Are Vortex Quasi-Crystals New Phases of Vortex Matter?
  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. However, quasi-crystals also exist in AMOM, thus a new phase of vortex matter is proposed here: the vortex quasi-crystal. It is argued that vortex quasi-crystals are stabilized due to imposed quasi-periodic potentials in large samples or due to boundary and surface energy effects for samples of special shapes and sizes. For finite size 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. 
Wei Zhang and C. A. R. Sa de Melo