Abstract
The search for robust experimental proof of supersolidity has encountered many complicating factors, such as temperature dependent changes in the mechanical properties of solid 4He 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 4He stabilized by a one-dimensional periodic potential whose lattice spacing is similar to the length scale of the 4He-4He 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 4He or changes in the mechanical properties of bulk solid 4He do not obscure it. The properties of experimentally achievable materials which could support this type of supersolid are also discussed.