High-temperature supersolid of He 4 in a one-dimensional periodic potential
The search for robust experimental proof of supersolidity has encountered many complicating factors, such as temperature dependent changes in the mechanical properties of solid 4 He which mimic the signature of superfluid flow. As a result, the physical existence and true nature of this unique state of matter are still under debate. Here we consider 4 He stabilized by a one-dimensional periodic potential whose lattice spacing is similar to the length scale of the 4 He- 4 He interaction. We use the Bogoliubov transformation to calculate the excitation spectrum, finding that when interactions between nearest or next-nearest neighbors are attractive, there is a finite positive gap in energy between the delocalized ground state and the lowest energy excitations which, under certain conditions, is significantly larger than both the melting temperature and the lambda temperature. This means that it should be possible to observe a supersolid at a high enough temperature that superfluidity in bulk liquid 4 He or changes in the mechanical properties of bulk solid 4 He do not obscure it. Lastly, we also discuss the properties of experimentally achievable materials which could support this type of supersolid.