{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Cohen-Bergstresser model\n",
    "\n",
    "This example considers the Cohen-Bergstresser model[^CB1966],\n",
    "reproducing the results of the original paper. This model is particularly\n",
    "simple since its linear nature allows one to get away without any\n",
    "self-consistent field calculation.\n",
    "\n",
    "[^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)"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "We build the lattice using the tabulated lattice constant from the original paper,\n",
    "stored in DFTK:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "using DFTK\n",
    "\n",
    "Si = ElementCohenBergstresser(:Si)\n",
    "atoms = [Si, Si]\n",
    "positions = [ones(3)/8, -ones(3)/8]\n",
    "lattice = Si.lattice_constant / 2 .* [[0 1 1.]; [1 0 1.]; [1 1 0.]];"
   ],
   "metadata": {},
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "source": [
    "Next we build the rather simple model and discretize it with moderate `Ecut`:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "model = Model(lattice, atoms, positions; terms=[Kinetic(), AtomicLocal()])\n",
    "basis = PlaneWaveBasis(model, Ecut=10.0, kgrid=(2, 2, 2));"
   ],
   "metadata": {},
   "execution_count": 2
  },
  {
   "cell_type": "markdown",
   "source": [
    "We diagonalise at the Gamma point to find a Fermi level …"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.4017310500214786"
     },
     "metadata": {},
     "execution_count": 3
    }
   ],
   "cell_type": "code",
   "source": [
    "ham = Hamiltonian(basis)\n",
    "eigres = diagonalize_all_kblocks(DFTK.lobpcg_hyper, ham, 6)\n",
    "εF = DFTK.compute_occupation(basis, eigres.λ).εF"
   ],
   "metadata": {},
   "execution_count": 3
  },
  {
   "cell_type": "markdown",
   "source": [
    "… and compute and plot 8 bands:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=18}",
      "image/png": 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      ]
     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "cell_type": "code",
   "source": [
    "using Plots\n",
    "using Unitful\n",
    "\n",
    "bands = compute_bands(basis; n_bands=8, εF, kline_density=10)\n",
    "p = plot_bandstructure(bands; unit=u\"eV\")\n",
    "ylims!(p, (-5, 6))"
   ],
   "metadata": {},
   "execution_count": 4
  }
 ],
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