# 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.]]
```

3×3 Matrix{Float64}: 0.0 5.13061 5.13061 5.13061 0.0 5.13061 5.13061 5.13061 0.0

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=(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)
```

0.3842999767141736

... 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))
```

- CB1966M. L. Cohen and T. K. Bergstresser Phys. Rev.
**141**, 789 (1966) DOI 10.1103/PhysRev.141.789