Superconductivity and Mean-Field Theory

A superconductor exhibits perfect conductivity (See Section 7.2) and the Meissner effect (See Section 7.3) below some critical temperature, Tc. The transition from a normal conductor to a superconductor is a second-order, phase-transition which is also well-described by mean-field theory. Note that the mean-field condensation is not a Bose condensation nor does it require and energy gap. The mean-field theory is combined with London-Ginzburg-Landau theory through the concentration of superconducting carriers as follows  

A perfect conductor is one that exhibits zero resistance. In this Section we describe both the observations and the theory. 

A schematic plot of the observed resistance-temperature relations of normal and superconductors is shown in Fig. 7.1 

The conduction in the low-Tc metallic superconductors is isotropic while in the high-Tc cuprate superconductors the conduction takes place along crystal planes 

Here q is the charge, ns(t) is the concentration and t is the mass of the superconducting carriers. The time-derivative of the current density is 

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