Critical Fluctuation of the Order Parameter in a Superconductor. I

Abstract

The fluctuation of the order parameter in a superconductor in the temperature slightly above the transition temperature is studied in the framework of the current microscopic theory. It is convenient to divide the temperature region where the fluctuation of the order parameter becomes important into two regions; the classical and the critical region. In the classical region the spatial correlation of the fluctuation is of the Ornstein-Zernike type, while in the critical region it depends on the relative distance like r-3/2. We show that the electrical resistivity, the nuclear spin lattice relaxation time and the ultrasonic attenuation coefficient decrease like 1-a|η|-1/2 and 1-a'|η|-1/3 in the classical and in the critical region respectively, where η=(T/Tc)-1 and a and a' are constants of the order (Tc/µ)1/2(lp0)-3/2 and (Tc/µ)1/3(lp0)-1 respectively. Here µ is the chemical potential, l is the electronic mean free path and p0 is the fermi momentum. It is also shown that the thermal conducivity has no singular term at the transition temperature.