  The quasiparticle states found in the vortex core of a high-T$_{\rm{c}}$
cuprate superconductor may be probed by scanning tunneling spectroscopy.
Results of such experiments have revealed typical spectra that are quite
different from what is seen in conventional low-Tc superconductors. In
particular the Caroli-deGennes-Matricon state at $E\sim 0$ in the core center
is not seen. Instead, in a high-T$_{\rm{c}}$ vortex core, quasiparticle states
are found at energies that are at a sizable fraction of the gap energy. One
explanation for this could be that a finite amplitude of a competing
orderparameter stabilizes in the vortex-core center. Here I will explore the
possibility of nucleating a vortex-core state that locally breaks inversion
symmetry. The vortex-core orderparameter is of mixed parity, a $[d + i
p]$-wave, and the quasiparticle spectra in the core center lacks the E=0
states.
