PAOFLOW.response.do_Hall#

Attributes#

comm

rank

Functions#

do_spin_Hall(data_controller, twoD, do_ac, P)

Compute the spin Hall conductivity tensor and optionally the AC spin Hall conductivity.

do_anomalous_Hall(data_controller, do_ac)

Compute the anomalous Hall conductivity and optionally the magneto-optical conductivity.

do_Berry_curvature(data_controller, jksp, pksp)

Compute the Berry curvature and its Fermi-energy integral via the Kubo formula.

do_ac_conductivity(data_controller, jksp, pksp, ipol, jpol)

Compute the frequency-dependent (optical) conductivity via the Kubo-Greenwood formula.

smear_sigma_loop(data_controller, ene, pksp_i, pksp_j, ...)

Evaluate the smeared off-diagonal conductivity sum for a single spin channel.

do_spin_current(data_controller, spol, ipol)

Compute the spin current operator \(j^{s}_{\rm pol}\) in the band basis.

Module Contents#

PAOFLOW.response.do_Hall.comm[source]#
PAOFLOW.response.do_Hall.rank[source]#
PAOFLOW.response.do_Hall.do_spin_Hall(data_controller, twoD, do_ac, P)[source]#

Compute the spin Hall conductivity tensor and optionally the AC spin Hall conductivity.

Parameters:

  • data_controller (DataController) – Object providing data_arrays and data_attributes. Required arrays: s_tensor (shape (n, 3) specifying \((i_{\rm pol}, j_{\rm pol}, s_{\rm pol})\) triplets), dHksp, v_k, degen, Sj, E_k, deltakp. Required attributes: dftSO, nk1, nk2, nk3, omega, alat, verbose, opath.

  • twoD (bool) – If True, normalise by the 2-D cross-sectional area instead of the 3-D volume.

  • do_ac (bool) – If True, also compute the AC spin Hall conductivity.

  • P (np.ndarray, shape (nawf, nawf)) – Projection operator used to symmetrize the spin current operator.

Returns:

Writes per-component output files to opath:

  • Spin_Berry_{spol}_{ipol}{jpol}.bxsf — spin Berry curvature on the k-grid.

  • shcEf_{spol}_{ipol}{jpol}.dat — spin Hall conductivity vs. Fermi energy.

  • When do_ac: ac_shcr_{...}.dat and ac_shci_{...}.dat.

Return type:

None

PAOFLOW.response.do_Hall.do_anomalous_Hall(data_controller, do_ac)[source]#

Compute the anomalous Hall conductivity and optionally the magneto-optical conductivity.

Parameters:

  • data_controller (DataController) – Object providing data_arrays and data_attributes. Required arrays: a_tensor (shape (n, 2) specifying \((i_{\rm pol}, j_{\rm pol})\) pairs), dHksp, v_k, degen, E_k, deltakp. Required attributes: dftSO, nk1, nk2, nk3, omega, alat, verbose, opath.

  • do_ac (bool) – If True, also compute the MCD (magneto-circular dichroism) optical conductivity.

Returns:

Writes per-component output files to opath:

  • Berry_{ipol}{jpol}.bxsf — Berry curvature on the k-grid.

  • ahcEf_{ipol}{jpol}.dat — anomalous Hall conductivity vs. Fermi energy.

  • When do_ac: MCDr_{...}.dat and MCDi_{...}.dat.

Return type:

None

PAOFLOW.response.do_Hall.do_Berry_curvature(data_controller, jksp, pksp)[source]#

Compute the Berry curvature and its Fermi-energy integral via the Kubo formula.

Parameters:

  • data_controller (DataController) – Object providing data_arrays and data_attributes. Required arrays: E_k (shape (snktot, nawf, nspin)), deltakp, deltakp2. Required attributes: npool, nkpnts, nk1, nk2, nk3, fermi_up, fermi_dw, deltaH, smearing, eminH, emaxH, esizeH, shift.

  • jksp (np.ndarray, shape (snktot, nawf, nawf, nspin), complex) – Left matrix element (spin current or momentum).

  • pksp (np.ndarray, shape (snktot, nawf, nawf, nspin), complex) – Right matrix element (momentum).

Returns:

  • ene (np.ndarray, shape (esizeH,)) – Energy grid (eV).

  • shc (np.ndarray or None) – Berry-curvature integral as a function of Fermi energy (rank 0 only).

  • Om_zk (np.ndarray or None) – Berry curvature on the k-grid reshaped to (nk1, nk2, nk3) evaluated at fermi_up minus the value at fermi_dw (rank 0 only).

Notes

Uses the Kubo formula

\[\Omega_n(\mathbf{k}) = -2 \sum_{m \ne n} \frac{\mathrm{Im}[j_{nm} p_{mn}]} {(\varepsilon_n - \varepsilon_m)^2 + \delta^2}\]

summed over occupied bands with occupation determined by the selected smearing scheme.

PAOFLOW.response.do_Hall.do_ac_conductivity(data_controller, jksp, pksp, ipol, jpol)[source]#

Compute the frequency-dependent (optical) conductivity via the Kubo-Greenwood formula.

Parameters:

  • data_controller (DataController) – Object providing data_arrays and data_attributes. Required arrays: E_k, deltakp, deltakp2. Required attributes: shift, esizeH, nkpnts, smearing, temp, delta.

  • jksp (np.ndarray, shape (snktot, nawf, nawf, nspin), complex) – Left matrix element.

  • pksp (np.ndarray, shape (snktot, nawf, nawf, nspin), complex) – Right matrix element.

  • ipol (int) – Polarisation index of the left operator (0=x, 1=y, 2=z).

  • jpol (int) – Polarisation index of the right operator.

Returns:

  • ene (np.ndarray or None) – Frequency grid (eV) on rank 0; None on other ranks.

  • sigxy (np.ndarray or None) – Complex optical conductivity \(\sigma_{ij}(\omega)\) on rank 0; None on other ranks.

PAOFLOW.response.do_Hall.smear_sigma_loop(data_controller, ene, pksp_i, pksp_j, ispin, ipol, jpol)[source]#

Evaluate the smeared off-diagonal conductivity sum for a single spin channel.

Parameters:

  • data_controller (DataController) – Object providing data_arrays and data_attributes. Required arrays: E_k, deltakp, deltakp2, delta. Required attributes: smearing, temp.

  • ene (np.ndarray, shape (esize,)) – Frequency grid (eV).

  • pksp_i (np.ndarray, shape (snktot, nawf, nawf, nspin), complex) – Left matrix elements.

  • pksp_j (np.ndarray, shape (snktot, nawf, nawf, nspin), complex) – Right matrix elements.

  • ispin (int) – Spin channel index.

  • ipol (int) – Left polarisation index.

  • jpol (int) – Right polarisation index.

Returns:

Per-rank partial sum of the conductivity; call MPI.Reduce to accumulate the global result.

Return type:

np.ndarray, shape (esize,), complex

PAOFLOW.response.do_Hall.do_spin_current(data_controller, spol, ipol)[source]#

Compute the spin current operator \(j^{s}_{\rm pol}\) in the band basis.

Parameters:

  • data_controller (DataController) – Object providing data_arrays. Required arrays: Sj (shape (3, nawf, nawf)), dHksp (shape (snktot, 3, nawf, nawf, nspin)).

  • spol (int) – Spin polarisation component index (0=x, 1=y, 2=z).

  • ipol (int) – Momentum/velocity component index.

Returns:

Symmetrised spin current matrix elements \(j^{s_\rm pol}_{nm}(\mathbf{k}) = \tfrac{1}{2}\{S^{s_\rm pol}, \partial_{i_\rm pol} H\}_{nm}\).

Return type:

np.ndarray, shape (snktot, nawf, nawf, nspin), complex