  The quantized vortex state appearing in the recently discovered new states in
hcp 4He since their discovery is discussed. Special attention is given to
evidence for the vortex state as the vortex fluid (VF) state and its transition
into the supersolid (SS) state. Its features are described. The historical
expla- nations for the SS state in quantum solids such as solid 4He were based
on the idea of Bose Einstein Condensation (BEC) of the imperfections such as
va- cancies, interstitials and other possible excitations in the quantum solids
which are expected because of the large zero-point motions. The SS state was
proposed as a new state of matter in which real space ordering of the lattice
structure of the solid coexists with the momentum space ordering of
superfluidity. A new type of superconductors, since the discovery of the
cuprate high Tc superconductors, HTSCs, has been shown to share a feature with
the vortex state, involving the VF and vortex solid states. The high Tcs of
these materials are being discussed in connection to the large fluctuations
associated with some other phase transitions like the antiferromagnetic
transition in addition to that of the low dimensionality. The supersolidity in
the hcp solid 4He, in contrast to the new superconductors which have multiple
degrees of freedom of the Cooper pairs with spin as well as angular momentum
freedom, has a unique feature of possessing possibly only the momentum
fluctuations and vortex ring excitations associated with the possible low
dimensional fluctuations of the subsystem(s). The high onset temperature of the
VF state can be understood by considering thermally excited low D quantized
vortices and it may be necessary to seek low dimensional sub-systems in hcp He
which are hosts for vortices.
