The metal-insulator transitions in the Peierls chain

Abstract

The ground state (at 0K) of a discrete molecular-crystal model for the Peierls chain with classical atoms and non-interacting spinless quantum electrons is calculated numerically as a function of the electron-phonon coupling for an 'irrational' electron concentration. A metal-insulator transition arising from the extinction of the Frohlich conductivity for the incommensurate system is observed when the Peierls gap is only 10% of the total unperturbed bandwidth. Beyond the critical coupling, the Frohlich mode disappears and the electrons are exponentially localised but the lattice distortion remains incommensurate (the polaron lattice). In this region, the Peierls-Nabarro barrier does not vanish and is calculated. The existence of metastable Fermi glasses is also proved, but they are shown to have an energy larger than that of the incommensurate ground state. The observed transition is identified as a transition by breaking of analyticity, which is similar to the one found previously in the Frenkel-Kontorova model. This behaviour is explained as being a consequence of the competition between the Fermi and the lattice wavevectors, which are incommensurate with each other.