Model for vortex pinning in a two-dimensional inhomogeneous d-wave superconductor

Abstract

We study a model for the pinning of vortices in a two-dimensional, inhomogeneous, type-II superconductor in its mixed state. The model is based on a Ginzburg-Landau (GL) free energy functional whose coefficients are determined by the mean-field transition temperature Tc0 and the zero-temperature penetration depth λ(0). We find that if (i) Tc0 and λ(0) are functions of position and (ii) λ2(0)∝Tc0y with y>0, then vortices tend to be pinned by regions where Tc0 and therefore the magnitude of the superconducting order parameter Δ are large. This behavior is in contrast to the usual picture of pinning in type-II superconductors, where pinning occurs in the small-gap regions. We also compute the local density of states of a model BCS Hamiltonian with d-wave symmetry, in which the pairing field Δ is obtained from the Monte Carlo simulations of a GL free energy. Several features observed in scanning tunneling spectroscopy measurements on YBa2Cu3O6+x and Bi2Sr2CaCu2O8+x are well reproduced by our model: far from vortex cores, the local density of states spectra have a small gap and sharp coherence peaks, while near the vortex cores, they have a larger gap with low, broad peaks. Additionally, also in agreement with experiment, the spectra near the core do not exhibit a zero-energy peak which is, however, observed in other theoretical studies.

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