band structure decomposition

[marmotte]

Dear ATK team,

I run band-structre calculation for a simple bulk material and I'd like to know if there is a script or tool under ATK 2012.8 able to give me which band is the valence band or conduction band. Is it possible to do a decomposition of the bandstructure such as with DOS ?

Best regards,

[Anders Blom]

It's possible to project the band structure, like the DOS, on orbitals and atoms. There is no GUI component for this yet, but here is an example which make a project of the band structure of SiO2 (cristobalite) on the oxygen p-orbitals:

Code: python

# Set up lattice
lattice = FaceCenteredCubic(7.166*Angstrom)

# Define elements
elements = [Silicon, Silicon, Oxygen, Oxygen, Oxygen, Oxygen]

# Define coordinates
fractional_coordinates = [[  0.125,   0.125,   0.125],
                          [  0.875,   0.875,   0.875],
                          [  0,   0,   0],
                          [  0,   0.5,  0],
                          [  0.5,   0,  0],
                          [  0,   0,   0.5]]

# Set up configuration
bulk_configuration = BulkConfiguration(
    bravais_lattice=lattice,
    elements=elements,
    fractional_coordinates=fractional_coordinates
    )
    
# -------------------------------------------------------------
# Calculator
# -------------------------------------------------------------

numerical_accuracy_parameters = NumericalAccuracyParameters(
    k_point_sampling=(3, 3, 3),
    )

calculator = LCAOCalculator(
    numerical_accuracy_parameters=numerical_accuracy_parameters,
    )

bulk_configuration.setCalculator(calculator)
nlprint(bulk_configuration)
bulk_configuration.update()
nlsave('sio2_bs_pO.nc', bulk_configuration)

# -------------------------------------------------------------
# Bandstructure
# -------------------------------------------------------------

################## THE IMPORTANT PART ##################
project_oxygen_p = ProjectionList(elements=[Oxygen], angular_momenta=[1])
####################################################

bandstructure = Bandstructure(
    configuration=bulk_configuration,
    route=['G', 'X', 'W', 'L', 'G', 'K', 'X', 'U', 'W', 'K', 'L'],
    points_per_segment=60,
    bands_above_fermi_level=All,
    projection_list=project_oxygen_p,     # IT GOES HERE
    )
nlsave('sio2_bs_pO.nc', bandstructure)

[kstokbro]

The projection is more like the MolecularEnergySpectrum, i.e. you project the Hamiltonian onto certain orbitals and diagonalizes this reduced Hamiltonian.

[zh]

It may be similar to the fat band plot, in which the line thickness of a band is proportional to the weight of an orbital of an atom.

[atk_user]

Dear, Dr. Anders Blom I have a further question. Is it possible to obtain two or three types of elements. I mean just wanted to obtain the band structure only for the scattering part of device model system. 2. Is it possible to analyze the band of each elements for spin up and down component? Lee

It's possible to project the band structure, like the DOS, on orbitals and atoms. There is no GUI component for this yet, but here is an example which make a project of the band structure of SiO2 (cristobalite) on the oxygen p-orbitals:

Code: python

# Set up lattice
lattice = FaceCenteredCubic(7.166*Angstrom)

# Define elements
elements = [Silicon, Silicon, Oxygen, Oxygen, Oxygen, Oxygen]

# Define coordinates
fractional_coordinates = [[  0.125,   0.125,   0.125],
                          [  0.875,   0.875,   0.875],
                          [  0,   0,   0],
                          [  0,   0.5,  0],
                          [  0.5,   0,  0],
                          [  0,   0,   0.5]]

# Set up configuration
bulk_configuration = BulkConfiguration(
    bravais_lattice=lattice,
    elements=elements,
    fractional_coordinates=fractional_coordinates
    )
    
# -------------------------------------------------------------
# Calculator
# -------------------------------------------------------------

numerical_accuracy_parameters = NumericalAccuracyParameters(
    k_point_sampling=(3, 3, 3),
    )

calculator = LCAOCalculator(
    numerical_accuracy_parameters=numerical_accuracy_parameters,
    )

bulk_configuration.setCalculator(calculator)
nlprint(bulk_configuration)
bulk_configuration.update()
nlsave('sio2_bs_pO.nc', bulk_configuration)

# -------------------------------------------------------------
# Bandstructure
# -------------------------------------------------------------

################## THE IMPORTANT PART ##################
project_oxygen_p = ProjectionList(elements=[Oxygen], angular_momenta=[1])
####################################################

bandstructure = Bandstructure(
    configuration=bulk_configuration,
    route=['G', 'X', 'W', 'L', 'G', 'K', 'X', 'U', 'W', 'K', 'L'],
    points_per_segment=60,
    bands_above_fermi_level=All,
    projection_list=project_oxygen_p,     # IT GOES HERE
    )
nlsave('sio2_bs_pO.nc', bandstructure)

[Anders Blom]

Sure, just use elements=[Oxygen,Silicon] instead, or similar.

[atk_user]

Oh, thanks so much. I used "space" instead of comma.

Spin decomposition (sum, up, and down) is automatically calculated?

[Anders Blom]

Yes the spin is specified later, in "evaluate"

[atk_user]

It means that I must using the evaluate to obtain the spin decomposed band structures? After running below script, I can't find any output band data. Could you explain more details?


bs = nlread("D:/ATK/Band.nc", Bandstructure)[0]
bs_up = bs.evaluate(spin=Spin.Up)
bs_dn = bs.evaluate(spin=Spin.Down)

[Anders Blom]

So, now you have two objects, bs_up and bs_dn that contain the data. Of course there is no output unless you print it, or plot it, etc. See e.g. http://quantumwise.com/forum/index.php?topic=566.0 (a bit old code, some things might not work - but the point is there).

[Anders Blom]

Here is a more complete example

Code: python

from NanoLanguage import *

ncfile = 'gold.nc'
plotfile = 'plot.png'
colors = ['r','b','g','m']
ymin = -10
ymax = 10

conf = nlread(ncfile, object_id='gID000')[-1]
bs_s = Bandstructure(conf, projection_list=ProjectionList(angular_momenta=[0]))
bs_p = Bandstructure(conf, projection_list=ProjectionList(angular_momenta=[1]))

bandstructures = [bs_s,bs_p]

import pylab as P
for j,bs in enumerate(bandstructures):
    P.plot(bs._axisGUI(), bs.evaluate(), colors[j])

kticks = [ tick[0] for tick in bs._ticksGUI() ]
ticklabels = [ tick[1].replace('Γ','$\Gamma$') for tick in bs._ticksGUI() ]
P.xticks(kticks,ticklabels)

P.grid(kticks)
P.ylim(ymin,ymax)

#P.savefig(plotfile)
P.show()

[atk_user]

Thank you very much. It looks little complicate. I'll try.

In VNL, I found the "band structure Analyzer..." In the Bandstructure Analyzer, I found the drop down menu for "sum", "up", and "down". It looks spin sum, up, and down component of band structure.

Is it different from the band extracted by using the script you gave above?

[Anders Blom]

Yes it's different because you cannot do the projection on elements or angular momenta in the Analyzer.

[atk_user]

I'm little confusing...

If I first projection on elements or angular momenta from reading the analysis.nc (optimized file) using below input file. Is that the same or different with the band from the script?

# -------------------------------------------------------------
# Bandstructure
# -------------------------------------------------------------
bandstructure = Bandstructure(
    configuration=configuration,
    route=['G', 'X', 'U', 'Z', 'G'],
    points_per_segment=20,
    bands_above_fermi_level=4,
    projection_list=ProjectionList(elements=[Silicon, Oxygen]),
    )
nlsave('Band1.nc', bandstructure)

# -------------------------------------------------------------
# Bandstructure
# -------------------------------------------------------------
bandstructure = Bandstructure(
    configuration=configuration,
    route=['G', 'X', 'U', 'Z', 'G'],
    points_per_segment=20,
    bands_above_fermi_level=4,
    projection_list=ProjectionList(elements=[Silicone]),
    )
nlsave('Band2.nc', bandstructure)

[Anders Blom]

I suppose it is I who is confusing If you combine your script with mine (minus a few lines) you get what you want - two band structures in the same plot, computed in different ways. First run your code, and then

Code: python

from NanoLanguage import *  
      
plotfile = 'plot.png'  
colors = ['r','b','g','m']  
ymin = -10  
ymax = 10  

bs1 = nlread('Band1.nc', BandStructure)[-1]
bs2 = nlread('Band2.nc', BandStructure)[-1]
...
# same as before
...