Difference between revisions of "Van Hove singularities"
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Shepplestone (talk | contribs) (Created page with "Van Hoove Singularities are divergences in the Density of states (that tend to infinity). i.e. <math>G(E)=A/((E-E_0)^n)</math> as the energy tends to <math>E_0</math>. Typ...") |
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Van | Van Hove Singularities are divergences in the Density of states (that tend to infinity). i.e. <math>g(E)=A/((E-E_0)^n)</math> as the energy tends to <math>E_0</math>. | ||
| Line 7: | Line 7: | ||
<math>g(E)dE=dN= </math> | <math>g(E)dE=dN= </math> | ||
<math> | <math>g(E) \frac{dE}{dk} dk = dN</math> | ||
So | So | ||
<math> | <math>g(E)=\frac{dN/dK} {dE/dK}</math> | ||
Note, this should be done in 3D form with <math>\nabla</math> notation, but this is the simple version for easy learning. | Note, this should be done in 3D form with <math>\nabla</math> notation, but this is the simple version for easy learning. | ||
A full version is presented on Wikipedia. | A full version is presented on Wikipedia. | ||
Latest revision as of 16:55, 9 October 2025
Van Hove Singularities are divergences in the Density of states (that tend to infinity). i.e. as the energy tends to .
Typically, they require the group velocity of the particle goes to zero.
It can be viewed as coming from the DOS
So
Note, this should be done in 3D form with notation, but this is the simple version for easy learning.
A full version is presented on Wikipedia.