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some considerations on the newly discovered superconducAnother measurable quantity which could unveil signativity at Tc = 39 in MgB2 [7]. This material has a structure tures of nonadiabaticity is the normal state Pauli suscepsimilar to that of GICs with the boron atoms forming tibility. As pointed out some time ago by Fay and layers of two-dimensional honeycomb lattices. However, Appel [17], the lowest order electron-phonon correction contrary to the GICs, the Fermi level crosses the in-plane to is a vertex diagram, so that the renormalization of -bands leading to a markedly two-dimensional character the Pauli susceptibility is of order P = ph/EF. In the of the electronic properties. Moreover, the charge transfer adiabatic regime, therefore, is expected to be unaffected of the intercalated Mg atoms is such that the -bands are by the electron-phonon interaction. Conversely, when P is no longer negligible, acquires a dependence on and ph slightly doped with holes and the distance of the Fermi level crossing from the top of the band is only about 0.5 eV [20].

which could be detected by suitable experiments. We have This feature, together with the high phonon frequency of calculated the nonadiabatic effects on the Pauli susceptibility the boron atoms (ph up to 0.1 eV) indicates that MgBfor different stages of a perturbation theory in P and the could be in the nonadiabatic regime of the electron-phonon results are shown in Fig. 3 [18]. In the figure, the dashed interaction. An additional interesting point is that MgB2 is lines refer to a simple ladder vertex correction while the solid far away fromhalf-filling and in this case it has been shown lines are the results obtained by including the second order that the vertex corrections are mainly positive leading to nonadiabatic terms for different values of the momentum an amplified pairing even in the absence of strong electron cut-off Qc = qc/2kF. For P 0, both approximation correlations [21]. Further analysis of the relevance of this schemes reduce to the ME results = 0 = 2BN0, where hypothesis is currently under development.

B is the Bohr magneton and N0 is the density of states at the Fermi level. The first main result (Fig. 3, a) is that in References the nonadiabatic regime (P = 0) is sensibly reduced with respect to the adiabatic limit 0. Hence, is no longer simply [1] A.B. Migdal. Sov. Phys. JETP 7, 996 (1958).

proportional to N0. This means that disregarding the electon[2] G.M. Eliashberg. Sov. Phys. JETP 11, 696 (1960).

phonon effects would lead to a substantial underestimation [3] O. Gunnarsson. Rev. Mod. Phys. 69, 575 (1997).

of the bare density of states from a spin susceptibility [4] Y.J. Uemura et al. Nature (London) 352, 605 (1991).

[5] S.K. Watson et al. Phys. Rev. B55, 3866 (1997).

measurement as long as the system is in the nonadiabatic [6] J.H. Schn, Ch. Kloc, B. Batlogg. Nature (London) 408, regime. A more striking consequence of the nonadiabatic (2000).

effects on is that now the Pauli susceptibility acquires [7] J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, J. Akian ion mass dependence which is reflected in a non-zero mitsu. Nature (London) 410, 63 (2001).

and negative isotope coefficient = -d ln()/d ln(M) [8] M. Schluter et al. Phys. Rev. Lett. 68, 526 (1992); M. Schluter (Fig. 3, b). The observation of such an isotope effect, et al. J. Phys. Chem. Solid 53, 1473 (1992); J.C.R. Faulhaber absent in the ME regime, represents a stringent test of the et al. Phys. Rev. B48, 661 (1993); C.M. Varma et al. Science nonadiabatic hypothesis.

254, 989 (1991); V.P. Antropov et al. Phys. Rev. B48, (1993); N. Breda et al. Chem. Phys. Lett. 286, 350 (1998).

A further interesting qualitative difference between the [9] M.S. Fuhrer, K. Cherrey, A. Zettl, M.L. Cohen, V.H. Crespi.

ME and the nonadiabatic regimes is the response of the Phys. Rev. Lett. 83, 404 (1999).

superconducting state to disorder and non-magnetic im[10] J.P. Carbotte. Rev. Mod. Phys. 62, 1027 (1990).

purities. Within the adiabatic regime, isotropic s-wave [11] E. Cappelluti, C. Grimaldi, L. Pietronero, S. Strssler. Phys.

superconductors are robust against the presence of weak Rev. Lett. 85, 4771 (2000).

disorder. In particular Tc is nearly independent of the [12] C. Grimadli, L. Pietronero, S. Strssler. Phys. Rev. Lett. 75, amount of disorder. This situation changes when we consider 1158 (1995).

nonadiabatic superconductors [19]. In fact, the vertex [13] L. Pietronero, S. Strssler, C. Grimaldi. Phys. Rev. B52, 10 correnctions are quite sensitive to the amount of disorder (1995); ibid. 52, 10 530 (1995).

[14] M.L. Kulic. Phys. Rep. 338, 1 (2000) and references therein.

in such a way that the effective nonadiabatic pairing is [15] P.J. Benning et al. Science 252, 1417 (1991).

reduced. Therefore, for an s-wave superconductor in the [16] C. Grimaldi, E. Cappelluti, L. Pietronero. Europhys. Lett.

nonadiabatic regime, disorder would reduce Tc contrary to 42,667 (1998).

the expectations of the ME theory [19]. It is remarkable [17] D. Fay. J. Appel. Phys. Rev. B20, 3705 (1979); ibid 22, that a Tc-reduction under ion irradiation has been recently (1980).

reported for K3C60 [5].

[18] E. Cappelluti, C. Grimaldi, L. Pietronero. Phys. Rev. B (to be In summary, we have shown how the breakdown of published).

Migdals theorem and the opening of nonadiabatic channels [19] M. Scattoni, C. Grimaldi, L. Pietronero. Europhys. Lett. 47, 588 (1999).

identify the fulleride superconductors as non-conventional [20] J.M. An, W.E. Pickett. Phys. Rev. Lett. 86, 4366 (2001).

materials. The physics of such systems is largely governed [21] A. Perali, C. Grimaldi, L. Pietronero. Phys. Rev. B58, by nonadiabatic interference effects which are reflected in (1998).

anomalous behaviors of observable quantities such as m,, , 2002, 44, .

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