Isotope effect on m * in high- T _c materials due to the breakdown of Migdal's theorem

Abstract

PACS. 71.38+i -Polarons and electron-phonon interactions. PACS. 74.25Kc -Phonons. PACS. 71.18+y -Fermi surface: calculations and measurements; effective mass, g factor.Abstract. -We show that the inclusion of effects beyond Migdal's limit in the electron-phonon interaction naturally leads to an isotope effect for the effective mass m * of the charge carriers even much before reaching the polaron limit. This is the situation already considered in our approach to nonadiabatic superconductivity [7]. Such a result provides a scenario different from the polaronic one for the interpretation of the recently observed isotope effect on m * in YBa2Cu3O6+x and La2−xSrxCuO4 [1, 2].The recent observation of an oxygen-mass dependent penetration depth λ(0) in YBa 2 Cu 3 O 6+x [1] and in La 2−x Sr x CuO 4 [2] has raised the question whether this effect could be attributed to the breakdown of the Migdal approximation [3]. In fact, according to the classical MigdalEliashberg theory of superconductivity, the zero temperature penetration depth in the London limit and in the absence of magnetic impurities [4] is given by:where m * is the electronic effective mass and n s is the supercarrier density. According to eq.(1), an isotope effect on λ(0) can therefore be induced by an isotope effect on m * and/or on n s . However, for T ≪ T c , also assuming an electron-phonon (el-ph) type of pairing, the dependence of n s on the ion-mass M is negligible [5] and a possible isotope-induced dependence of n s on the hole concentration has been ruled out [1,2]. Zhao et al. therefore concluded that the observed isotope effect on λ(0) can be entirely attributed to an oxygen-mass dependent m * . In this hypothesis and by using eq.(1), the oxygen isotope effect on m * , α m * = −d ln(m * )/d ln(M ), has been estimated to be α m * = −0.61 ± 0.09 for YBa 2 Cu 3 O 6.94 [1] and α m * ≃ −0.8 (−0.5) for Typeset using EURO-L a T E X

Pauli susceptibility of nonadiabatic Fermi liquids

“…The effective mass m * represents therefore a clear example of a quantity for which a well established property in the ME regime (α m * = 0) is drastically modified in the nonadiabatic one (α m * = 0). So far, strong evidences for isotopedependent m * have been reported for YBa 2 Cu 3 O 6+x and La 2−x Sr x CuO 4 [13] and theoretical calculations have shown that already the inclusion of the first nonadiabatic vertex correction to the ME limit provides values of α m * with sign and order of magnitude in agreement with those estimated by the experiments [12].…”

Nonadiabatic contribution to the quasiparticle self-energy in systems with strong electron-phonon interaction

“…Cappelluti, C. Grimaldi, L. Pietronero, and S. Strässler [16][17][18][19] give correct estimations of the order of magnitude and sign of the nonadiabatic corrections to the self-energy. The analytical results were compared with numerical calculations.…”

“…An approximation for q → 0 was used 24 and then q c = Q c · 2p F was set to q c = 2p F giving the following result 19 for Z:…”

HighTcSuperconductivity inMgB2by Nonadiabatic Pairing

“…The detection of isotope effects on various quantities receives a crucial importance in the nonadiabatic framework since it directly probes the nonadiabatic nature of el-ph interaction. In particular it has been shown that nonadiabatic effects give rise to a finite isotope effect on quantities which in conventional ME theory are expected to not show it, for instance the effective electron mass m * [29] and the spin susceptibility χ [30]. The actual discovery of an anomalous isotope effects on these or other quantities represents therefore a precise prediction of the nonadiabatic theory which could be experimentally checked.…”