Superconductivity interpreted as k-space magnetism

Abstract

In preceding papers the author proposed a new mechanism of Cooper pair formation that follows within an extended Heisenberg model. The new mechanism operates in narrow, partly filled "superconducting" energy bands of special symmetry and shows resemblances, and also great differences as compared with the familiar BCS mechanism. In the present paper the resulting superconducting state is interpreted as a state in which the spins are ordered within the k space. In this picture, the peculiar features of the new mechanism, as compared with the BCS mechanism, can be understood in a straightforward manner. On the one hand, the new mechanism resembles the BCS picture, because the formation of Cooper pairs is still mediated by bosons (having dominant phonon character in the isotropic lattices of the conventional superconductors). On the other hand, however, the pair formation is not the result of an attractive electron-electron interaction mediated by these bosons. Rather, the bosons carry the crystal-spin angular momentum $hbar$ and generate in a new way constraining forces that constrain the electrons to form Cooper pairs. The scale of the transition temperatures in conventional and high-temperature superconductors is set by the excitation energies of stable crystal-spin-1 bosons that are different in isotropic and anisotropic materials.