Dispersion relation diagrams, phonons

  • Thread starter _Andreas
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  • #1
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In dispersion relation diagrams, where omega is plotted against k, omega is sometimes nonzero at k=0. How is this possible? I thought a wave had to have a nonzero wavenumber :confused:
 

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  • #2
Dr Transport
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Optical phonons have non-zero components at the center of the Brillouin zone.
 
  • #3
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The reason this is possible (as Dr T says, the optical branch has non-zero energy at k=0) is because k is not really a wavenumber.

p = [hbar]k is the 'crystal momentum', which is not a real momentum.
 
  • #4
ZapperZ
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Also, you could easily be reading a reduced zone scheme, in which the band from the next zone is folded back into the first zone.

Zz.
 
  • #5
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Optical phonons occur in crystals which have more than one atom per unit cell. If you have a phonon with k=0 that means the displacement of atoms is the same in every cell. When you have only one atom per cell, then a k=0 displacement is just a shift of the whole crystal, so there can't be a restoring force (hence, [tex]\omega=0[/tex]). But if you have more than one atom per unit cell then the atoms could displace relative to one another (eg. like a bond-stretching mode). Then you can have a k=0 wave, where the displacement is the same in each cell, but the atoms in the cell move relative to one another. Then you will have a restoring force, and have [tex]\omega > 0[/tex] for this type of phonon.
 
  • #6
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Wow, thanks guys!
 

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