phonons in metals - kohn anomaly - eth z
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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)
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