THEORY OF SUPERCONDUCTIVITY - NEW FORMULA FOR THE CRITICAL-TEMPERATURE

Based on the BCS Hamiltonian, the normal-to-super phase transition is investigated, approaching the critical temperature T(c) from the high temperature side. Non-zero momentum Cooper pairs, that is, pairs of electrons (holes) with antiparallel spins and nearly opposite momenta above T(c) in the bulk limit, are shown to move like free bosons with the energy (epsilon)-momentum (p) relation epsilon = 1/2nu(F)p, where nu(F) represents the Fermi velocity. The system of free Cooper pairs undergoes a phase transition of the second order at the critical temperature T(c) given by k(B)T(c) = 1.00856HBARnu(F)n1/3, where n is the number density of Cooper pairs. The ratio of the jump of the heat capacity, DELTAC, to the maximum heat capacity, C(s), is a universal constant: DELTAC/C(s) = 0.60874; this number is close to the universal constant 0.588 obtained by the finite-temperature BCS theory.