Effect of $^{3}$He impurity on the supersolid transition of $^{4}$He

The supersolid phase of $^{4}$He was reported by a series of torsional oscillator experiments [1]. One of the most striking features of the supersolid transition is the intriguing $^{3}$He impurity effect. The addition of an extremely small amount of $^{3}$He impurity broadens the transition and enhances the transition temperature T$_{c}$. This effect is very different from that in helium film and that in `bulk' superfluid helium. We have studied the influence of $^{3}$He impurity on the supersolid transition systematically by progressively diluting isotopically-pure $^{4}$He ($^{3}$He impurity less than 2ppb) with $^{3}$He. The transition temperature is monotonically enhanced with increasing $^{3}$He concentration and the supersolid fraction shows a broad maximum around 0.2 ppm. [1] E. Kim and M. H. W. Chan, \textit{Science} \textbf{305}, 1941 (2004); \textit{Nature} \textbf{425}, 227 (2004); \textit{J. Low Temp. Phys.} \textbf{138}, 859 (2005); \textit{Phys. Rev. Lett. }\textbf{97}, 115302 (2006).