# Model for Vortex Pinning in a Two-Dimensional Inhomogeneous d-wave Superconductor - Condensed Matter > Superconductivity

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 ona Ginzburg-Landau GL free energy functional whose coefficients are determinedby the mean-field transition temperature T {c0} and the zero-temperaturepenetration depth \lambda0. We find that if i T {c0} and \lambda0 arefunctions of position, and ii \lambda^20 is proportional to T {c0}^y, withy greater than 0, then the vortices tend to be pinned where T {c0}, and hencethe magnitude of the superconducting order parameter \Delta, are large. Thisbehavior is in contrast to the usual picture of pinning in Type-IIsuperconductors, where pinning occurs in the small-gap regions. We also computethe local density of states of a model BCS Hamiltonian with d-wave symmetry, inwhich the pairing field is obtained from Monte Carlo simulations of a GL freeenergy. Several features observed in scanning tunneling spectroscopymeasurements on YBa 2Cu 3O {6+x} and Bi 2Sr 2CaCu 2O {8+x} are well reproducedby our model: far from the cores, the local density of states spectrum has asmall gap and sharp coherence peaks, while near the cores it has a larger gapwith low, broad peaks. Additionally, also in agreement with experiment, thespectrum near the core does not exhibit a zero-energy peak which is, however,observed in other theoretical studies.

Author: Daniel Valdez-Balderas, David Stroud

Source: https://arxiv.org/