Phonon DOS

By the post-processing by yaml2dos.rb, total and partial phonon DOS are obtained. Total phonon DOS is calculated by,

$$D(\omega) = \frac{1}{n} \sum_{\mathbf{k},\nu}g(\omega - \omega(\mathbf{k},\nu)),$$ (3.10)

where $\omega$ is the phonon frequency, $n$ is the number of calculated q-points and $g(\omega)$ is the broadening function. In yaml2dos.rb, Gauss function is employed for the $g(\omega)$. Partial phonon DOS is calculated by,

$$D_{i,\mu}(\omega) = \frac{1}{n} \sum_{\mathbf{k},\nu}\vert\mathbf{e}_{i,\mu}(\mathbf{k},\nu)\vert^2 g(\omega - \omega(\mathbf{k},\nu)),$$ (3.11)

where, the indices $i$ and $\mu$ indicate the atom number and fraction of three directional parts, respectively. The $\mathbf{e}_{i,\mu}(\mathbf{k},\nu)$ is polarization vector which is the eigenvector of dynamical matrix.