PAOFLOW.boltzmann.do_transport#

Functions#

do_transport(data_controller, temps, ene, velkp, ...)

Compute electronic transport tensors from Boltzmann transport theory.

Module Contents#

PAOFLOW.boltzmann.do_transport.do_transport(data_controller, temps, ene, velkp, channels, weights, do_hall, write_to_file, save_tensors)[source]#

Compute electronic transport tensors from Boltzmann transport theory.

Parameters:

  • data_controller (DataController) – Object providing data_arrays and data_attributes. Required attributes: smearing, nspin, dftSO, omega, opath.

  • temps (array_like of float) – Sequence of temperatures in Kelvin at which transport properties are evaluated.

  • ene (np.ndarray, shape (esize,)) – Energy grid (eV) at which the transport tensors are sampled.

  • velkp (np.ndarray) – Band velocities at each k-point, passed directly to do_Boltz_tensors().

  • channels (array_like) – Channel specification passed to do_Boltz_tensors().

  • weights (array_like) – k-point weights passed to do_Boltz_tensors().

  • do_hall (bool) – If True, also compute the antisymmetric Hall coefficient tensor.

  • write_to_file (bool) – If True, write all transport tensors to formatted .dat files in opath.

  • save_tensors (bool) – If True, store computed tensors in data_controller.data_arrays and broadcast them across MPI ranks.

Returns:

On rank 0, writes (when write_to_file is True) one file per spin channel and transport quantity:

  • sigma[smearing]_{ispin}.dat: electrical conductivity \(\sigma\) in S m⁻¹.

  • Seebeck[smearing]_{ispin}.dat: Seebeck coefficient \(S\) in V K⁻¹.

  • kappa[smearing]_{ispin}.dat: electron thermal conductivity \(\kappa\) in W m⁻¹ K⁻¹.

  • PF[smearing]_{ispin}.dat: power factor \(S^2 \sigma\) in W m⁻¹ K⁻².

  • hall_trace_{ispin}.dat (if do_hall): trace of the Hall coefficient tensor \(R_H\) in m³ C⁻¹.

When save_tensors is True, adds the following keys to data_controller.data_arrays:

  • sigma : np.ndarray, shape (3, 3, esize) — conductivity tensor in S m⁻¹.

  • S : np.ndarray, shape (3, 3, esize) — Seebeck tensor in V K⁻¹.

  • kappa : np.ndarray, shape (3, 3, esize) — thermal conductivity tensor in W m⁻¹ K⁻¹.

  • R_hall_trace : np.ndarray, shape (esize,) — averaged Hall coefficient in m³ C⁻¹ (only if do_hall).

Return type:

None

Notes

The transport tensors are derived from the generalised transport integrals \(\mathcal{L}^{(\alpha)}\) via the Boltzmann transport equation in the relaxation-time approximation:

\[\sigma = e^2 \mathcal{L}^{(0)}, \quad S = -\frac{1}{eT} (\mathcal{L}^{(0)})^{-1} \mathcal{L}^{(1)}, \quad \kappa = \frac{1}{T}\left[ \mathcal{L}^{(2)} - T\, \mathcal{L}^{(1)} (\mathcal{L}^{(0)})^{-1} \mathcal{L}^{(1)} \right]\]

The Hall coefficient is obtained from the antisymmetric part of the Hall transport tensor \(\mathcal{L}^{(0,\text{Hall})}\) as

\[R_H = (\sigma^{-1})\, \mathcal{L}^{(0,\text{Hall})}\, (\sigma^{-1})\]

and reported as the average of the three even-permutation components \((R_{012} + R_{201} + R_{120}) / 3\).

Conversion factors: siemen_conv = 6.9884 converts internal units to S m⁻¹ × 10⁻²¹; temp_conv = 11604.525 converts Kelvin to eV⁻¹; hall_SI = 9.249\times10^{-13} converts to m³ C⁻¹.