Phonons in metals - Kohn in metals - Kohn anomaly anomaly - PowerPoint PPT Presentation

Phonons in metals - Kohn in metals - Kohn anomaly anomaly Phonons ion background oscillation relative to (fixed) electron analog to plasma oscillation ion mass ion density ion charge screening of Coulomb by (fast) electrons Kohn anomaly sound velocity singular at 2k F

Peierls instability in 1D in 1D metal metal Peierls instability electrons & elastic ionic background (Jellium model) electron elastic energy kinetic energy deformation along x electron-phonon coupling screened Coulomb (short range) ion density electron ion-electron fluctuation density

Peierls instability in 1D in 1D metal metal Peierls instability electrons & elastic ionic background (Jellium model) Fourier: phonon dispersion electron-phonon coupling as perturbation

Peierls instability in 1D in 1D metal metal Peierls instability screening essentially no q-dependence 2 nd -order Rayleigh-Schrödinger perturbation Lindhard function correction to phonon dispersion

Peierls instability in 1D in 1D metal metal Peierls instability instability Bose-Einstein condensation break down of of coherent phonons perturbation theory periodically modulated density modulation of (weak) ion potential ion background case for nearly free electron approximation

Peierls instability in 1D in 1D metal metal Peierls instability nearly free electron approximation secular equation empty total ground state energy occupied elastic electronic expense gain

Peierls instability in 1D in 1D metal metal Peierls instability minimize w.r.t. elastic electronic expense gain density of states at Fermi energy Peierls instability electron-phonon coupling constant instability of energy gap Fermi surface of insulating phase

Peierls instability in 1D in 1D metal metal Peierls instability experimental systems charge modulation of electrons and ions TTF-TCNQ electron wave function (NFEA) organic conductor S. Yasuzuka et al. H. Alves et al. JPSJ(2007) Nature Materials resistivity metal- insulator transition NbSe 3 STM Charge Density Wave charge density modulation