Towards Room-Temperature Superconductivity

Abstract

By taking advantage of a stability criterion established recently, the critical temperature Tc is reckoned with help of the microscopic parameters, characterising the normal and superconducting electrons, namely the independent-electron band structure and a repulsive two-electron force. The emphasis is laid on the sharp Tc dependence upon electron concentration and inter-electron coupling, which might offer a practical route toward higher Tc values and help to understand why high-Tc compounds exhibit such remarkable properties.

Properties of Bound Electron Pairs

“…Thus let us begin with analysing the dependence of T c upon decreasing U 0 /t for the Hubbard Hamiltonian H 0 . Hence, as done elsewhere [5][6][7][8] , the conduction electrons are taken to comprise bound and independent electrons, in respective temperature dependent concentration c s (T ), c n (T ), such that…”

“…( 9) expresses the property that the set of conduction electrons is at stable, thermal equilibrium 5 at T c , whereas Eq. ( 10) ensures that the superconducting phase is stable 7,8 with respect to the normal one for T < T c .…”

“…Eqs. ( 13) are seen to have no solution K ∈ [0, π] for c 0 < 1.64 and there is no U 0 > 0 for c 0 > 1.74, whereas U 0 > 0 has been known as a prerequisite for persistent currents 5 , thermal equilibrium 6 , occurrence of a second order transition 7,8 at the critical temperature T c and the Josephson effect 9 . Likewise there is no solution for TABLE I.…”

“…The paramount role of bound electron pairs in superconductivity 1,2 has ever been known since Cooper's seminal work 3 , even though assuming an attractive interaction between electrons, as done by Cooper and furthermore by BCS 4 , has been shown to be inconsistent with persistent currents 5 , thermal equilibrium 6 , occurrence of a second order transition 7,8 at the critical temperature T c and the Josephson effect 9 . Nevertheless it has been established 6 that the bound electron pair of energy ε B turns continuously into a many bound electron (MBE) state, carrying persistent currents, at finite electron concentration c s .…”

“…Regarding these materials, exhibiting no isotope effect, no cogent explanation has been offered so far, whereas a theory, based on Eliashberg's work 20 , has been widely used for those which do so. Unfortunately it relies heavily on the BCS theory 4 , which has been proved to be marred [5][6][7][8][9] by major inconsistencies, recalled above. Likewise a cornerstone assumption of the BCS scheme 4 requires that the electron-phonon interaction reverse the sign of the Coulomb repulsive force and thus give rise eventually to an effective, attractive coupling between two electrons, located on the same atomic site.…”