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  • Phonons Phonons in metals - Kohn in metals - Kohn anomalyanomaly ion background oscillation relative to (fixed) electron

    analog to plasma oscillation ion mass

    ion density

    ion charge screening of Coulomb by (fast) electrons

    sound velocity

    Kohn anomaly

    singular at 2kF

  • Peierls instability Peierls instability in 1Din 1D metalmetal

    electrons & elastic ionic background (Jellium model)

    electron kinetic energy

    elastic energy deformation along x

    electron-phonon coupling

    screened Coulomb (short range) ion-electron ion density

    fluctuation electron density

  • Peierls instability Peierls instability in 1Din 1D metalmetal

    electrons & elastic ionic background (Jellium model)

    phonon dispersion

    electron-phonon coupling as perturbation

    Fourier:

  • Peierls instability Peierls instability in 1Din 1D metalmetal

    2nd-order Rayleigh-Schrödinger perturbation

    essentially no q-dependencescreening

    correction to phonon dispersion

    Lindhard function

  • Peierls instability Peierls instability in 1Din 1D metalmetal

    instability Bose-Einstein condensation of coherent phonons

    density modulation of ion background

    break down of perturbation theory

    periodically modulated (weak) ion potential

    case for nearly free electron approximation

  • Peierls instability Peierls instability in 1Din 1D metalmetal

    nearly free electron approximation

    secular equation

    occupied

    empty total ground state energy

    elastic expense

    electronic gain

  • Peierls instability Peierls instability in 1Din 1D metalmetal

    elastic expense

    electronic gain

    minimize w.r.t.

    density of states at Fermi energy

    electron-phonon coupling constant

    energy gap of insulating phase

    Peierls instability

    instability of Fermi surface

  • Peierls instability Peierls instability in 1Din 1D metalmetal charge modulation of electrons and ions electron wave function (NFEA)

    Charge Density Wave

    experimental systems

    TTF-TCNQ

    re si

    st iv

    ity metal- insulator transition

    NbSe3

    STM

    charge density modulation

    organic conductor

    H. Alves et al. Nature Materials

    S. Yasuzuka et al. JPSJ(2007)