This example considers the Cohen-Bergstresser model1, 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) lattice = Si.lattice_constant / 2 .* [[0 1 1.]; [1 0 1.]; [1 1 0.]] atoms = [Si => [ones(3)/8, -ones(3)/8]];
Next we build the rather simple model and discretise it with moderate
model = Model(lattice; atoms=atoms, terms=[Kinetic(), AtomicLocal()]) basis = PlaneWaveBasis(model, Ecut=10.0, kgrid=(1, 1, 1));
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.fermi_level(basis, eigres.λ)
... and compute and plot 8 bands:
using Plots using Unitful p = plot_bandstructure(basis; n_bands=8, εF, kline_density=10, unit=u"eV") ylims!(p, (-5, 6))
Computing bands along kpath: Γ -> X -> U and K -> Γ -> L -> W -> X Diagonalising Hamiltonian kblocks: 100%|████████████████| Time: 0:00:01