Vortex quasi-crystals in mesoscopic superconducting samples*

There seems to be a one to one correspondence between the phases of atomic and molecular matter (AMOM) and vortex matter (VM) in superfluids and superconductors. Crystals, liquids, and glasses have been experimentally observed in both AMOM and VM. Here, we propose a vortex quasi-crystal state which can be stabilized due to boundary and surface energy effects for samples of special shapes and sizes. For finite sized pentagonal samples, it is proposed that a phase transition between a vortex crystal and a vortex quasi-crystal occurs as a function of magnetic field and temperature as the sample size is reduced.