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Anharmonic Phonons and the Isotope Effect in Superconductivity



V Crespi, Marvin Cohen, David R. Penn


Anharmonic interionic potentials are examined in an Einstein model to study the unusual isotope-effect exponents for the high-T(c) oxides. The mass dependences of the electron-phonon coupling constant λ and the average phonon frequency square-root <ω2> are computed from weighted sums over the oscillator levels. The isotope-effect exponent is depressed below 1⁄2 by either a double-well potential or a potential with positive quadratic and quartic parts. Numerical solutions of Schrodinger's equation for double-well potentials produce lambda's in the range 1.5-4 for a material with a vanishing isotope-effect parameter-alpha. However, low phonon frequencies limit T(c) to roughly 15 K. A negative quartic perturbation to a harmonic well can increase-alpha above 1⁄2. In the extreme-strong-coupling limit, alpha is 1⁄2, regardless of anharmonicity.
Physical Review B (Condensed Matter and Materials Physics)


Crespi, V. , Cohen, M. and Penn, D. (1991), Anharmonic Phonons and the Isotope Effect in Superconductivity, Physical Review B (Condensed Matter and Materials Physics) (Accessed June 4, 2023)
Created December 31, 1990, Updated October 12, 2021