Doc for transport calculations.

doc/Transport.rst

@@ -9,44 +9,118 @@ Transport calculations
 
 Formalism
 ---------
-The optical conductivity and the Seebeck coefficient in the direction :math:`\alpha\beta` are defined as
+The conductivity and the Seebeck coefficient in direction :math:`\alpha\beta` are defined as [#transp]_:
 
 .. math::
 
-   \sigma_{\alpha\beta} = \beta e^{2} A_{0,\alpha\beta}  \ \ \  \text{and} \ \ \  S_{\alpha\beta} = -\frac{k_B}{|e|}\frac{A_{1,\alpha\beta}}{A_{0,\alpha\beta}} 
+   \sigma_{\alpha\beta} = \beta e^{2} A_{0,\alpha\beta}  \ \ \  \text{and} \ \ \  S_{\alpha\beta} = -\frac{k_B}{|e|}\frac{A_{1,\alpha\beta}}{A_{0,\alpha\beta}}, 
 
 in which the kinetic coefficients :math:`A_{n,\alpha\beta}` are given by
 
 .. math::
   
-   A_{n,\alpha\beta} = N_{sp} \pi \hbar \int{d\omega \left(\beta\omega\right)^n f\left(\omega\right)f\left(-\omega\right)\Gamma_{\alpha\beta}\left(\omega\right)}
+   A_{n,\alpha\beta} = N_{sp} \pi \hbar \int{d\omega \left(\beta\omega\right)^n f\left(\omega\right)f\left(-\omega\right)\Gamma_{\alpha\beta}\left(\omega\right)}.
 
-with the transport distribution
+Here :math:`N_{sp}` is the spin factor and :math:`f(\omega)` is the Fermi function. The transport distribution :math:`\Gamma_{\alpha\beta}\left(\omega\right)` is defined as
 
 .. math::
   
-   \Gamma_{\alpha\beta}\left(\omega\right) = \frac{1}{V} \sum_k Tr\left(v_{k,\alpha}A_{k}\left(\omega\right)v_{k,\beta}A_{k}\left(\omega\right)\right)
+   \Gamma_{\alpha\beta}\left(\omega\right) = \frac{1}{V} \sum_k Tr\left(v_{k,\alpha}A_{k}(\omega)v_{k,\beta}A_{k}\left(\omega\right)\right),
+
+where :math:`V` is the unit cell volume. In multi-band systems the velocities :math:`v_{k}` and the spectral function :math:`A(k,\omega)` are matrices in the band indices :math:`i` and :math:`j`.
+The frequency depended optical conductivity is given by
+
+.. math::
+
+   \sigma(\Omega) = N_{sp} \pi e^2 \hbar \int{d\omega \Gamma_{\alpha\beta}(\omega+\Omega/2,\omega-\Omega/2)\frac{f(\omega-\Omega/2)-f(\omega+\Omega/2)}{\Omega}}.
 
 .. index:: Prerequisite
 
 Prerequisites
 -------------
+First perform a standard DFT+DMFT calculation for your desired material (see :ref:`DFTDMFTmain`) and obtain the real-frequency self energy by doing an
+analytic continuation.
 
 .. note::
-   Coming soon!
+   It is crucial to perform the analytic continuation in such a way that the obtained real-frequency self energy is accurate around the Fermi energy as only its
+   low energy structure influences the final results!
 
+Besides the self energy the Wien2k files read by the transport converter are:
+   * :file:`.struct`: The lattice constants specified in the struct file are used to calculate the unit cell volume.
+   * :file:`.outputs`: In this file the k-point symmetries are given.
+   * :file:`.oubwin`: Contains the indices of the bands within the projected subspace (written by :program:`dmftproj`) for each k-point.
+   * :file:`.pmat`: This file is the output of the Wien2k optics package and contains the velocity (momentum) matrix elements between all bands in the desired energy
+     window for each k-point. How to use the optics package is described below.
+   * :file:`.h5`: The hdf file has to be present and should contain the dft_input subgroup. Otherwise :class:`convert_dft_input` needs to be called before :class:`convert_transport_input`.
+
+.. index:: Wien2k optics package
+
+Wien2k optics package
+---------------------
+
+The basics steps to calculate the matrix elements of the momentum operator with the Wien2k optics package are:
+    1) Perform a standard Wien2k calculation for your material.
+    2) Run `x kgen` to generate a dense k-mesh. 
+    3) Run `x lapw1`.
+    4) For metals change TETRA to 101.0 in :file:`case.in2`.
+    5) Run `x lapw2 -fermi`.
+    6) Run `x optic`. 
+
+Additionally the input file :file:`case.inop` is required. A detail description on how to setup this file can be found in the Wien2k user guide [#userguide]_ on page 166.
+Here the energy window can be chosen according to the window used for :program:`dmftprj`. However, keep in mind that energies have to be specified in absolute values! Furthermore it is important 
+to set line 6 to ON for printing the matrix elements to the :file:`.pmat` file.
 
 .. index:: Using the transport code.
 
 Using the transport code
 ------------------------
 
-.. note::
-   Coming soon!
+First we have to read the Wien2k files and store the relevant information in the hdf-file::
 
+    from pytriqs.applications.dft.converters.wien2k_converter import *
+    from pytriqs.applications.dft.sumk_dft_tools import *
+
+    Converter = Wien2kConverter(filename='case', repacking=True)
+    Converter.convert_transport_input()
+
+    SK = SumkDFTTools(hdf_file='case.h5', use_dft_blocks=True)
+
+Additionally we need to read and set the self energy::
+
+    ar = HDFArchive('case_Sigma.h5', 'a')
+    SK.put_Sigma(Sigma_imp = [ar['dmft_transp_output']['Sigma_w']])
+    del ar
+
+As next step we can calculate the transport distribution :math:`\Gamma_{\alpha\beta}(\omega)`::
+
+    SK.transport_distribution(directions=['xx'], Om_mesh=[0.00, 0.02], energy_window=[-0.3,0.3], 
+                                                 with_Sigma=True, broadening=0.0, beta=40)
+
+The parameters are:
+    * `directions`: :math:`\alpha` and :math:`\beta` (e.g. xx, yy, xz, ...)
+    * `Om_mesh`: :math:`\Omega`-mesh for the optical conductivity. Note that the code repines this mesh to the closest values on the self energy mesh! The new mesh is stored in `Om_meshr`. 
+      The Seebeck coefficient is only calculated if :math:`\Omega=0.0` is included.
+    * `energy_window`: Limits for the integration over :math:`\omega`. (Due to the Fermi functions the integrand is only of considerable size in a small 
+      window around the Fermi energy.)
+    * `with_Sigma`: If this parameter is set to False then Sigma is set to 0 (i.e. the DFT band structure :math:`A(k,\omega)` is taken).
+    * `broadening`: The numerical broadening should be set to a finite value for with_Sigma = False.
+
+The resulting transport distribution is not automatically saved, but this can be easily achieved with::
+    
+    SK.save(['Gamma_w','Om_meshr','omega','directions'])
+    SK.load(['Gamma_w','Om_meshr','omega','directions'])  
+
+Finally the optical conductivity :math:`\sigma(\Omega)` and the Seebeck coefficient :math:`S` can be obtained with::
+
+    SK.conductivity_and_seebeck(beta=40)
+    SK.save(['seebeck','optic_cond']) 
+
+It is strongly advised to check convergence in the number of k-points!
 
 .. index:: References
 
 References
 ----------
 
+.. [#transp] `V. S. Oudovenko, G. Palsson, K. Haule, G. Kotliar, S. Y. Savrasov, Phys. Rev. B 73, 035120 (2006) <http://link.aps.org/doi/10.1103/PhysRevB.73.0351>`_
+.. [#userguide] `P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvasnicka, J. Luitz, ISBN 3-9501031-1-2 <http://www.wien2k.at/reg_user/textbooks/usersguide.pdf>`_

doc/documentation.rst

@@ -18,6 +18,7 @@ A (not so) quick tour
    analysis
    selfcons
    Ce-HI
+   Transport
 
 Projective Wannier functions: the dmftproj package
 --------------------------------------------------