ISOTOPE EFFECT IN MgB2
The presence of an isotope effect is a strong indicator of phonon
mediation of the superconducting coupling. The large isotope effect
measured by Bud'ko et al[PRL 86, 1877 (2001)] for boron (alphaB=0.26
+/- 0.03) clearly shows that phonons associated with boron vibrations
play a significant role in the superconductivity of MgB2.
Recent work of D. G. Hinks, H. Claus, and J. D. Jorgensen (to be appear
in Nature) indicates a very small isotope effect (alphaMg = 0.02) for Mg,
suggesting that Mg phonons are not important in the superconductivity.
They obtained a total isotope effect of 0.32, much reduced from the
BCS HARMONIC PHONON VALUE of 0.5.
Since in our theory of superconductivity of MgB2, the most important
phonons are identified to be the in-plane boron modes, we expect no isotope effect
(i.e. alphaMg = 0) for Mg, in agreement with Hinks et al's measurements.
For the boron isotope effect, we showed that the
canonical potential for the
in-plane boron modes are very anharmonic. Because of this giant anharmonicity, the
phonon energies are no longer proportional to 1/sqrt(mass), suggesting significant
reduction of the isotope coefficient from 0.5.
Indeed, we solved the 1D Schrodinger equation for different boron mass using
the anharmonic E2g potential and calculated the mass dependence of
phonon energies, EP-coupling lambda, and the TC. The results are
summarized in this figure .
From ln(Tc) versus ln(mass) plot,
we calculated the boron isotope effect
to be 0.21, in good agreement with the experimental value of 0.26 =/-0.03.
In conclusion, within our theory of anharmonic and non-linear EP coupling,
we can explain not only the high TC but also the large reduction
of the boron isotope effect.