wannier90: Tutorial

1 wannier90 : TutorialVersion January 2017 ContentsPreliminaries3 Parallel execution3 About this tutorial4 Contact us41: Gallium Arsenide MLWFs for the valence bands52: Lead Wannier-interpolated Fermi surface63: Silicon Disentangled MLWFs64: Copper Fermi surface, orbital character of energy bands8 Examples Using thepwscfInterface105: Diamond MLWFs for the valence bands106: Copper Fermi surface117: Silane (SiH4) Molecular MLWFs using -point sampling128: Iron Spin-polarized WFs, DOS, projected WFs versus MLWFs139: Cubic BaTiO31510: Graphite1712wannier90: Tutorial11: Silicon Valence and low-lying conduction states1712: Benzene Valence and low-lying conduction states1913: (5,5) Carbon Nanotube Transport properties2014: Linear Sodium Chain Transport properties2115: (5,0) Carbon Nanotube Transport properties2416: Silicon Boltzmann transport2617: Iron Spin-orbit-coupled bands and Fermi-surface contours2818: Iron Berry curvature, anomalous Hall conductivity and optical conductivity 3019: Iron Orbital magnetization3420: Disentanglement restricted inside spherical regions ofkspace3621: Gallium Arsenide Symmetry-adapted Wannier functions3722: Copper Symmetry-adapted Wannier functions38wannier90: Tutorial3 PreliminariesWelcome towannier90!

2 The examples contained in this Tutorial are designed to help you becomefamiliar with the procedure of generating, analysing and using maximally-localised Wannier functions(MLWFs). As a first step, installwannier90following the instructions in theREADME file of thewannier90distribution. For an introduction to the theory underlying MLWFs, you are encouragedto refer to the brief overview given in thewannier90 User Guide [1], to the two seminal papers ofRefs. [2, 3], a recent review article [4] and to a paper [5] following additional programs may be installed in order to visualise the output ofwannier90(theyare optional, not all of them are necessary) gnuplotis used to plot bandstructures. It is available for many operating systems and is ofteninstalled by default on Unix/Linux xmgracemay also be used to plot XCrySDenis used to visualise crystal structures, MLWFs, and Fermi surfaces.

3 It is availablefor Unix/Linux, Windows (using cygwin), and OSX. To correctly display files fromwannier90,version or later must be vmdcan also be used to visualise crystal structures and pythonwith thenumpyandmatplotlibmodules is used in examples 17 19 executionPresently, a serial-only executable, so itcannot be run in parallel using MPI the contrary, be run in parallel to speed up the calculations, using the MPI enable the parallel version to be built, you must specify some flags in ofwannier90andpostw90; for further information, please refer to in the top directory , to run with 8 processors, you typically need to run a command similar topostw90as follows:mpirun -np 8 seedname(thempiruncommand and its flags may differ depending on the MPI libraries installed on your system:refer to your MPI manual and/or to your system administrator for further information).

4 4wannier90: TutorialAbout this tutorialThe first part of this Tutorial comprises four examples taken from Refs. [2, 3]: gallium arsenide, lead,silicon and copper. All of thewannier90input files have been second part of the Tutorial covers the generation ofwannier90input files starting from a fullelectronic structure calculation. We have provided input files for thepwscfinterface ( ) towannier90. Therefore, you will need to install and compile elements ofthequantum-espressopackage, , in order to run these download the package, and for installation instruc-tions. The Tutorial examples work and The exception are the exampleson symmetry adapted Wannier functions which require together with the very latest version This can be found in the the wannier distribution.

5 Itshould be moved toPP/srcin thepwscfdistribution and compiled usingmake pp. Later should have the most up-to-date version of already included in the QuantumESPRESSO are interfaces to a number of other electronic structure codes includingabinit( ),fleur( ),OpenMX( ),GPAW( ),VASP( ), andWien2k( )Contact usIf you have any suggestions regarding ways in which this Tutorial may be improved, then send us other questions, email thewannier90forum Note that firstyou will need to register in order to post emails. Emails from non-registered users are deleted auto-matically. You can register by following the links : Tutorial51: Gallium Arsenide MLWFs for the valence bands Outline:Obtain and plot MLWFs for the four valence bands of GaAs.

6 Generation details:Frompwscf, using norm-conserving pseudopotentials and a 2 2 2 k-pointgrid. Starting guess: four bond-centred Gaussians. Directory:examples/example1/ Input Files master input file overlap matricesM(k,b) (k)of the Bloch states onto a set of trial localised orbitals Bloch states in the real space unit cell. For plotting Runwannier90to minimise the MLWFs gaasInspect the output The total spread converges to its minimum value after just afew iterations. Note that the geometric centre of each MLWF lies along a Ga-As bond, slightlycloser to As than Ga. Note also that the memory requirement for the minimisation of the spreadis very low as the MLWFs are defined at each k-point by just the 4 4 unitary matricesU(k).

7 2. Plot the MLWFs by adding the following keywords to the input = trueand re-runningwannier90. To visualise the MLWFs we must represent them explicitly on a realspace grid (see Ref. [1]). As a consequence, plotting the MLWFs is slower and uses more memorythan the minimisation of the spread. The four files that are created ( , etc.) canbe viewed usingXCrySDen, ,xcrysden --xsf large systems, plotting the MLWFs may be time consuming and require a lot of the keywordwannier_plot_listto plot a subset of the MLWFs. , to plot the 1st and3rd MLWFs usewannier_plot_list = 1 3 The MLWFs are plotted in a supercell of the unit cell. The size of this supercell is set throughthe keywordwannier_plot_supercell. The default value is 2 (corresponding to a supercell witheight times the unit cell volume).

8 We recommend not using values great than 3 as the memoryand computational cost scales cubically with supercell the 3rd MLWFs in a supercell of size 3. Choose a low value for the isosurface (say ). Canyou explain what you see?Hint:For a finite k-point mesh, the MLWFs are in fact periodic and the period is related to thespacing of the k-point mesh. For mesh withndivisions in theithdirection in the Brillouin zone,the MLWFs live in a supercellntimes the unit , click onTools Data Gridin order to specify an isosurface value to : Tutorial2: Lead Wannier-interpolated Fermi surface Outline:Obtain MLWFs for the four lowest states in lead. Use Wannier interpolation to plot theFermi surface. Generation Details:Frompwscf, using norm-conserving pseudopotentials and a 4 4 4 k-pointgrid.

9 Starting guess: atom-centred sp3hybrid orbitals Directory:examples/example2/ Input Files master input file overlap matricesM(k,b) (k)of the Bloch states onto a set of trial localised orbitals Bloch eigenvalues at each k-point. For interpolation onlyThe four lowest valence bands in lead are separated in energy from the higher conduction states (seeFig. 1). The MLWFs of these states have partial occupancy. MLWFs describing only the occupiedstates would be poorly Runwannier90to minimise the MLWFs leadInspect the output Use Wannier interpolation to generate the Fermi surface of lead. Rather than re-running thewhole calculation we can use the unitary transformations obtained in the first calculation andrestart from the plotting routine.

10 Add the following keywords to :restart = plotfermi_energy = = trueand re-runwannier90. The value of the Fermi energy ( eV) was obtained from the initialfirst principles the band energies, through wannier interpola-tion, on a dense mesh of k-points in the Brillouin zone. The density of this grid is controlled bythe keywordfermi_surface_num_points. The default value is 50 ( , 503points). The Fermisurface be viewed usingXCrySDen, ,xcrysden --bxsf : Silicon Disentangled MLWFs Outline:Obtain disentangled MLWFs for the valence and low-lying conduction states of Si. Plotthe interpolated bandstructure Generation Details:Frompwscf, using norm-conserving pseudopotentials and a 4 4 4 k-pointgrid. Starting guess: atom-centred sp3hybrid orbitalswannier90: Tutorial7 5 0 5 10 15 G K X G LEnergy (eV)Figure 1: Bandstructure of lead showing the position of the Fermi level.