Supersolid Phase in Helium-4

Abstract

The probable observation of a supersolid helium phase was recently reported by Kim {\it et al}. In this article, we confirm their speculation. Based on a theoretical model for solid helium-4, we show that the emergence of such a phase is inevitable. This is the first instance of Bose-Einstein condensation (BEC) in a solid. We calculate the BEC transition temperature ($T_c$) and the Landau critical velocity ($v_c$) from the model, which respectively are 215 mK and $251 μ\rm{ms^{-1}}$. They are in excellent agreement with the experimental results; $T_c=$175 mK and $v_c \leq 300 μ\rm{ms^{-1}}$. We also prove that our model possesses the necessary and sufficient condition for the emergence of supersolidity. We briefly comment about similar behaviour in $^3$He.