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Register a new userDisorder Effects in d-wave Superconductors
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In the theoretical analyses of impurity effects in superconductors the assumption is usually made that all quantities, except for the Green functions, are slowly varying functions of energy. When this so-called Fermi Surface Restricted Approximation is combined with the assumption that impurities can be represented by delta-function potentials of arbitrary strength, many reasonable looking results can be obtained. The agreement with experiments is not entirely satisfactory and one reason for this might be the assumption that the impurity potential has zero range. The generalization to finite range potentials appears to be straightforward, independent of the strength of the potential. However, the selfenergy resulting from scattering off finite range impurities of infinite strength such as hard spheres, diverges in this approximation at frequencies much larger than the gap amplitude! To track down the source of this unacceptable result we consider the normal state. The elementary results for scattering off a hard sphere, including the result that even an infinitely strong delta-function potential does not lead to scattering at all in systems of two and more dimensions, are recovered only when the energy dependencies of all quantities involved are properly taken into account. To obtain resonant scattering, believed to be important for the creation of mid-gap states, the range of the potential is almost as important as its strength.
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We analyze the complex interplay of the strong correlations and impurities in a high temperature superconductor and show that both the nature and degree of the inhomogeneities at zero temperature in the local order parameters change drastically from what are obtained in a simple Hartree-Fock-Bogoliubov theory. While both the strong electronic repulsions and disorder contribute to the nanoscale inhomogeneity in the population of charge-carriers, we find them to compete with each other leading to a relatively smooth variation of the local density. Our self-consistent calculations modify the spatial fluctuations in the pairing amplitude by suppressing all the double-occupancy within a Gutzwiller formalism and prohibit the formation of distinct superconducting-`islands. In contrast, presence of such `islands controls the outcome if strong correlations are neglected. The reorganization of the spatial structures in the Gutzwiller method makes these superconductors surprisingly insensitive to the impurities. This is illustrated by a very weak decay of superfluid stiffness, off-diagonal long range order and local density of states up to a large disorder strength. Exploring the origin of such a robustness we conclude that the underlying one-particle normal states reshape in a rich manner, such that the superconductor formed by pairing these states experiences a weaker but spatially correlated effective disorder. Such a route to superconductivity is evocative of Andersons theorem. Our results capture the key experimental trends in the cuprates.
The concept of broken symmetry, that the symmetry of the vacuum may be lower than the Hamiltonian of a quantum theory, plays an important role in modern physics. A manifestation of this phenomena is the Higgs boson in particle physics whose long awaited discovery is imminent. An equivalent mode in superconductors is implicit in the early theories of their collective fluctuations. Spurred by some mysterious experimental results, the theory of the oscillation of the amplitude of superconductivity order parameter, which is the equivalent to the Higgs modes in s-wave superconductors and its identification in the experiments, was explicitly provided. It was also shown that a necessary condition for this to occur is the emergent Lorentz invariance in the superconducting state while the metallic state and the region just below $T_c$ is manifestly non-Lorentz invariant. Here we show that d-wave superconductors, such as the high temperature Cuprate superconductors, should have a rich assortment of Higgs bosons, each in a different irreducible representation of the point-group symmetries of the lattice. We also show that these modes have a characteristic singular spectral structure which can be discovered in Raman scattering experiments.
We have investigated whether the electron-phonon interaction can support a d-wave gap-anisotropy. On the basis of models derived from LDA calculations, as well as LDA linear-response calculations we argue that this is the case, for materials with buckled or dimpled CuO2 planes, for the so-called buckling modes, which involve out-of-plane movements of the plane oxygens.
Very recently impurity scattering effects on quasiparticles in d-wave superconductors have attracted much attention. Especially, the thermodynamic properties in magnetic fields H are of interest. We have measured the low-temperature specific heat C(T,H) of La_1.78Sr_0.22Cu_1-xNi_xO4. For the first time, the impurity scattering effects on C(T,H) of cuprate superconductors were clearly observed, and are compared with theory of d-wave superconductivity. It is found that impurity scattering leads to gamma(H)=gamma(0)(1+D((H/H_c2)(ln(H_c2/H)) in small magnetic fields. Most amazingly, the scaling of C(T,H) breaks down due to impurity scattering.
We discuss a new mechanism of microwave absorption in s- and d-wave superconductors, which arises in the presence of a dc supercurrent in the system. It produces a contribution to the ac conductivity that is proportional to the inelastic quasiparticle relaxation time. This contribution also determines the supercurrent dependence of the conductivity. It may significantly exceed the conventional contribution because in typical superconductors the inelastic relaxation time is several orders of magnitude longer than the elastic one. We show that the aforementioned contribution to the conductivity may be expressed in terms of the single particle density of states in superconductors in the presence of a dc supercurrent. Our results may enable determination of the inelastic relaxation time in superconductors from microwave absorption measurements.
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