Crespi, V.
, Cohen, M.
and Penn, D.
(1991),
Anharmonic Phonons and the Isotope Effect in Superconductivity, Physical Review B (Condensed Matter and Materials Physics), [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=620376 (Accessed April 27, 2026)
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Anharmonic Phonons and the Isotope Effect in Superconductivity
Published
Author(s)
V Crespi, Marvin Cohen,
Abstract
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.Citation
Physical Review B (Condensed Matter and Materials Physics)
Volume
43
Issue
16
Pub Type
Journals
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Created January 1, 1991, Updated April 21, 2026