Charge-density-wave instability in a strongly anisotropic three-dimensional electronic system in a magnetic field

We consider a superlattice of parallel two-dimensional electron layers in a perpendicular magnetic field strong enough so that only a fraction of the lowest Landau level in each layer is filled. It is demonstrated that due to the macroscopically large degeneracy of the ground state for noninteracting electrons, the system becomes unstable once the small interaction is turned on. We construct an approximate Hamiltonian for the interacting system that admits the mean-field solution for the ground state, correct to the leading power of 1/D, where D is the degeneracy of the Landau level. The order parameter, the amplitude of the 2${\mathit{k}}_{\mathit{f}}$ charge-density wave along the field, develops an essential singularity in a coupling constant as a result of the nonperturbative approach presented. We speculate on the possible interplay between the incompressibility of Laughlin liquids in the layers formed at certain filling factors and charge-density-wave instability along the field.