Magnetic field density of perfect and imperfect flux line lattices in type II superconductors. I. Application of periodic solutions

Abstract

The densityn(B) of the spatially varying magnetic fieldB inside a type II superconductor can be measured by nuclear magnetic resonance or muon-spin rotation (μ+SR). For a perfect flux-line latticen(B) exhibits van Hove singularities at the maximum, minimum, and saddle point values of the ideally periodicB(r). In a real superconductor, these singularities are smeared due to distortions of the flux-line lattice caused by, e.g., the interaction of flux lines with inhomogeneities in the material (pinning), structural defects in the flux-line lattice, the nonellipsoidal shape of the specimen, or fluctuations of the applied field and temperature. Such perturbations of the periodicity ofB(r) typically broaden the idealn(B) by convolution with a Gaussian whose width in general depends onB and which thus smears each singularity differently. Knowledge of the broadening is required for the interpretation of μ+SR experiments in the new ceramic superconductors and also in pure niobium, where it competes with the broadening caused by the diffusion of the positive muons. In this paper (Part I), the broadening ofn(B) is discussed in detail and some of its features are derived from the periodic solutions of the Ginzburg-Landau and BCS-Gorkov theories. Forthcoming parts will deal with the application of nonperiodic solutions and with computer simulations.