Fermi surface

[qiuweicheng]

How to draw the picture of Fermi surface using ATK?  the picture is shown in the attachment.

a script maybe better

Thank you very much!

[Daniele Stradi]

Fermi surface plotting will be available starting from ATK 2017.

[qiuweicheng]

Thank you for your reply. We just Just bought the ATK 2016,  it is failure to calculate the fermi surface. However, the analysis  of  fermi surface is very important for us,  could you offer a relevant script for me please?

[Anders Blom]

No, as the previous reply said it will be available in ATK 2017.

[Anders Blom]

However, I don't think you need a traditional 3D Fermi surface functionality to make such a plot as shown in the paper. You just need to compute the 2D band structure in the kxky plane and make some 2D contour plots, pretty straightforward.

[qiuweicheng]

In general,  we compute the band structure around the Brillouin zone. But,how to compute the 2D band structure in the kxky plane?

[zh]

Sample the k points in a given plane, and then calculate their eigenvalues.

[Jess Wellendorff]

Have a look at this section in our tutorial on the Bi2Se3 topological indulator: http://docs.quantumwise.com/tutorials/topological_insulator_bi2se3/topological_insulator_bi2se3.html#fermi-surface-and-spin-directions The script "fermi_surface.py" gives an example of how to instruct the Bandstructure analysis object to sample a grid of k-points:

Code

# -------------------------------------------------------------
# Reading Bi2Se3 slab configuration
# -------------------------------------------------------------
configuration = nlread('Bi2Se3_slab.nc', BulkConfiguration)[1]
lattice = configuration.bravaisLattice()

# -------------------------------------------------------------
# Create cartesian k-grid around the Gamma point
# -------------------------------------------------------------
# Generate a k-point grid in Cartesian kx,ky around kG.
# Ensure to have a point at G by choosing Nk odd!
Nk = 51
k_max = 0.1
x = numpy.linspace(-k_max, k_max, Nk)
y = numpy.linspace(-k_max, k_max, Nk)
kXkY = numpy.array(list(itertools.product(y,x)))
kXkYkZ = numpy.vstack((kXkY[:,0], kXkY[:,1], numpy.array([0,]*len(kXkY)))).transpose()

# Convert to fractional kx,ky coordinates for evaluation.
kAkB = cartesian2fractional(kXkYkZ*Ang**-1, lattice.reciprocalVectors())

# -------------------------------------------------------------
# Compute eigenenergies in these k-points
# -------------------------------------------------------------
bandstructure = Bandstructure(configuration, kpoints=kAkB)

# -------------------------------------------------------------
# Read the bandstructure eigenenergies and kpoints
# -------------------------------------------------------------
energies = bandstructure.evaluate().inUnitsOf(eV)
kpoints_fractional = bandstructure.kpoints()
tmp = fractional2cartesian(kpoints_fractional, lattice.reciprocalVectors())
kpoints_cartesian = tmp.inUnitsOf(Angstrom**-1)

[qiuweicheng]

I understand, thank you very much

[qiuweicheng]

Another small problem,according to this fermi surface script, we can get the shape of constant energy surface in brillouin  zone. But, we can't get the information of  k-resolution  DOS in the  constant energy surface shape. More important,  we want to get the k-resolution  DOS in  brillouin  zone for  an energy. Could you add the related Dos information in the constant energy surface shape for the script? we don't know how to add this information.

[Ulrik G. Vej-Hansen]

I apologize, but we do not understand your question. Could you please clarify and/or provide an example of the kind of figure you would like to create?

[qiuweicheng]

It is just the projection of  the density of states (DOS) onto a equal energy surface, such as E=Ef (Fermi surface).

[Daniele Stradi]

I guess that what you mean is to have the weights of the individual k-points, as by definition the DOS is a weighed integral over the Brillouin zone.

For a given Monkhorst-Pack grid, you can retrieve (i) all the k-points before symmetry reduction and (ii) all the corresponding weights by querying the  MonkhorstPackGrid class with (i) allKpoints and (ii) allKpointsWeights:

http://docs.quantumwise.com/manuals/Types/MonkhorstPackGrid/MonkhorstPackGrid.html