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Isotope Effect in Superconductors

The effect:

  • Any physical property that depends directly or indirectly on the mass of the ions building up the lattice of a superconductor may display an isotope effect: substituting an element by one of its isotopes (e.g. 16O<->18O) leads to a shift in the value of an observable. The most studied of these quantities are the superconducting transition temperature Tc and the critical magnetic field Hc2. The penetration depth of a magnetic field $\lambda$ is another interesting example (see below).

    While most conventional superconductors display a rather well-understood variation of Tc upon isotopic substitution of one element, high-Tc superconductors exhibit a great variety of behaviours. Giant magnetoresistive (GMR) systems or fullerenes have an uncommonly large isotope coefficient as well [see the review article Ref. [1].]


  • The isotope effect is generally expressed in terms of its isotope coefficient defined as
    $\displaystyle \alpha = -\frac{M}{T_c}\,\frac{\Delta T_c}{\Delta M}$     (1)
    where Tc$T_c \sim M^{-\alpha}$, is the mass of the element substituted by its isotope, $\Delta T$Tc describes the shift of the critical temperature when substituting an element for its isotope and $\Delta M$ is the mass difference between the isotopes. For many one-component metallic superconductors the isotope coefficient is about $\alpha=0.5$. There are, however, a large number of conventional materials (alloys, transition metal elements etc.) where the coefficient take quite different values [1]. High-temperature superconductors also display an unconventional behaviour of the isotope effect with doping.


    Some results:

  • We have shown that number of factors not related to the pairing mechanism strongly affect the value of the isotope coefficient while leaving the phonon spectrum essentially unaltered. Examples of such factors are the presence of magnetic impurities, non-adiabatic charge transfer (in doped systems) or the proximity effect (cf. the review article, Ref. [1]). These novel types of isotope effects affect both conventional and unconventional (such as high-Tc or organic) superconductors.

    The results we have obtained imply that the isotope effect does not allow to draw unambiguous conclusions on the pairing mechanism responsible for the superconducting state. In particular, a small value of the isotope coefficient does not imply that phonons are irrelevant for the pairing mechanism. The opposite is true as well. Indeed, the Coulomb interaction, magnetic impurities, particularities of the band structure, proximity effect can lead to very different values of the isotope coefficient, depending on the specificities of the system studied.


  • We have described quantitatively the isotopic shift of Tc for several high-temperature superconductors [8,13]. Figure 1 shows the results obtained for oxygen substitution (16O <-> 18O) in YBa2(Cu1-xZnx)3O7-$\lambda$. Doping with Zn can be seen as introducing magnetic impurities in the system. The calculated solid line is universal: the isotope coefficient is independent of any free parameter within Abrikosov-Gork'ov's theory Ref. [2].

    isotope effect in presence of magnetic impurities

    Fig. 1: Isotope coefficient in the presence of magnetic impurites normalized to the value in absence of impurities (from Ref. [2]) The line
    is the theoretical prediction (universal curve independent of any parameter). Points are from experiments on YBa2(Cu1-xZnx)3O7-delta;

  • Figure 2 shows the effect of Pr-doping on the isotope coefficient. Doping with Pr affects the doping of the layers and introduces magnetic impurities (cf. Ref. [4]). The effect of each contribution is shown separately. The lower line corresponds to the non-adiabatic channel (charge-transfer of quasiparticles between the conducting layer and the charge reservoir) in absence of magnetic impurities. The middle line shows the effect of adding magnetic impurities to the non-adiabatic channel (the case of magnetic impurities only is shown in Fig.1). The solid, upper line is the fit (with one free parameter) to the data.

    isotope effect for Y<sub>1-x</sub>Pr<sub>x</sub>Ba<sub>2</sub>Cu<sub>3</sub>O<sub>7-delta</sub>

    Fig. 2: Isotope coefficient (absolute) in the presence of magnetic impurities and non-adiabaticity (from Ref. [4]). Lines see text above. The points are from magnetic susceptibility and resistivity measurements performed on Y1-xPrxBa2Cu3O7-delta at various doping x.

    It is worth noting that the isotope effect in the presence of magnetic impurities or the proximity effect diverges when Tc goes to zero. This feature is related to the fact that one is approaching the superconducting-normal state phase transition.

  • We have introduced a new isotope effect, namely that of the shift of the magnetic field penetration depth upon isotopic substitution (Ref. [3]). This latter effect has been observed recently by torque magnetometry [J. Hofer et al., Phys. Rev. Lett. 84, 4192 (2000)]. One interesting feature of the penetration depth is that the isotope coefficient is temperature dependent [Ref. [3] and Z. Phys. Chem. 201, 271 (1997).] A similar dependence is also observed for the isotope effect in systems displaying the proximity effect. This effect has not been verified experimentally up to date. Finally, in the case of non-adiabatic charge-transfer in doped superconductors, we have established an analytical relation between the isotope coefficient of Tc and the penetration depth Ref. [3].


    Selected publications:

    1. The isotope effect in superconductors (Review article, PDF)
      in Pair Correlations in Many-Fermion Systems, p. 25, Plenum Press (1998); cond-mat/9801222.
    2. Unconventional Isotope Effects in Superconductors (PDF)
      Phys. Rev. B. 56, 107 (1997).
    3. Isotope Effect for the Penetration Depth in Superconductors (PDF)
      Phys. Rev. B 57, 10814 (1998); cond-mat/9801186.
    4. Isotope Effect in High-Tc Materials: Role of Non-Adiabaticity and Magnetic Impurities. (PDF)
      Z. Phys. B 104, 759 (1997).


    Collaboration:
    V.Z. Kresin Lawrence Berkeley National Laboratory.
    S.A. Wolf Naval Research Laboratory and DARPA.
    Yu. Ovchinnikov Landau Institute of Physics.
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    Andreas Bill
    Last modified: Mon Oct 13 23:51:24 CEST 2003