Lattice dynamics and electrical properties of commensurate one-dimensional charge-density-wave systems

Abstract

The ground-state properties, the phonon dispersion, and the electrical properties of systems with a commensurate superstructure are calculated. The superstructure leads to the appearance of a gap at the Fermi energy. Phonon branches representing oscillations of the phase and amplitude of the superstructure show strong anomalies at $q=0\mathrm{}$. The smaller the electronic energy gap, the stronger these anomalies are. For general commensurate cases the phase mode of finite frequency ${\omega }_{\mathrm{ph}}$ couples to an external field leading to a $\delta$ singularity in the electrical conductivity at $\omega ={\omega }_{\mathrm{ph}}$. This is in contrast to the incommensurate case, where, due to the translational invariance, the phase-mode frequency vanishes, resulting in metallic electrical properties. In the special case of a half-filled band the phase and amplitude of the superstructure have the same degree of freedom in the system. In this case the corresponding phonon mode does not couple to an external field. However, the lower symmetry of the state with superstructure leads to a coupling of usually infrared-inactive intramolecular modes to an external field, and, correspondingly, these modes lead to peaks in the frequency-dependent conductivity.