PDOS

sisl.physics.electron.PDOS(E, eig, state, S=None, distribution='gaussian', spin=None)[source]

Calculate the projected density of states (PDOS) for a set of energies, E, with a distribution function

The \(\mathrm{PDOS}(E)\) is calculated as:

\[\mathrm{PDOS}_i(E) = \sum_\alpha \psi^*_{\alpha,i} [\mathbf S | \psi_{\alpha}\rangle]_i D(E-\epsilon_\alpha)\]

where \(D(\Delta E)\) is the distribution function used. Note that the distribution function used may be a user-defined function. Alternatively a distribution function may be aquired from distribution.

In case of an orthogonal basis set \(\mathbf S\) is equal to the identity matrix. Note that DOS is the sum of the orbital projected DOS:

\[\mathrm{DOS}(E) = \sum_i\mathrm{PDOS}_i(E)\]

For non-colinear calculations (this includes spin-orbit calculations) the PDOS is additionally separated into 4 components (in this order):

Total projected DOS
Projected spin magnetic moment along \(x\) direction
Projected spin magnetic moment along \(y\) direction
Projected spin magnetic moment along \(z\) direction

These are calculated using the Pauli matrices \(\boldsymbol\sigma_x\), \(\boldsymbol\sigma_y\) and \(\boldsymbol\sigma_z\):

\[\begin{split}\mathrm{PDOS}_i^\sigma(E) &= \sum_\alpha \psi^*_{\alpha,i} \boldsymbol\sigma_z \boldsymbol\sigma_z [\mathbf S | \psi_\alpha\rangle]_i D(E-\epsilon_\alpha) \\ \mathrm{PDOS}_i^x(E) &= \sum_\alpha \psi^*_{\alpha,i} \boldsymbol\sigma_x [\mathbf S | \psi_\alpha\rangle]_i D(E-\epsilon_\alpha) \\ \mathrm{PDOS}_i^y(E) &= \sum_\alpha \psi^*_{\alpha,i} \boldsymbol\sigma_y [\mathbf S | \psi_\alpha\rangle]_i D(E-\epsilon_\alpha) \\ \mathrm{PDOS}_i^z(E) &= \sum_\alpha\psi^*_{\alpha,i} \boldsymbol\sigma_z [\mathbf S | \psi_\alpha\rangle]_i D(E-\epsilon_\alpha)\end{split}\]

Note that the total PDOS may be calculated using \(\boldsymbol\sigma_\gamma\boldsymbol\sigma_\gamma\) where \(\gamma\) may be either of \(x\), \(y\) or \(z\).

Parameters:

E (array_like) – energies to calculate the projected-DOS from
eig (array_like) – eigenvalues
state (array_like) – eigenvectors
S (array_like, optional) – overlap matrix used in the \(\langle\psi|\mathbf S|\psi\rangle\) calculation. If None the identity matrix is assumed. For non-colinear calculations this matrix may be halve the size of len(state[0, :]) to trigger the non-colinear calculation of PDOS.
distribution (func or str, optional) – a function that accepts \(E-\epsilon\) as argument and calculates the distribution function.
spin (str or Spin, optional) – the spin configuration. This is generally only needed when the eigenvectors correspond to a non-colinear calculation.