Density of States in High- $T_c$ Superconductor Vortices

We calculated the electronic structure of a vortex in a pseudogapped superconductor within a model featuring strong correlations. With increasing strength of the correlations, the BCS core states are suppressed and the spectra inside and outside the core become similar. If the correlations are short range, we find new core states in agreement with the observations in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ and ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$. Our results point to a common phenomenology for these two systems and indicate that normal-state correlations survive below $T_c$ without taking part in the overall phase coherence.