Formation of Cooper Pairs as a Consequence of Exchange Interaction

Abstract

Analyzing the exchange energy of two conduction electrons in a crystal we find that the exchange energy may be negative and, thus, a singlet state may be favorable. A full overlap in real space of wave functions of two conduction electrons leads to a deeper exchange energy. Thus, the exchange interaction causes a bond between two conduction electrons in real space. The singlet bond is possible because the singlet electrons can simultaneously and permanently occupy one spatial ground state, so the average energy of paired electrons is lower than the energy of unpaired electrons. Thus, the pairing is a result of the Pauli Exclusion Principle. If conduction electrons, before pairing, are put on the Fermi surface in the momentum space, then every pair may exist permanently in time. The motion of conduction electrons in the crystal may prevent the formation of Cooper pairs, because the kinetic energy of the motion is usually larger than the binding energy in the pair. Conduction electrons as standing waves are local and have zero momenta, hence their momenta are synchronous; therefore, weak singlet bonds are stable despite the large kinetic energy on the Fermi surface. The local pairing of standing waves explains the inverse isotope effect, Tc-dome, insulator-superconductor transitions and many other facts about superconductors. The electron pairs, as bosons, can form a macroscopically coherent Bose-Einstein-Condensate and, thus, become non-dissipative and non-local.