Low Temperature Physics: 34, 351 (2008); https://doi.org/10.1063/1.2911654 (6 pages)
Физика Низких Температур: Том 34, Выпуск 4-5 (Апрель 2008), c. 440-446    ( к оглавлению , назад )

Bose-Einstein condensation in a decorated lattice: an application to the problem of supersolid He

D.V. Fil

Institute for Single Crystals, National Academy of Sciences of Ukraine, 60 Lenin Ave., Kharkov 61001, Ukraine
E-mail: fil@isc.kharkov.ua

S.I. Shevchenko

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine 47 Lenin Ave., Kharkov 61103, Ukraine
E-mail: shevchenko@ilt.kharkov.ua

Received November 1, 2007


The Bose–Einstein condensation of vacancies in a three-dimensional decorated lattice is considered. The model describes possible scenario of superfluidity of solid helium, caused by the presence of zero-point vacancies in a dislocation network. It is shown that the temperature of Bose–Einstein condensation decreases under increase of the length of the network segments, and the law of decrease depends essentially on the properties of the vertexes of the network. If the vertexes correspond to barriers with a small transparency, the critical temperature is inversely as the square of the length of the segment. On the contrary, if the vertexes correspond to traps for the vacancies (it is energetically preferable for the vacancies to be localized at the vertexes), an exponential lowering of the temperature of transition takes place. The highest temperature of Bose–Einstein condensation is reached in the intermediate case of vertexes with large transparency, but in the absence of tendency of localization at them. In the latter case the critical temperature is inversely as the length of the segment.

PACS: 67.80.–s Quantum solids;
PACS: 67.10.Ba Boson degeneracy.

Ключевые слова: supersolid, zero-point vacancies, dislocations.