PDOS

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

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

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

$${\mathrm{PDOS}}_i(E)=\sum _{\alpha }{\psi }_{\alpha ,i}^{\ast }[\mathbf{S}|{\psi }_{\alpha }⟩{]}_{i}D(E-{ϵ}_{\alpha })$$

where $D(\mathrm{\Delta }E)$ is the distribution function used. Note that the distribution function used may be a user-defined function. Alternatively a distribution function may be acquired from Distribution functions.

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 ${\mathit{\sigma }}_x$, ${\mathit{\sigma }}_y$ and ${\mathit{\sigma }}_z$:

$$\begin{array}{rl}{\mathrm{PDOS}}_i^{\sigma }(E)& =\sum _{\alpha }{\psi }_{\alpha ,i}^{\ast }{\mathit{\sigma }}_z{\mathit{\sigma }}_z[\mathbf{S}|{\psi }_{\alpha }⟩{]}_{i}D(E-{ϵ}_{\alpha })\\ {\mathrm{PDOS}}_i^x(E)& =\sum _{\alpha }{\psi }_{\alpha ,i}^{\ast }{\mathit{\sigma }}_x[\mathbf{S}|{\psi }_{\alpha }⟩{]}_{i}D(E-{ϵ}_{\alpha })\\ {\mathrm{PDOS}}_i^y(E)& =\sum _{\alpha }{\psi }_{\alpha ,i}^{\ast }{\mathit{\sigma }}_y[\mathbf{S}|{\psi }_{\alpha }⟩{]}_{i}D(E-{ϵ}_{\alpha })\\ {\mathrm{PDOS}}_i^z(E)& =\sum _{\alpha }{\psi }_{\alpha ,i}^{\ast }{\mathit{\sigma }}_z[\mathbf{S}|{\psi }_{\alpha }⟩{]}_{i}D(E-{ϵ}_{\alpha })\end{array}$$

Note that the total PDOS may be calculated using ${\mathit{\sigma }}_{\gamma }{\mathit{\sigma }}_{\gamma }$ where $\gamma$ may be either of $x$, $y$ or $z$.

Parameters:

• E (ndarray) – energies to calculate the projected-DOS from

• eig (ndarray) – eigenvalues

• state (ndarray) – eigenvectors

• S (ndarray, optional) – overlap matrix used in the $⟨\psi |\mathbf{S}|\psi ⟩$ 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 (Literal['gaussian', 'lorentzian', 'fermi', 'bose-einstein', 'cold', 'step-function', 'heaviside'] | ~typing.Callable[[~collections.abc.Buffer | ~numpy._typing._array_like._SupportsArray[~numpy.dtype[~typing.Any]] | ~numpy._typing._nested_sequence._NestedSequence[~numpy._typing._array_like._SupportsArray[~numpy.dtype[~typing.Any]]] | bool | int | float | complex | str | bytes | ~numpy._typing._nested_sequence._NestedSequence[bool | int | float | complex | str | bytes]], ~numpy.ndarray]) – a function that accepts $E-ϵ$ 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.

See also

Distribution functions

a selected set of implemented distribution functions

DOS

total DOS (same as summing over orbitals)

COP

calculate COOP or COHP curves

spin_moment

spin moment

Geometry.apply

allows one to convert orbital data, to atomic data

Returns:

projected DOS calculated at energies, has dimension (1, state.shape[1], len(E)). For non-colinear calculations it will be (4, state.shape[1] // 2, len(E)), ordered as indicated in the above list. For Nambu calculations it will be (8, state.shape[1] // 4, len(E)).

Return type:

numpy.ndarray

Parameters:

distribution (Literal['gaussian', 'lorentzian', 'fermi', 'bose-einstein', 'cold', 'step-function', 'heaviside'] | ~typing.Callable[[~collections.abc.Buffer | ~numpy._typing._array_like._SupportsArray[~numpy.dtype[~typing.Any]] | ~numpy._typing._nested_sequence._NestedSequence[~numpy._typing._array_like._SupportsArray[~numpy.dtype[~typing.Any]]] | bool | int | float | complex | str | bytes | ~numpy._typing._nested_sequence._NestedSequence[bool | int | float | complex | str | bytes]], ~numpy.ndarray])