Bose-Einstein condensation in a decorated lattice: an application to supersolid

TL;DR

This paper models Bose-Einstein condensation of vacancies in a decorated lattice to explore superfluidity in solid helium, showing how network properties influence the critical temperature of condensation.

Contribution

It introduces a detailed model of vacancy condensation in a dislocation network, analyzing how vertex properties affect the transition temperature.

Findings

Critical temperature decreases with segment length.

Vertex transparency significantly influences the transition temperature.

Different vertex properties lead to distinct temperature scaling laws.

Abstract

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 segments of the network, 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 localize 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 in them. In the latter case the critical temperature is inversely as the length of the segment.