Quantized Vortex State in hcp Solid 4He

The quantized vortex state appearing in the recently discovered new states in hcp He-4 since their discovery (Kim and Chan, Nature, 427:225-227, 2004; Science, 305:1941, 2004) is discussed. Special attention is given to evidence for the vortex state as the vortex fluid (VF) state (Anderson, Nat. Phys., 3:160-162, 2007; Phys. Rev. Lett., 100:215301, 2008; Penzev et al., Phys. Rev. Lett., 101:065301, 2008; Nemirovskii et al., arXiv:0907.0330,, 2009) and its transition into the supersolid (SS) state (Shimizu et al., arXiv:0903.1326,, 2009; Kubota et al., J. Low Temp. Phys., 158:572-577, 2010; J. Low Temp. Phys., 162:483-491, 2011). Its features are described. The historical explanations (Reatto and Chester, Phys. Rev., 155(1):88-100, 1967; Chester, Phys. Rev. A, 2(1):256-258, 1970; Andreev and Lifshitz, JETP Lett., 29:1107-1113, 1969; Leggett, Phys. Rev. Lett., 25(22), 1543-1546, 1970; Matsuda and Tsuneto, Prog. Theor. Phys., 46:411-436, 1970) for the SS state in quantum solids such as solid He-4 were based on the idea of Bose Einstein Condensation (BEC) of the imperfections such as vacancies, 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 T (c) superconductors, HTSCs (Bednorz and Mueller, Z. Phys., 64:189, 1986), has been shown to share a feature with the vortex state, involving the VF and vortex solid states. The high T (c) s 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 He-4, 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.