Effective Field Approach to Metallic Superconductors

Abstract

The paired electrons of a formed Cooper pair, orbiting each other, behave like tiny magnets. This suggests a simple and straightforward effective field approach to superconductivity, at least for the simplest superconductors: some metallic elements in the periodic table. For temperatures below the transition temperature TC, one may assume a spontaneous magnetic field BS= 4π NS μ, where NS is the number of bound pairs, and μ the elementary dipole moment of a Cooper pair. Simple statistical mechanics allows us to obtain the effective field expression for BS as a function of temperature for T ≤ TC. Only two experimental pieces of information, the critical temperature TC and BS0, the critical magnetic field al 0 K, are then necessary to describe the superconductive behaviour. Groups of elements such us [Ti, Zr, and Hf (hcp)], [V, Nb and Ta (bcc)], and [Cr, Mo and W (bcc)] are examined, as well as groups of alloys with relatively high T C values.