Abstract
The effects of a single impurity in the mixed state of a d-wave superconductor is studied by solving the lattice Bogoliubov--de Gennes equations self-consistently. The mechanism for the vortex pinning by the impurity is carefully elucidated. It is shown that the impurity sitting at the core center is not repulsive to the vortex core states and the zero-energy resonant state induced by itself is still visible in the local quasiparticle spectrum. The calculated imaging shows a fourfold ``star'' shape of the local density of states whose orientation is energy dependent.
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