  We study theoretically the vortex matter structure in low dimensional (LD)
systems with superconducting order induced by proximity to a bulk
superconductor. We analyze the effects of microscopic coupling mechanisms
between the two systems and the effects of possible mismatch in the band
structures of these materials on the energy spectrum of vortex-core electrons.
The unusual structure of vortex cores is discussed in the context of recent
tunneling microscopy/spectroscopy experiments.
