Anharmonic phonons and the isotope effect in superconductivity

Vincent Henry Crespi, Marvin L. Cohen, David R. Penn

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34 Scopus citations


Anharmonic interionic potentials are examined in an Einstein model to study the unusual isotope-effect exponents for the high-Tc oxides. The mass dependences of the electron-phonon coupling constant and the average phonon frequency 2 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 Schrödinger's equation for double-well potentials produce 's in the range 1.5-4 for a material with a vanishing isotope-effect parameter . However, low phonon frequencies limit Tc to roughly 15 K. A negative quartic perturbation to a harmonic well can increase above 1/2. In the extreme-strong-coupling limit, is 1/2, regardless of anharmonicity.

Original languageEnglish (US)
Pages (from-to)12921-12924
Number of pages4
JournalPhysical Review B
Issue number16
StatePublished - Jan 1 1991

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics


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