Effects of Lattice Fluctuation on an Electron Band in Quasi-One-Dimensional Electron-Phonon System

Abstract

We investigate the effects of lattice vibrations on an electron gap in the Peierls-Frolich state using the Hartree-Fock approximation with respect to the electron-phonon coupling, considering both amplitude mode and phase mode with anisotropic dispersion. In the one-dimensional electron-phonon system, the electron gap is induced by the Umklapp scattering intermediated by the amplitude-mode phonon with momentum transfer of 2 k F . However, the phase-mode phonon gives the large fluctuation to the electron band and reduces the band gap. The band gap is determined by the competetion between the amplitude mode and the phase mode. We find that the band gap becomes narrower as the velocity of the phase-mode phonon u is increased. The band gap tail appears from the electron-phonon scattering. The electron scattering rate due to phonon is estimated to be π u Δ 0 /2 v F , where Δ 0 is the electron band gap and v F is the Fermi velocity.