Continuity of Self-Consistent Solutions between Commensurate and Incommensurate Phases of the Peierls Instability. I. Analytic Investigations

Abstract

Self-consistent treatments of the Peierls instability both for a commensurate (C) phase with Q=π⁄a arid an incommensurate (IC) phase are made with the mean-field approximation, Q and a being the wave number of the lattice displacement and the lattice constant, respectively. The behaviors of harmonics with wave numbers nQ are studied in the IC-phase. When Q is well away from π⁄a, the amplitudes of harmonics are very small, but as Q approaches π⁄a, odd harmonics grow remarkably. The self-consistent solution of the IC-phase is shown to become equivalent, in the limit of Q→π⁄a, to that of the C-phase, only when all the odd harmonics are taken into account self-consistently.