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Can someone explain how these two plots are related?

enter image description here

How are the peaks in the right are associated with the left figure?

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    $\begingroup$ Peaks in the DoS occur when dispersion is near zero in a large area of $k$-space. But do you understand what Gamma, X, S, and Y mean? $\endgroup$ – Pieter May 8 '18 at 11:26
  • $\begingroup$ Peaks of DoS always stands for van-Hove singularities $\endgroup$ – FangXie Apr 11 '19 at 19:06
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as you can from the plot many different k values correspond to the same energy near about -0.75eV for example. While in the plot the number of k values appears infinite, in reality they are actually spaced by 2Pi/a, where a is the lattice constant. This means there is a discrete number of k values at a specific energy. ie (DOS/eV)*(energy of the state) = Number of electrons at that energy

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If you have dispersions of the form $\epsilon_\mu(k)$ where $\mu$ is the band index and $k$ is momentum, the DOS is given by:

$$ \rho(\omega) = \sum_\mu \int \frac{dk}{(2\pi)^d} \delta ( \omega- \epsilon_\mu(k)) $$

Where $d$ is the spatial dimension. It should be pretty self-explanatory. For every value of $\omega$ you "sum" over all possible states that contribute to that value. In a translational invariant systems you count states by counting momenta (with a certain factor of $2\pi$).

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Gamma, X, S... are some k-points (wavenumbers), connected among them, defining a path of highly symmetric points in the first Brillouin of a crystal.

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    $\begingroup$ This doesn't answer the question. The question was not what the points are, but how DoS peaks are related to features of the band structure. $\endgroup$ – Ruslan Apr 11 '19 at 20:08

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