Charge-density-wave instability in layered charged quantum liquids

For boson and electron superlattices with a superlattice period d, analytical results for the local-field correction are derived within the Hubbard approximation. A charge-density-wave instability is found for a boson superlattice: ${\mathit{r}}_{\mathit{s}\mathit{c}}$∝${\mathit{d}}^{3/4}$. ${\mathit{r}}_{\mathit{s}\mathit{c}}$ is the random-phase-approximation parameter ${\mathit{r}}_{\mathit{s}}$ at the charge-density-wave instability. We discuss a recently proposed charge-density-wave instability in an electron superlattice and find ${\mathit{r}}_{\mathit{s}\mathit{c}}$∝d.