A Theory of Structural Phase Transition in One-Dimensional Metallic Systems

Abstract

Here is presented a model for one-dimensional metallic systems which is based on the pseudopotential theory. Each metallic chain has a finite size cross-section and has the band energy as well as the electrostatic energy, while the interaction between chains is assumed to be only electrostatic. When vibrational states of the atomic (Einstein) type are restricted to the zero- and one-quantum states, the phonon Hamiltonian in the 1-D case is equal to the “Ising model with a transverse field” and existing exact solutions for this model can be used to discuss the structural phase transition. The temperature-dependence of the Peierls instability arises both from the vibrational and the electronic freedoms, and a numerical calculation is made for the latter.