  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 T_{c0} and the zero-temperature
penetration depth \lambda(0). We find that if (i) T_{c0} and \lambda(0) are
functions of position, and (ii) \lambda^2(0) is proportional to T_{c0}^y, with
y greater than 0, then the vortices tend to be pinned where T_{c0}, and hence
the magnitude of the superconducting order parameter \Delta, 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 YBa_2Cu_3O_{6+x} and Bi_2Sr_2CaCu_2O_{8+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.
