Theory of High Temperature Superconductivity

Abstract

Abstract.We deal with a model for high-temperature superconductivity which maintains that in cuprates spin-singlet bonds are formed between electrons running in the neighbouring layers of copper oxide found in lattice of these materials. This model reutilizes the BCS scheme, but with the essential difference that the electron pairs are characterized by equal, rather than opposite, momenta as in Cooper pairs. In the present paper, we consider the electron pair formation and a peculiar canonical transformation analogous to the transformation once applied to the theory of pairing correlations in nuclear matter. It is shown that the quasi-particle energy spectrum remains that of the BCS theory, including the linear relationship between forbidden energy gap and critical temperature. The model is also applied to superconductivity of some copperless perovskites of mixed stoichiometry, whose features are of special worth in understanding the mechanism of the phenomenon. The possibility of enhancing critical temperature in cuprates by inserting monovalent ions into the lattice is considered.PACS: 74.20.-z; 74.72.JT.

Quantum Statistical Theory of Superconductivity in MgB<sub>2</sub>

“…which indicates a close connection between the zero temperature gap ( ) g 0 ε and the critical temperature c T . A rigorous treatment of the BEC of free pairons shows a phase transition of the third order [13]. The molar heat rises like 2 T , reaches 4.38 R (R = gas constant) at c T , and then decreases to 2R in the high-temperature limit [14] as shown in Figure 4.…”

“…BCS [5] assumed the existence of Cooper pairs [12] in a superconductor, and wrote down a Hamiltonian containing the "electron" and "hole" kinetic energies and the pairing interaction Hamiltonian with the phonon variables eliminated. We start with a BCS-like Hamiltonian  for the QHE: [13]…”

“…The pairing interaction terms in Equation 12are formally identical with those in the generalized BCS Hamiltonian [13]. Only we deal here with c-fermions instead of conduction electrons.…”

“…The c-bosons, having the linear dispersion relation, can move in all directions in the plane with the constant [13]. For completeness we show the linear dispersion relation in Appendix.…”