phonons in metals - kohn anomalyedu.itp.phys.ethz.ch/fs14/sst/slides/peierls.pdf · phonons in...
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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
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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
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Peierls instability Peierls instability in 1Din 1D metalmetal
electrons & elastic ionic background (Jellium model)
phonon dispersion
electron-phonon coupling as perturbation
Fourier:
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Peierls instability Peierls instability in 1Din 1D metalmetal
2nd-order Rayleigh-Schrödinger perturbation
essentially no q-dependencescreening
correction to phonon dispersion
Lindhard function
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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
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Peierls instability Peierls instability in 1Din 1D metalmetal
nearly free electron approximation
secular equation
occupied
empty total ground state energy
elasticexpense
electronicgain
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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
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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)