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quanshengwu committed Jul 24, 2023
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99 changes: 84 additions & 15 deletions doc/source/features.rst
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Expand Up @@ -82,14 +82,19 @@ Consequently, there are 30 weights (for Bi2Se3), one for each projectors.
Line mode
------------

Calculate bulk energy band for a series k lines. This is the basic calculation after the
Calculate bulk energy band for a series k lines and project the selected orbitals onto the band structures. This is the basic calculation after the
construction of Wannier functions. You have to compare your Wannier interpolated bands
with the DFT bands. Those two bands should match well around the Fermi level.
This comparison can help verify the accuracy of the Wannier functions,
and ensure that they provide an appropriate description of the electronic structure of the system under study.
In order to obtain the parameter **NumOccupied**, you also need to calculate the bulk energy bands and plot it with
the software xmgrace.

In order to get the weight onto the projections, we need to set **SELECTED_WANNIERORBITALS** card. it
The orbital index is corresponding to the **PROJECTOS** card, nothing related to spin freedom. For example
In Bi2Se3, there are 30 Wannier functions in the hr.dat, however, there are only 15 projectors (orbitals).
So indices in **SELECTED_WANNIERORBITALS** are from 1 to 15.

.. _bulkekin:

Input
Expand All @@ -103,6 +108,12 @@ Typical flags for bulk band calculation in the wt.in. ::
Nk1 = 101 ! Number of k points for each k line
/

! get projected bands onto different orbitals, here we only consider orbital and omit the spin freedom
SELECTED_WANNIERORBITALS
2
1-6 ! Bi
7-15 ! Se

KPATH_BULK ! k point path
4 ! number of k lines only for bulk band
G 0.00000 0.00000 0.0000 Z 0.00000 0.00000 0.5000
Expand Down Expand Up @@ -141,31 +152,74 @@ The data structure for **bulkek.dat** ::

The subrotine for this feature is ek_bulk.f90 .

Examples
>>>>>>>>>

Two examples Bi2Se3 and Graphene were prepared:

Strong topological insulator Bi2Se3 (in order to get the fat-band plot, you need to modify bulkek.gnu following the instruction inside)

.. code:: console
$ cd examples/Bi2Se3
$ cp wt.in-bands wt.in
$ ../../bin/wt.x
$ gnuplot bulkek.gnu
2D Dirac semimetal Graphene

.. code:: console
$ cd examples/Graphene
$ cp wt.in-bands wt.in
$ ../../bin/wt.x
$ gnuplot bulkek.gnu
The band plots of Bi2Se3 and Graphene should be like this

.. image:: images/bulkbands.png
:scale: 30 %

.. note::

In order to get the latex symbol :math:`\Gamma` in gnuplot, you need to replace **"G"** to **"{/Symbol G}"** in the bulkek.gnu like this

set xtics ("M " 0.00000,"K " 0.84848, **"{/Symbol G}"** 2.54543,"M " 4.01504)

Plane mode
--------------

Calculate band structure in a k slice(plane) specified by KPLANE_BULK card.
The mode is very useful to visualize the Dirac/Weyl cone. You have to set the following tags in **wt.in** ::
The mode is very useful to visualize the Dirac/Weyl cone. You have to set the following necessary tags in **wt.in** ::


!> bulk band structure calculation flag
&CONTROL
BulkBand_plane_calc = T
/
&SYSTEM
NumOccupied = 1 ! only write out 4 bands around NumOccpuied
SOC = 0 ! soc
E_FERMI = -1.2533 ! e-fermi
/
&PARAMETERS
Nk1 = 51 ! Number of k points along the first vector in KPLANE_BULK
Nk2 = 51 ! Number of k points along the second vector in KPLANE_BULK
Nk1 = 201 ! number k points
Nk2 = 201 ! number k points
/

KPLANE_BULK ! fractional coordinates
0.00 0.00 0.30 ! Middle point for a k slice(plane) in 3D BZ. Usually, the position of Dirac points.
0.50 0.00 0.00 ! The first vector to define k plane(slice) in 3D BZ
0.00 0.50 0.00 ! The second vector to define k plane(slice) in 3D BZ

0.333333 0.333333 0.000000 ! Middle point for a k slice(plane) in 3D BZ. Usually, the position of Dirac points.
0.100000 0.000000 0.000000 ! The first vector to define k plane(slice) in 3D BZ
0.000000 0.100000 0.000000 ! The second vector to define k plane(slice) in 3D BZ

The output file is **bulkek_plane.dat**, **bulkek_plane-matlab.dat** and **bulkek_plane.gnu**. You can get
**bulkek_plane.png** with ::
**bulkek_plane.png** with

.. code:: console
gnuplot bulkek_plane.gnu
$ gnuplot bulkek_plane.gnu
The **bulkek_plane-matlab.dat** is in MATLAB data format. You can plot the Dirac cone with matlab.

Expand All @@ -181,8 +235,23 @@ where the x and y direction are line in the k plane and the z direction is perpe
Column 7-10th are energies at each k point. Here we only print out 4 energy bands around the fermilevel. It depends on **NumOccupied**.
Usually, I choose column 4th and 5th as k coordinates and choose 8 and 9 as energy bands to show the Dirac cone shown below.

.. image:: images/bulk_plane.jpeg
:scale: 30 %

Example
--------------

There is one example in the examples/Graphene

.. code:: console
$ cd examples/Graphene
$ cp wt.in-bands-plane wt.in
$ ../../bin/wt.x
$ gnuplot bulkek_plane.gnu
The output is bulkek_plane.png and should like this

.. image:: images/graphene_dirac_cone.png
:scale: 50 %


.. _bulkfscalculation:
Expand All @@ -192,9 +261,9 @@ Usually, I choose column 4th and 5th as k coordinates and choose 8 and 9 as ener
Fermi surface calculation of the bulk system.

When calculating systems with SOC=0, meaning no spin-orbit coupling,
WannierTools computes 12 bands from the *NumOccupied-5* to NumOccupied+6 energy levels.
WannierTools computes 12 bands from the **NumOccupied-5** to **NumOccupied+6** energy levels.
However, when calculating systems with SOC=1, meaning spin-orbit coupling is present,
WannierTools computes 16 bands from the *NumOccupied-7* to NumOccupied+8 energy levels.
WannierTools computes 16 bands from the **NumOccupied-7** to **NumOccupied+8** energy levels.

.. NOTE::
1. In order to reduce the storage of the Fermi surface, we only write out few energy bands around NumOccupied'th bands.
Expand Down
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68 changes: 8 additions & 60 deletions examples/Bi2Se3/wt.in
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@@ -1,6 +1,5 @@
&TB_FILE
Hrfile = 'wannier90_hr.dat'
!Hrfile = 'wannier90_hr.dat_nsymm12'
Package = 'VASP' ! obtained from VASP, it could be 'VASP', 'QE', 'Wien2k', 'OpenMx'
/

Expand All @@ -27,45 +26,27 @@ Se pz px py
Se pz px py
Se pz px py

SURFACE ! See doc for details
1 0 0
0 1 0


!> bulk band structure calculation flag
&CONTROL
SlabBandWaveFunc_calc = F
BulkBand_calc = T
BulkBand_points_calc = F
SlabBand_calc = T
WireBand_calc = F
SlabSS_calc = F
SlabArc_calc = F
Z2_3D_calc = F
SlabSpintexture_calc = F
Wanniercenter_calc = F
SHC_calc = F
BulkBand_points_calc = T
/

&SYSTEM
NSLAB = 20 ! for thin film system
NSLAB1= 4 ! nanowire system
NSLAB2= 4 ! nanowire system
NumOccupied = 18 ! NumOccupied
SOC = 1 ! soc
E_FERMI = 4.4195 ! e-fermi
/

! get projected bands onto different orbitals, here we only consider orbital and omit the spin freedom
SELECTED_WANNIERORBITALS
2
1-6 ! Bi
7-15 ! Se


&PARAMETERS
Eta_Arc = 0.050 ! infinite small value, like brodening
E_arc = 0.0 ! energy for calculate Fermi Arc
OmegaNum = 300 ! omega number
OmegaMin = -5.0 ! energy interval
OmegaMax = 5.0 ! energy interval
Nk1 = 41 ! number k points odd number would be better
Nk2 = 41 ! number k points odd number would be better
Nk3 = 41 ! number k points odd number would be better
NP = 2 ! number of principle layers
/

KPATH_BULK ! k point path
Expand All @@ -75,34 +56,6 @@ Z 0.00000 0.00000 0.5000 F 0.50000 0.50000 0.0000
F 0.50000 0.50000 0.0000 G 0.00000 0.00000 0.0000
G 0.00000 0.00000 0.0000 L 0.50000 0.00000 0.0000

KPATH_SLAB
2 ! numker of k line for 2D case
K 0.33 0.67 G 0.0 0.0 ! k path for 2D case
G 0.0 0.0 M 0.5 0.5

KPLANE_SLAB
-0.1 -0.1 ! Original point for 2D k plane
0.2 0.0 ! The first vector to define 2D k plane
0.0 0.2 ! The second vector to define 2D k plane for arc plots

KPLANE_BULK
0.00 0.00 0.50 ! Original point for 3D k plane
1.00 0.00 0.00 ! The first vector to define 3d k space plane
0.00 0.50 0.00 ! The second vector to define 3d k space plane


KCUBE_BULK
0.00 0.00 0.00 ! Original point for 3D k plane
1.00 0.00 0.00 ! The first vector to define 3d k space plane
0.00 1.00 0.00 ! The second vector to define 3d k space plane
0.00 0.00 1.00 ! The third vector to define 3d k cube


EFFECTIVE_MASS ! optional
2 ! The i'th band to be calculated
0.01 ! k step in unit of (1/Angstrom)
0.0 0.0 0.0 ! k point where the effective mass calculated.

KPOINTS_3D
4
Direct
Expand All @@ -111,11 +64,6 @@ Direct
0.0 0.5 0.0
0.0 0.0 0.5

SINGLEKPOINT_2D
Direct
0.0 0.0


WANNIER_CENTRES ! copy from wannier90.wout
Cartesian
-0.000040 -1.194745 6.638646
Expand Down
99 changes: 99 additions & 0 deletions examples/Bi2Se3/wt.in-bands
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@@ -0,0 +1,99 @@
&TB_FILE
Hrfile = 'wannier90_hr.dat'
Package = 'VASP' ! obtained from VASP, it could be 'VASP', 'QE', 'Wien2k', 'OpenMx'
/

LATTICE
Angstrom
-2.069 -3.583614 0.000000 ! crystal lattice information
2.069 -3.583614 0.000000
0.000 2.389075 9.546667

ATOM_POSITIONS
5 ! number of atoms for projectors
Direct ! Direct or Cartisen coordinate
Bi 0.3990 0.3990 0.6970
Bi 0.6010 0.6010 0.3030
Se 0.0000 0.0000 0.5000
Se 0.2060 0.2060 0.1180
Se 0.7940 0.7940 0.8820

PROJECTORS
3 3 3 3 3 ! number of projectors
Bi pz px py ! projectors
Bi pz px py
Se pz px py
Se pz px py
Se pz px py

!> bulk band structure calculation flag
&CONTROL
BulkBand_calc = T
BulkBand_points_calc = T
/

&SYSTEM
NumOccupied = 18 ! NumOccupied
SOC = 1 ! soc
E_FERMI = 4.4195 ! e-fermi
/

! get projected bands onto different orbitals, here we only consider orbital and omit the spin freedom
SELECTED_WANNIERORBITALS
2
1-6 ! Bi
7-15 ! Se


&PARAMETERS
Nk1 = 41 ! number k points odd number would be better
/

KPATH_BULK ! k point path
4 ! number of k line only for bulk band
G 0.00000 0.00000 0.0000 Z 0.00000 0.00000 0.5000
Z 0.00000 0.00000 0.5000 F 0.50000 0.50000 0.0000
F 0.50000 0.50000 0.0000 G 0.00000 0.00000 0.0000
G 0.00000 0.00000 0.0000 L 0.50000 0.00000 0.0000

KPOINTS_3D
4
Direct
0.0 0.0 0.0
0.5 0.0 0.0
0.0 0.5 0.0
0.0 0.0 0.5

WANNIER_CENTRES ! copy from wannier90.wout
Cartesian
-0.000040 -1.194745 6.638646
0.000038 -1.196699 6.640059
-0.000032 -1.192363 6.640243
-0.000086 -3.583414 2.908040
0.000047 -3.581457 2.906587
-0.000033 -3.585864 2.906443
-0.000001 1.194527 4.773338
0.000003 1.194538 4.773336
-0.000037 1.194536 4.773327
0.000006 -1.194384 1.130261
-0.000018 -1.216986 1.140267
0.000007 -1.172216 1.140684
0.000011 -3.583770 8.416406
-0.000002 -3.561169 8.406398
-0.000007 -3.605960 8.405979
0.000086 -1.194737 6.638626
-0.000047 -1.196693 6.640080
0.000033 -1.192286 6.640223
0.000040 -3.583406 2.908021
-0.000038 -3.581452 2.906608
0.000032 -3.585788 2.906424
0.000001 1.194548 4.773330
-0.000003 1.194537 4.773332
0.000037 1.194539 4.773340
-0.000011 -1.194381 1.130260
0.000002 -1.216981 1.140268
0.000007 -1.172191 1.140687
-0.000006 -3.583766 8.416405
0.000018 -3.561165 8.406400
-0.000007 -3.605935 8.405982

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