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) is proportional to Tc0y, with y greater than 0, then the vortices tend to be pinned where Tc0, and hence the magnitude of the superconducting order parameter , 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 is obtained from 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 the cores, the local density of states spectrum has a small gap and sharp coherence peaks, while near the cores it has a larger gap with low, broad peaks. Additionally, also in agreement with experiment, the spectrum near the core does not exhibit a zero-energy peak which is, however, observed in other theoretical studies.