/
cohen_bergstresser.jl
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/
cohen_bergstresser.jl
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# # 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.
#
# [^CB1966]: M. L. Cohen and T. K. Bergstresser Phys. Rev. **141**, 789 (1966) DOI [10.1103/PhysRev.141.789](https://doi.org/10.1103/PhysRev.141.789)
# 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
# … 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))