Electronically Induced Crystallographic Transition

In this paper a model is presented which exhibits a so-called electronically induced crystallographic transition. The model consists of two interpenetrating one-dimensional identical lattices of attractive $\delta$ potentials. Shifting one sublattice with respect to the other defines a distortion, where the nondistorted system is assumed to have a periodicity which is half the periodicity of such a sublattice. The model is closely related to one discussed by Adler and Brooks. It is shown by a computer calculation that the competition between the lattice and electronic energies results in a second-order phase transition. The narrow band limit is discussed in terms of a two- and four-level scheme. It appears that only a second-order phase transition can occur, unless the repulsive term in the lattice energy is too weak. In that case the two sublattices will coincide at zero temperature, which is an unphysical situation.