We carry out a microscopic study of the vortex lattice in a strongly correlated, type-II, d-wave superconductor (SC), addressing two independent questions: (a) Does a vortex get pinned by an impurity in accordance with conventional wisdom derived for conventional weakly coupled s-wave SCs? (b) What are the manifestations of competing subdominant orders in a vortex core of such Scs?

While weak-coupling theories generally predict that a vortex core binds to impurities, our study reveals that this behavior is not universal. In particular, in unconventional superconductors close to a Mott-insulating phase, the binding of vortices to impurities is sensitive to system parameters. We demonstrate that this dependence is influenced by the nature of the impurity—whether attractive or repulsive—as well as by the doping level. Our results highlight that this nontrivial behavior stems from strong correlation effects, which are fundamentally absent in weak-coupling scenarios. We also demonstrate that in the underdoped region, the presence of subdominant charge and bond modulation introduces low-energy core states in the local density of states (LDOS) at the vortex core instead of a U-shaped (i.e., with a hard gap) Mott core in a strongly correlated d-wave superconductor. Intriguingly, the LDOS at the vortex core is distinct from a metallic core with a Caroli–de Gennes–Matricon (CdGM) peak in the case of weakly coupled superconductors. We have investigated that such subdominant order changes the structure and spectrum of the d-wave vortex in the underdoped region. We have demonstrated the formation of charge and bond modulation at the vortex center by decreasing the doping and reaching an underdoped zone.