Cohen-Bergstresser model

This example considers the Cohen-Bergstresser model^[CB1966], reproducing the results of the original paper. This model is particularly simple since its linear nature allows one to get away without any self-consistent field calculation.

We build the lattice using the tabulated lattice constant from the original paper, stored in DFTK:

using DFTK

Si = ElementCohenBergstresser(:Si)
atoms = [Si, Si]
positions = [ones(3)/8, -ones(3)/8]
lattice = Si.lattice_constant / 2 .* [[0 1 1.]; [1 0 1.]; [1 1 0.]];

Next we build the rather simple model and discretize it with moderate Ecut:

model = Model(lattice, atoms, positions; terms=[Kinetic(), AtomicLocal()])
basis = PlaneWaveBasis(model, Ecut=10.0, kgrid=(2, 2, 2));

We diagonalise at the Gamma point to find a Fermi level …

ham = Hamiltonian(basis)
eigres = diagonalize_all_kblocks(DFTK.lobpcg_hyper, ham, 6)
εF = DFTK.compute_occupation(basis, eigres.λ).εF

0.40173105002149057

… and compute and plot 8 bands:

using Plots
using Unitful

bands = compute_bands(basis; n_bands=8, εF, kline_density=10)
p = plot_bandstructure(bands; unit=u"eV")
ylims!(p, (-5, 6))