The Motivation for an Alternative Pairing Mechanism

For the high-T_c superconductors, there are several experimental and theoretical reasons for seriously questioning traditional BCS theory with a simple phonon-induced electron-electron interaction. Experimentally, an extremely small isotope effect measured for $\mbox{YBa$_{2}$ Cu$_{3}$ O$_{7- \delta}$ }$is often cited as one such deterrent [17]. BCS theory predicts an isotope shift if T_c is determined by the motion of the oxygen ions; however, substitution of ¹⁸O for ¹⁶O in $\mbox{YBa$_{2}$ Cu$_{3}$ O$_{7- \delta}$ }$ does not significantly change T_c. Ruling out a phonon-induced pairing mechanism based on these observations is premature however. The presence of an isotope shift implies that the lattice is certainly involved in the pairing mechanism. However, one cannot assume that the lack of an isotope effect necessarily implies that the pairing mechanism does not involve phonons. Superconductors such as ruthenium and zirconium exhibit virtually no isotope effect, while uranium shows a negative isotope effect [46]. The problem is that there are many additional factors which can effect the strength of the isotope shift. Thus, by itself the lack of a significant isotope effect in $\mbox{YBa$_{2}$ Cu$_{3}$ O$_{7- \delta}$ }$ is not enough to rule out an electron-phonon mechanism.

The anomalous normal-state properties of the cuprates suggest that these materials are not just a normal Fermi liquid above T_c, and therefore may not be adequately described by BCS theory below T_c. The electrical dc resistivity $\rho (T)$, exhibits a linear dependence in temperature over a wide range of temperatures above T_c. For a conventional Fermi liquid associated with normal metals, $\rho(T) \sim T^{2}$. This is a manifestation of the long lifetime of electrons near the Fermi surface in a conventional Fermi liquid [47]. The nuclear spin-lattice relaxation rate T₁^-1 (T)shows a temperature dependence substantially different from that of normal metals. Other anomalous normal-state properties of the copper-oxide superconductors include the thermal conductivity $\kappa (T)$, the optical conductivity $\sigma (\omega)$, the Raman scattering intensity $S(\omega)$, the tunneling conductance as a function of voltage g(V), and the Hall coefficient R_H (T) [48]. All of these normal-state properties are quite uncharacteristic of the Fermi liquid usually associated with the normal state of conventional superconductors. In fact, it is possible that the unusual normal-state properties of the high-T_c compounds cannot be appropriately described by a Fermi liquid.

Some argue on theoretical grounds that BCS theory cannot explain the high transition temperatures of the cuprates. For example, it has been suggested that an electron-phonon mechanism probably cannot account for transition temperatures in excess of 40 to 50K [49]. The magnitude of the electron-phonon interaction required to generate a T_c comparable to that of $\mbox{YBa$_{2}$ Cu$_{3}$ O$_{7- \delta}$ }$, would substantially weaken the lattice. This structural instability would greatly reduce the density of electron states at the Fermi surface and hence destroy superconductivity [18]. This argument is not accepted by all. It has been suggested that the calculations leading to the above conclusion are not valid, so that an electron-phonon mechanism may still be the basis for superconductivity in the high-temperature superconductors [50].