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update with wannierisation and other
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161 changes: 21 additions & 140 deletions source/capabilities.rst
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.. _sec-capabilities:

********************************
Capabilities (incomplete list)
********************************
**************
Capabilities
**************

.. role:: red
.. role:: green
Expand All @@ -14,142 +14,20 @@ Capabilities (incomplete list)
Integration
-----------

see `Calculators <https://docs.wannier-berri.org/en/master/docs/calculators.html>`__ for details

The code may be used to evaluate the following quantities, represented
as Brillouin zone integrals.

Static (frequency-independent) quantities
++++++++++++++++++++++++++++++++++++++++++

- ``'ahc'`` : intrinsic anomalous Hall conductivity
:math:`\sigma_{\alpha\beta}^{\rm AHE}` (`Nagaosa et al. 2010 <https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.82.1539>`_) via

.. math:: \sigma_{\alpha\beta}^{\rm AHE}=-\frac{e^2}{\hbar}\epsilon_{\alpha\beta\gamma}\int \frac{d{\bf k}}{(2\pi)^3}\Omega_\gamma({\bf k}).


- Anomalous Nernst conductivity (`Xiao et al. 2006 <https://doi.org/10.1103/PhysRevLett.97.026603>`_)
:math:`\alpha_{\alpha\beta}^{\rm ANE}` may be obtained from
:math:`\sigma_{\alpha\beta}(\epsilon)^{\rm AHE}` evaluated over a
dense grid of Fermi levels :math:`\epsilon`

.. math::
:label: eq-ANE
\alpha_{\alpha\beta}^{\rm ANE}=-\frac{1}{e}\int d\varepsilon \frac{\partial f}{\partial\varepsilon}\sigma_{\alpha\beta}(\varepsilon)\frac{\varepsilon-\mu}{T}, \label{eq:ANE}
where
:math:`f(\varepsilon)=1/\left(1+e^\frac{\varepsilon-\mu}{k_{\rm B}T}\right)`;

- ``'Morb'`` : orbital magnetization (`Lopez et al. 2012 <https://doi.org/10.1103/PhysRevB.85.014435.>`_)

.. math::
M^\gamma_n({\bf k})=\frac{e}{2\hbar}{\rm Im\,}\epsilon_{\alpha\beta\gamma}\int[d{\bf k}]\sum_n^{\rm occ}\Bigl[
\langle\partial_a u_{n{\bf k}}\vert H_{\bf k}+E_{n{\bf k}}-2E_F\vert\partial_b u_{n{\bf k}}\rangle\Bigr];
- ``'berry_dipole'`` and ``'berry_dipole_fsurf'`` : berry curvature dipole

.. math::
D_{\alpha\beta}(\mu)=\int[d{\bf k}]\sum_n^{\rm occ} \partial_\alpha \Omega_n^{\beta}= \int[d{\bf k}]\sum_n^{\rm occ} \partial_\alpha E_{n\mathbf{k}} \Omega_n^{\beta} \delta(E_{n\mathbf{k}}-\mu)
which describes nonlinear Hall effect (`Sodemann and Fu 2015 <https://link.aps.org/doi/10.1103/PhysRevLett.115.216806>`_);


- ``'gyrotropic_Korb'`` and ``'gyrotropic_Kspin' :`` gyrotropic
magnetoelectric effect (GME) (`Zhong, Moore, and Souza 2016 <https://link.aps.org/doi/10.1103/PhysRevLett.116.077201>`_) tensor
(orbital and spin contributions) in the Fermi-sea formulation:

.. math:: K_{\alpha\beta}(\mu)=\int[d{\bf k}]\sum_n^{\rm occ} \partial_\alpha m_n^{\beta} ; \label{eq:gyro-K}

- ``'gyrotropic_Korb_fsurf'`` and ``'gyrotropic_Kspin_fsurf'`` : gyrotropic
magnetoelectric effect (GME) (`Zhong, Moore, and Souza 2016 <https://link.aps.org/doi/10.1103/PhysRevLett.116.077201>`_) tensor
(orbital and spin contributions) in the Fermi-surface formulation:

.. math::
K_{\alpha\beta}(\mu)=\int[d{\bf k}]\sum_n^{\rm occ} \partial_\alpha E_{n\mathbf{k}} m_n^{\beta} \delta (E_{n{\bf k}}-\mu)
- ``'conductivity_Ohmic'`` and ``'conductivity_Ohmic_fsurf'`` ohmic conductivity within the Boltzmann
transport theory in constant relaxation time (:math:`\tau`)
- Femi-sea and Fermi-surface formula approximation:

.. math::
\sigma_{\alpha\beta}^{\rm Ohm}(\mu)
=\tau\int[d{\bf k}]\sum_n^{E_{n{\bf k}}<\mu} \partial^2_{\alpha\beta} E_{n{\bf k}}
=\tau\int[d{\bf k}]\sum_n^{\rm occ} \partial_\alpha E_{n{\bf k}}\partial_\beta E_{n{\bf k}} \delta(E_{n{\bf k}}-\mu)
; \label{eq:ohmic}
- ``'dos'``: density of states :math:`n(E)`

- ``'cumdos'``: cumulative density of states

.. math::
N(E) = \int\limits_{-\infty}^En(\epsilon)d\epsilon.
\label{eq:cDOS}
- ``'shc_static_ryoo'`` and ``'shc_static_qiao'``: Kubo-Greenwood formula for static spin Hall conductivity (SHC) (`Ryoo, Park, and Souza 2019 <https://journals.aps.org/prb/abstract/10.1103/PhysRevB.99.235113>`_) or (`Qiao, Zhou, Yuan, and Zhao 2018 <https://journals.aps.org/prb/abstract/10.1103/PhysRevB.98.214402>`_). Equivalent to setting :math:`\omega=0` in ``'opt_SHCryoo'`` and ``'opt_SHCqiao'``.

.. math::
\sigma^{\gamma}_{\alpha\beta}(\mu) =
\frac{e\hbar}{N_k\Omega_c} \sum_{\bf k} \sum_n^{\rm occ}
\Omega^{{\rm spin};\,\gamma}_{\alpha\beta, n}({\bf k}),
where

.. math::
\Omega^{{\rm spin};\,\gamma}_{\alpha\beta, n}({\bf k}) = -2 {\rm Im} \sum_l^{\rm unocc}
\frac{\langle\psi_{n{\bf k}}\vert \frac{1}{2} \{ s^{\gamma}, v_\alpha \} \vert\psi_{l{\bf k}}\rangle
\langle\psi_{l{\bf k}}\vert v_\beta\vert\psi_{n{\bf k}}\rangle}
{(\varepsilon_{n{\bf k}}-\varepsilon_{l{\bf k}})^2}.
see `StaticCalculator <https://docs.wannier-berri.org/en/master/docs/calculators.html#static-dependent-only-on-fermi-level>`__ for details

Dynamic (frequency-dependent) quantities
++++++++++++++++++++++++++++++++++++++++++

- ``'opt_conductivity'``: Kubo-greenwood formula for optical conductivity (:ref:`example <sec-optconf-example>`)

.. math::
:label: optcondform
\sigma_{\alpha\beta}(\hbar\omega)=\frac{ie^2\hbar}{N_k\Omega_c}
\sum_{\bf k}\sum_{n,m}
\frac{f_{m{\bf k}}-f_{n{\bf k}}}
{\varepsilon_{m{\bf k}}-\varepsilon_{n{\bf k}}}
\frac{\langle\psi_{n{\bf k}}\vert v_\alpha\vert\psi_{m{\bf k}}\rangle
\langle\psi_{m{\bf k}}\vert v_\beta\vert\psi_{n{\bf k}}\rangle}
{\varepsilon_{m{\bf k}}-\varepsilon_{n{\bf k}}-(\hbar\omega+i\eta)}.
- ``'opt_shiftcurrent'``: shift photocurrent (`PRB 2018 <https://doi.org/10.1103/PhysRevB.97.245143>`_)

.. math::
:label: shiftcurrent
\sigma^{abc}(0;\omega,-\omega) = -\frac{i\pi e^3}{4\hbar^2}
\sum_{\bf k}\sum_{n,m}\left( f_{n{\bf k}}-f_{m{\bf k}} \right)
\left(I^{abc}_{mn}+I^{acb}_{mn}\right)
\times \left[\delta(\omega_{mn}-\omega)+\delta(\omega_{nm}-\omega)\right].
where :math:`I^{abc}_{mn}=r^b_{mn}r^{c;a}_{nm}`; :math:`r^a_{\mathbf{k}nm}=(1-\delta_{nm})A^a_{\mathbf{k} nm}`;
:math:`r^{a;b}_{\mathbf{k} nm}=\partial_b r^a_{\mathbf{k} nm} -i\left(A^b_{\mathbf{k}nn}-A^b_{\mathbf{k} mm}\right)r^a_{\mathbf{k} nm}`;
:math:`A^a_{\mathbf{k} nm}=i\langle{u_{\mathbf{k} n}}|{\partial_a u_{\mathbf{k} m}}\rangle`.

- ``'opt_SHCryoo'`` and ``'opt_SHCqiao'``: Kubo-Greenwood formula for spin Hall conductivity (SHC) under time-reversal symmetry (`Ryoo, Park, and Souza 2019 <https://journals.aps.org/prb/abstract/10.1103/PhysRevB.99.235113>`_) or (`Qiao, Zhou, Yuan, and Zhao 2018 <https://journals.aps.org/prb/abstract/10.1103/PhysRevB.98.214402>`_)

.. math::
\sigma^{\gamma}_{\alpha\beta}(\hbar\omega)=\frac{-e\hbar}{N_k\Omega_c}
\sum_{\bf k}\sum_{n,m}
\left(f_{n{\bf k}}-f_{m{\bf k}}\right)
\frac{\textrm{Im}\left[\langle\psi_{n{\bf k}}\vert \frac{1}{2}\{ s^{\gamma}, v_\alpha \} \vert\psi_{m{\bf k}}\rangle
\langle\psi_{m{\bf k}}\vert v_\beta\vert\psi_{n{\bf k}}\rangle\right]}
{(\varepsilon_{n{\bf k}}-\varepsilon_{m{\bf k}})^2-(\hbar\omega+i\eta)^2}.
see `DynamicCalculator <https://docs.wannier-berri.org/en/master/docs/calculators.html#dynamic-dependent-on-fermi-level-and-frequency>`__ for details


Tabulating
Expand All @@ -171,21 +49,21 @@ visualization software is straightforward.

Some of the quantites that are available to tabulate are:

- ``'berry'``: Berry curvature [Å\ :sup:`2`\]
- Berry curvature [Å\ :sup:`2`\]

.. math:: \Omega^\gamma_n({\bf k})=-\epsilon_{\alpha\beta\gamma}{\rm Im\,}\langle\partial_\alpha u_{n{\bf k}}\vert\partial_\beta u_{n{\bf k}}\rangle;

- ``'morb'``: orbital moment of Bloch states [eV·Å\ :sup:`2`\]
- orbital moment of Bloch states [eV·Å\ :sup:`2`\]

.. math:: m^\gamma_n({\bf k})=\frac{e}{2\hbar}\epsilon_{\alpha\beta\gamma}{\rm Im\,}\langle\partial_\alpha u_{n{\bf k}}\vert H_{\bf k}-E_{n{\bf k}}\vert\partial_\beta u_{n{\bf k}}\rangle;

- ``'spin'``: the expectation value of the Pauli operator [ħ]
- the expectation value of the Pauli operator [ħ]

.. math:: \mathbf{s}_n({\bf k})=\langle u_{n{\bf k}}\vert\hat{\bf \sigma}\vert u_{n{\bf k}}\rangle;

- ``'V'``: the band gradients [eV·Å] :math:`\nabla_{\bf k}E_{n{\bf k}}`.
- the band gradients [eV·Å] :math:`\nabla_{\bf k}E_{n{\bf k}}`.

- ``'spin_berry'``: Spin Berry curvature [ħ·Å\ :sup:`2`\]. Requires an additional parameter ``spin_current_type`` which can be ``"ryoo"`` or ``"qiao"``.
- Spin Berry curvature [ħ·Å\ :sup:`2`\]. Requires an additional parameter ``spin_current_type`` which can be ``"ryoo"`` or ``"qiao"``.

.. math::
Expand All @@ -194,6 +72,9 @@ Some of the quantites that are available to tabulate are:
\langle\psi_{l{\bf k}}\vert v_\beta\vert\psi_{n{\bf k}}\rangle}
{(\varepsilon_{n{\bf k}}-\varepsilon_{l{\bf k}})^2}.
- k-space derivatives of the above quantities (following the `paper <https://arxiv.org/abs/2303.10129>`__)

see `full list here <https://docs.wannier-berri.org/en/master/docs/calculators.html#tabulating>`__

Evaluation of additional matrix elements
-----------------------------------------
Expand All @@ -204,6 +85,9 @@ have been developed:
mmn2uHu
++++++++++++++++++

see `documentation <https://docs.wannier-berri.org/en/master/docs/mmn2uHu.html>`__ for more details


The |mmn2uHu| module evaluates the (``.uHu`` file) containing the matrix elements needed for orbital moment calculations

.. math::
Expand All @@ -226,26 +110,23 @@ on the basis of the ``.mmn``, ``.spn`` and ``.eig`` files by means of the sum-ov
\langle u_{m{\bf q}}\vert\hat{s}\vert u_{n{\bf q}+\mathbf{b}}\rangle \approx \sum_l^{l_{\rm max}} \left(s_{lm}({\bf q})\right)^* M_{ln}^{\mathbf{b}}({\bf q}).
see :ref:`sec-mmn2uHu` for more details
vaspspn
+++++++

see `documentation <file://///wsl.localhost/Ubuntu-24.04/home/stepan/github/wannier-berri-org/docs/html/capabilities.html#vaspspn>`__ for more details

The |vaspspn| computes the spin matrix

.. math:: s_{mn}({\bf q})=\langle u_{m{\bf q}}\vert\hat{\sigma}\vert u_{n{\bf q}}\rangle

based on the normalized pseudo-wavefunction read from the ``WAVECAR`` file written by
`VASP <https://www.vasp.at/>`_

see :ref:`sec-vaspspn` for more details




The |mmn2uHu| and |vaspspn| modules were initially developed and
used in (`Tsirkin, Puente, and Souza 2018 <https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.035158>`_) as separate scripts, but were
not published so far. Now they are included in the ``WannierBerri``
package with a hope of being useful for the community.
used in (`Tsirkin, Puente, and Souza 2018 <https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.035158>`_) as separate scripts.

.. include:: shortcuts.rst
34 changes: 27 additions & 7 deletions source/index.rst
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Expand Up @@ -20,27 +20,47 @@ a code to calculate different properties by means of Wannier interpolation: Berr
Advantages
#############

* |NEW| Symmetry adapted Wannier functions (R. Sakuma `Phys. Rev. B 87, 235109 (2013) <https://journals.aps.org/prb/abstract/10.1103/PhysRevB.87.235109>`__ )with

- spin-orbit coupling
- time-reversal symmetry
- magnetic symmetries
- frozen window
- compatible with Quantum ESPRESSO, VASP, and Abinit

See `documentation <https://docs.wannier-berri.org/en/master/docs/wannierisation.html>`__
and `tutorial <https://tutorial.wannier-berri.org/tutorials/6_wannierisation/wannierise.html>`__ for details

* **speed** - it may be upto **1000 or more times faster** then ``postw90.x`` : :ref:`comparison <sec-timing>`

* **extensive functionality** -- see :ref:`sec-capabilities`

* **felxibility** -- may be used with Wannier functions and tight-binding models
* **felxibility** -- may be used with
- Wannier functions calculated by
+ WannierBerri itself ( `docs <https://docs.wannier-berri.org/en/master/docs/wannierisation.html>`__ )
+ Wannier90 ( `docs <https://docs.wannier-berri.org/en/master/docs/system.html#id1>`__ )
+ FPLO ( `docs <https://docs.wannier-berri.org/en/master/docs/system.html#fplo>`__ )
+ ASE ( `docs <https://docs.wannier-berri.org/en/master/docs/system.html#ase>`__ )
- tight-binding models
+ PythTB ( `docs <https://docs.wannier-berri.org/en/master/docs/system.html#pythtb>`__ )
+ TBmodels ( `docs <https://docs.wannier-berri.org/en/master/docs/system.html#tbmodels>`__ )
- :math:`k\cdot p` `models <https://docs.wannier-berri.org/en/master/docs/system.html#mathbf-k-cdot-mathbf-p-models>`__

* use of `symmetries <https://docs.wannier-berri.org/en/master/symmetries.html>`__ to reduce evaluation to symmetry-irreducible **k** points and increase precision.

* use of :ref:`symmetries <sec-symmetry>` to reduce evaluation to symmetry-irreducible **k** points.
* `fast Fourier transform <https://www.nature.com/articles/s41524-021-00498-5/figures/1>`__

* :ref:`fast Fourier transform <sec-FFT>`
* Recursive adaptive `refinement <https://www.nature.com/articles/s41524-021-00498-5/figures/1>`__ for enhanced accuracy.

* Recursive adaptive :ref:`refinement <sec-refine>` for enhanced accuracy.

* :ref:`Fermi scan <sec-fermisea>` and :ref:`minimal distance replica selection <sec-replica>` have no cost
* `Fermi scan <https://www.nature.com/articles/s41524-021-00498-5/figures/4>`__ and
`minimal distance replica selection <https://www.nature.com/articles/s41524-021-00498-5/figures/3>`__ have no cost

#############
Please cite
#############

* Stepan S. Tsirkin. High performance Wannier interpolation of Berry curvature and related quantities with WannierBerri code. `npj Comput Mater 7, 33 (2021). <https://www.nature.com/articles/s41524-021-00498-5>`_ (Open Access).


################
Documentation
################
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Expand Up @@ -110,40 +110,39 @@ Contributed
:height: 200px
:alt: Seung-Ju

-
- Óscar Pozo Ocaña

Centro de Física de Materiales

San Sebastián, Spain

Working on
============
.. image:: imag/photo/Oscar.jpg
:width: 200px
:alt: Oscar Pozo
:target: https://cfm.ehu.es/team/oscar-pozo-ocana/

.. list-table::
:align: left
:widths: 33 33
:header-rows: 0


.. Working on
.. ============
* - Iñigo Robredo Magro
.. .. list-table::
.. :align: left
.. :widths: 33 33
.. :header-rows: 0
Donostia International Physics Center
San Sebastián, Spain
.. image:: https://pbs.twimg.com/profile_images/1166671811062501376/YBQfHmSm_400x400.jpg
:width: 200px
:alt: Inigo Robredo
.. * - Iñigo Robredo Magro
- Óscar Pozo Ocaña
.. Donostia International Physics Center
Centro de Física de Materiales
.. San Sebastián, Spain
San Sebastián, Spain
.. .. image:: https://pbs.twimg.com/profile_images/1166671811062501376/YBQfHmSm_400x400.jpg
.. :width: 200px
.. :alt: Inigo Robredo
.. image:: imag/photo/Oscar.jpg
:width: 200px
:alt: Oscar Pozo
:target: https://cfm.ehu.es/team/oscar-pozo-ocana/
Consultants
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