Which software is suitable for visualizing the electron wavefunctions in a crystal?

Question

I'd like to use the tight-binding model with a linear combination of atomic orbitals.

It should show the full energy bands, as well as the spatial probability distribution for each eigenfunction of the Hamiltonian. Ideally it would be easy to use with many tunable parameters.

Can anyone recommend a software for this?

Answer 1

The sisl python package might be useful to you. It has:

• Tools to build hamiltonians with user-defined basis orbitals.
• A very high level API to visualize the most common analysis from your hamiltonian (bands, PDOS, wavefunctions, etc...).
• Lower level APIs to customize your analysis as you wish.

Here's an example of how you might define a tight binding Hamiltonian for graphene:

import sisl
import sisl.viz
import numpy as np

# Define a basis orbital, with a radial function that is defined by us
r = np.linspace(0, 3.5, 50)
f = np.exp(-r)
orb = sisl.AtomicOrbital('2pzZ', (r, f))

# Build a graphene structure using our orbital as basis for the C atoms.
geom = sisl.geom.graphene(atoms=sisl.Atom(6, orb))

# Initialize a hamiltonian matrix for the geometry
H = sisl.Hamiltonian(geom)
# And set the non zero values.
# In this case, matrix elements of atoms that are closer than 0.1 Ang
# (i.e. the same atom) are assigned 0 eV and connections of less than
# 1.44 Ang (first neighbours) are assigned -2.7 eV. 
H.construct([(0.1, 1.44), (0, -2.7)], )
# To make it more interesting, we will change the on-site energies of
# the two atoms
H[0,0] = -1
H[1,1] = 1

Now, you can go on and use any of the methods of the Hamiltonian (see docs).

However, if you want a quick analysis you can use the high level API of the visualization module (docs). Following I show you some of the quick analysis you can do. I tweak some parameters of each analysis, but there are more parameters for which I'm using the defaults.

• PDOS:

pdos_plot = H.plot.pdos(
    kgrid=[90,90,1], nE=500, Erange=[-4, 4],
    distribution={"method": "gaussian", "smearing": 0.1}
)

pdos_plot.split_DOS(on="atoms", name="Atom $atoms")

• Wavefunctions (given your defined basis):

H.plot.wavefunction(
    i=1, grid_prec=0.05, axes="xy", 
    represent="mod", nsc=[2,2,1], zsmooth="best"
)

• Bands:

# We need to define a path for the band structure
bz = sisl.BandStructure(
    H, points=[[0, 0, 0], [2/3, 1/3, 0], [1/2, 0, 0]],
    divisions=30, names=["Gamma", "M", "K"]
)

# Then just plot it
bz.plot()

• Fatbands:

fatbands = bz.plot.fatbands()

fatbands.split_groups(on="atoms", name="Atom $atoms")

If you have doubts you can go through the documentation or ask specific questions on the discord server.