Tcsuppression and resistivity in cuprates with out of plane defects

Abstract

Recent experiments introducing controlled disorder into optimally doped cuprate superconductors by both electron irradiation and chemical substitution have found unusual behavior in the rate of suppression of the critical temperature Tc vs. increase in residual resistivity. We show here that the unexpected discovery that the rate of Tc suppression vs. resistivity is stronger for out-of-plane than for in-plane impurities may be explained by consistent calculation of both Tc and resistivity if the potential scattering is assumed to be nearly forward in nature. For realistic models of impurity potentials, we further show that significant deviations from the universal Abrikosov-Gor'kov Tc suppression behavior may be expected for out of plane impurities.PACS numbers: 74.25.Jb, 74.20.Fg The destruction of superconductivity by disorder has been traditionally used to probe the nature of the superconducting state. In classic superconductors, pairbreaking is caused only by magnetic impurities 1 , and the functional form of the T c suppression, when plotted vs. impurity concentration or change in normal state resistivity, is known to follow the universal curve predicted by Abrikosov and Gor'kov (AG) 2 . In unconventional superconductors, ordinary nonmagnetic impurities are also expected to break pairs, and in the simplest approximation where the impurities are treated as point-like (deltafunction) potential scatterers, the T c suppression also follows the AG form.As in so many other respects, the experimental situation in the cuprates agrees qualitatively with the simplest notions of what should happen to d-wave superconductors in the presence of disorder, but differs in some important details. For example, when Zn is substituted for Cu in the Cu-O planes, T c is suppressed rapidly as expected for a d-wave superconductor. Here, "rapidly" means that the disorder-induced scattering rate required to destroy superconductivity is on the order of the gap scale rather than the Fermi energy E F , as would be expected in an swave system. Nevertheless, the initial slope of the T c vs. ∆ρ curve found in experiment is a factor of 2-3 smaller than the universal AG curve 3 . This discrepancy has been attributed to scattering in higher angular momentum channels by several authors, who modelled the scattering potential with a separable form describing scattering in both s-and a single higher ℓ-wave channel 4,5 . This is a simple and tractable way of including the finite range of the scatterers qualitatively, but is neither consistent by the microscopics of screened impurities in the cuprates, nor capable of treating the limit of extreme forward scattering, claimed to be of relevance in the cuprate case 6,7,8 . Furthermore, in these studies T c is calculated as a function of the single-particle normal state scattering rate 1/τ N , as opposed to the transport rate 1/τ tr relevant for comparison to resistivity measurements.A further paradox was reported recently by Fujita et al. 13 , who showed that the rate of suppression dT c /dρ is s...

Gap symmetry and structure of Fe-based superconductors

“…Second, "slow" and "fast" T c suppression cannot be determined by plotting T c vs. impurity concentration, but only vs. a scattering rate directly comparable to a theoretical scattering rate (see below), which is generally difficult to determine. The alternative is to plot T c vs. residual resistivity change ∆ρ, but a) this is only possible if the ρ(T ) curve shifts rigidly with disorder, and b) if comparisons with theory include a proper treatment of the transport rather than the quasiparticle lifetime [115]. Finally, the effect of a chemical substitution in a Fe-based superconductor is quite clearly not describable solely in terms of a potential scatterer, but the impurity may dope the system or cause other electronic structure changes which influence the pairing interaction.…”

Magnetism and superconductivity inU2PtxRh1−xC2

“…Such insensitivity to impurities is difficult to reconcile with a scenario of non-s-wave superconductivity. However, several established unconventional superconductors, such as organic 22 , cuprate 28 , pnictide 29 and heavy-fermion superconductors 30,31 , deviate from the Abrikosov-Gor'kov theory , with explanations ranging from spatial variation of the gap function 32 , the effect of a combination of magnetic and non magnetic impurities 33 , or interactions between paramagnetic impurities 34 . Hence, a definitive statement about the nature of the superconducting state will require further investigation, and in particular would benefit from the growth of single crystals and detailed studies of the gap symmetry.…”

Insensitivity ofd-wave pairing to disorder in the high-temperature cuprate superconductors

“…Several authors attempted to account for the slowness of the T c suppression by assuming that the scattering potential of planar impurities was extended, or anisotropic [16,17,18,19]. Recently, Graser et al [20] calculated both T c and the impurity resistivity ρ within a consistent model of extended potential scatterers, and concluded that the unusual T c vs. ρ behavior seen in cuprate experiments should be attributed to strong correlations or strong coupling corrections to BCS theory. In general, the effect of correlations on the structure and scattering of quasiparticle states in a disordered d-wave superconductors is still an open and very important question for cuprates and other unconventional superconductors.…”