Cooper, and Robert Schrieffer, provides complicated mathematical equations that satisfactorily explain the superconductivity of the classical low temperature superconductors with... 

At the outset, it must be emphasised that the definition of low temperature is arbitrary. A life scientist would normally equate low temperature with subzero Celsius temperature , whereas to a physicist, perhaps studying superconductivity phenomenon, the term signifies temperatures in the neighbourhood of 1 Kelvin. The reason why low temperature is often equated with freezing is probably because the freezing point of ordinary water lies near the centre (measured in degree Celsius) of the temperature range —40 to - -40°C, which we associate with life processes on this planet. 

Equation 31 shows that the maximum superconducting transition temperature expected in the BCS theory is limited by the Debye temperature. This temperature plays a central role because the distortion ofthe lattice in response... 

---