Phonons Phonons in metals - Kohn in metals - Kohn anomalyanomalyion background oscillation relative to (fixed) electron

analog to plasma oscillationion mass

ion density

ion chargescreening 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 energydeformation along x

electron-phonon coupling

screened Coulomb(short range)ion-electron ion density

fluctuationelectrondensity

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 condensationof coherent phonons

density modulation ofion background

break down of perturbation theory

periodically modulated(weak) ion potential

case fornearly free electron approximation

Peierls instability Peierls instability in 1Din 1D metalmetal

nearly free electron approximation

secular equation

occupied

empty total ground state energy

elasticexpense

electronicgain

Peierls instability Peierls instability in 1Din 1D metalmetal

elasticexpense

electronicgain

minimize w.r.t.

density of statesat Fermi energy

electron-phononcoupling constant

energy gap of insulating phase

Peierls instability

instability of Fermi surface

Peierls instability Peierls instability in 1Din 1D metalmetalcharge modulation of electrons and ionselectron wave function (NFEA)

Charge Density Wave

experimental systems

TTF-TCNQ

resi

stiv

ity metal-insulatortransition

NbSe3

STM

charge densitymodulation

organicconductor

H. Alves et al. Nature Materials

S. Yasuzuka et al. JPSJ(2007)