velocity¶
-
sisl.physics.electron.
velocity
(state, dHk, energy=None, dSk=None, degenerate=None)[source]¶ Calculate the velocity of a set of states
These are calculated using the analytic expression (\(\alpha\) corresponding to the Cartesian directions):
\[\mathbf{v}_{i\alpha} = \frac1\hbar \langle \psi_i | \frac{\partial}{\partial\mathbf k}_\alpha \mathbf H(\mathbf k) | \psi_i \rangle\]In case of non-orthogonal basis the equations substitutes \(\mathbf H(\mathbf k)\) by \(\mathbf H(\mathbf k) - \epsilon_i\mathbf S(\mathbf k)\).
Parameters: - state : array_like
vectors describing the electronic states, 2nd dimension contains the states. In case of degenerate states the vectors may be rotated upon return.
- dHk : list of array_like
Hamiltonian derivative with respect to \(\mathbf k\). This needs to be a tuple or list of the Hamiltonian derivative along the 3 Cartesian directions.
- energy : array_like, optional
energies of the states. Required for non-orthogonal basis together with dSk. In case of degenerate states the eigenvalues of the states will be averaged in the degenerate sub-space.
- dSk : list of array_like, optional
\(\delta \mathbf S_k\) matrix required for non-orthogonal basis. This and energy must both be provided in a non-orthogonal basis (otherwise the results will be wrong). Same derivative as dHk
- degenerate: list of array_like, optional
a list containing the indices of degenerate states. In that case a prior diagonalization is required to decouple them. This is done 3 times along each of the Cartesian directions.
Returns: - numpy.ndarray
velocities per state with final dimension
(state.shape[0], 3)
, the velocity unit is Ang/ps. Units may change in future releases.
See also
inv_eff_mass_tensor
- inverse effective mass tensor