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The lattice structure of a high Tc superconductor. |
The copper oxide superconductors are one of the most unusual new classes of materials to be discovered in the past few decades. These materials become superconducting at very high temperatures (relative to other superconductors). The exact mechanism of the superconductivity is still an object of intense study. We have examined the possible roles of anharmonicity in the lattice vibrations, particularly in suppressing the signature of electron-phonon coupling that normally appears in the mass dependence of the transition temperature. We have also studied transport properties, including the possible roles of strongly anisotropic electron scattering.
In the harmonic approximation the phonon frequencies vary as the inverse square root of the atomic mass and the coupling strength lambda is mass independent. Within a simple model anharmonicity changes the mass dependence of the phonon frequencies and gives lambda a mass dependence. For multiple-well potentials, the frequency becomes more strongly mass dependent while the coupling strength gains the opposite mass dependence. For example, a double delta function potential yields a frequency which varies inversely with the first power of the mass while lambda is proportional to the mass. The two mass dependences roughly cancel, yielding a small residual isotope effect at moderate coupling.
The oxygen isotope effect in the doped 214 materials undergoes an unusual evolution as a function of doping. At low doping the transition temperature is small and the isotope effect is about 0.4. At higher doping the isotope effect increases well above one half before plummeting to 0.1 near optimal doping for the material with highest transition temperature. This variation can be modelled with an potential in which a single harmonic well develops side lobes as a function of doping. The side lobes initially weaken the central well, which enhances the isotope effect. As the side lobes begin to dominate, the isotope effect is suppressed. Such a potential might be associated with the incipient structural or electronic phase transitions present around the relevant doping levels.