PREFACE

A unified theory of superconductivity in elements, compound and cuprates is presented. Superconductivity is the most striking phenomenon in solid state physics. The electrical resistance due to impurities and phonons in a metal suddenly drops to zero below a critical temperature Tc. Not all elemental metals show superconductivity, which suggests that the phenomenon depends on the lattice structure and the Fermi surface. In a histric 1957 paper Bardeen, Cooper and Schrieffer (BCS) start with a reduced Hamiltonian H0 containing “electron” and “hole” kinetic energies and a pairing interaction, calculate the ground-state energy E0 to obtain E0 = N0w0, where N0 is the number of the Cooper pairs (pairons) and w0 the ground-state energy of a pairon, using the energy minimum principle. They also obtain the zero temperature energy gap equation (18.32), the solution of which yields the ground-state energy w0 and the excitation energy Ek = √ 2 k + 0, where k is the “electron” (or “hole”) energy with the momentum k, and 0 the energy gap. The reduced Hamiltonian H0 and the trial ground-state vector can be written in terms of the pairon variables only while only quasi-electron variables appear in the gap equation. Hence it is impossible to guess even the existence of a gap in the quasi-electron energy spectrum. We recalculate the ground-state energy and the quasi-electron energy, using the standard quantum statistical methods. Our calculations are lengthy, but we have a major advantage: no need of guessing of the trial ground-state vector. BCS extended their theory to a finite temperature. They obtained a temperature-dependent energy gap equation, the solution of which yields the famous connection between the critical temperature Tc and the zero-temperature gap 0: kB Tc = (1.77)−1 0. The cause of superconductivity is well established by the BCS theory. It is the phonon exchange attraction, which binds a Cooper pair composed of two electrons with opposite spin directions. The Center-of-Mass (CM) motion of a composite is bosonic (fermionic) according to whether the composite contains an even (odd) number of elementary fermions. The Cooper pairs, each having two electrons, move as bosons. In the ground state there can be no currents super or normal. We must consider moving pairons with finite CM momenta for the supercurrents. Cooper found that Cooper pairs move with a linear dispersion relation: = w0 + (1/2)vFp, where vF is the Fermi velocity (magnitude). This relation was obtained for a three-