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

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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

SLIDE 1

Phonons Phonons in metals - Kohn in metals - Kohn anomaly anomaly

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

SLIDE 2

Peierls instability Peierls instability in 1D in 1D metal metal

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

SLIDE 3

Peierls instability Peierls instability in 1D in 1D metal metal

electrons & elastic ionic background (Jellium model)

phonon dispersion

electron-phonon coupling as perturbation

Fourier:

SLIDE 4

Peierls instability Peierls instability in 1D in 1D metal metal

2nd-order Rayleigh-Schrödinger perturbation

essentially no q-dependence screening

correction to phonon dispersion

Lindhard function

SLIDE 5

Peierls instability Peierls instability in 1D in 1D metal metal

instability

Bose-Einstein condensation

f coherent phonons

density modulation of ion background

break down of perturbation theory

periodically modulated (weak) ion potential

case for nearly free electron approximation

SLIDE 6

Peierls instability Peierls instability in 1D in 1D metal metal

nearly free electron approximation

secular equation

ccupied

empty

total ground state energy

elastic expense electronic gain

SLIDE 7

Peierls instability Peierls instability in 1D in 1D metal metal

elastic expense electronic gain

minimize w.r.t.

density of states at Fermi energy electron-phonon coupling constant

energy gap

f insulating phase

Peierls instability instability of Fermi surface

SLIDE 8

Peierls instability Peierls instability in 1D in 1D metal metal

charge modulation of electrons and ions

electron wave function (NFEA)

Charge Density Wave experimental systems

TTF-TCNQ resistivity

metal- insulator transition

NbSe3 STM

charge density modulation

rganic

conductor

H. Alves et al.

Nature Materials

S. Yasuzuka et al.

JPSJ(2007)