Pinning of vortices by impurities in unconventional superconductors

We carry out a microscopic study of a vortex lattice in a strongly correlated, type-II, $d$-wave superconductor (SC) using Bogoliubov-de Gennes (BDG) formalism. In weak-coupling theory, a commonly accepted truism is that a vortex binds to an impurity. We demonstrate that in a class of unconventional SCs proximity to a Mott insulator, the binding of a vortex to an impurity depends on relevant parameters. In particular, we illustrate this dependency on the sign of impurity, i.e., attractive or repulsive, as well as doping. We emphasize that this seemingly unanticipated behavior arises from strong correlation effects and is absent in weak-coupling descriptions.