Symmetry, Disorder and the Josephson Effect in d-Wave Superconductors

Doktorsavhandling, 1995

This thesis focuses on aspects of symmetry, disorder and the Josephson effect in d-wave superconductors which are generically characterized by sign changes of the gap function .DELTA.k in certain directions with respect to the underlying crystal lattice. A basic feature for the pure d-wave superconductors is the linear quasiparticle density of states at low energies: n(E) - E We consider the influence of disorder on a 2D d-wave superconductor. The central result of our solution is that the exponent .alpha. for the density of states decreases under the influence of weak non-magnetic disorder n(E) - E.alpha., and 0 < .alpha. < 1 and we calculate .alpha. for several types of non-magnetic disorder. We use a combination of numerical, perturbative, self-consistent and field theoretical methods in our calculation. The perturbative approach reveals the presence of strong vertex corrections i.e. a partial summation of Feynman diagrams is insufficient. The non-perturbative field theoretical approach gives asymptotically exact result for the density of states and we find that the property n(0) = 0 vanishes density of states at zero energy for non-magnetic disorder is a consequence of a continuous symmetry in the effective model which remains unbroken. We study the Josephson effect in d-wave superconductors within a tunneling Hamiltonian approach. We use a systematic expansion of the tunneling matrix element to investigate the effects of its anisotropy on the Ic Rn product in bicrystal junctions. The Ic Rn product is strongly varying as function of crystal orientation at constant relative misorientation angle. The comparison of the theoretical results with experiments on YBa2Cu3O7-.delta. bicrystal Josephson junctions gives qualitative agreement for gap functions of generalized s- and d(x2-y2)-wave symmetry showing that the combination of anisotropy in the superconducting gap and in the tunneling matrix is required to explain the experimental results. We investigate the generic weak-coupling BCS states in a singlet paired translationally invariant tetragonal superconductor. We classify the possible order parameters and find a possibility of a nodeless (d(x2-y2) + i dxy) - pairing in the presence of short-range antiferromagnetic interactions. We discuss the relevance of our results to the order parameter symmetry in the high-Tc cuprate superconductors.