{
 "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",
    "lattice = Si.lattice_constant / 2 .* [[0 1 1.]; [1 0 1.]; [1 1 0.]]\n",
    "atoms = [Si => [ones(3)/8, -ones(3)/8]];"
   ],
   "metadata": {},
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "source": [
    "Next we build the rather simple model and discretise it with moderate `Ecut`:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "Ecut = 10.0\n",
    "model = Model(lattice; atoms=atoms, terms=[Kinetic(), AtomicLocal()])\n",
    "basis = PlaneWaveBasis(model, Ecut, kgrid=(1, 1, 1));"
   ],
   "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": "0.38429997671377913"
     },
     "metadata": {},
     "execution_count": 3
    }
   ],
   "cell_type": "code",
   "source": [
    "ham = Hamiltonian(basis)\n",
    "eigres = diagonalize_all_kblocks(DFTK.lobpcg_hyper, ham, 6)\n",
    "εF = DFTK.fermi_level(basis, eigres.λ)"
   ],
   "metadata": {},
   "execution_count": 3
  },
  {
   "cell_type": "markdown",
   "source": [
    "... and compute and plot 8 bands:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computing bands along kpath:\n",
      "       Γ -> X -> W -> K -> Γ -> L -> U -> W -> L -> K  and  U -> X\n",
      "\rDiagonalising Hamiltonian kblocks:   2%|▍               |  ETA: 0:00:19\u001b[K\rDiagonalising Hamiltonian kblocks:   8%|█▎              |  ETA: 0:00:06\u001b[K\rDiagonalising Hamiltonian kblocks:  13%|██▏             |  ETA: 0:00:04\u001b[K\rDiagonalising Hamiltonian kblocks:  18%|███             |  ETA: 0:00:04\u001b[K\rDiagonalising Hamiltonian kblocks:  25%|████            |  ETA: 0:00:03\u001b[K\rDiagonalising Hamiltonian kblocks:  32%|█████           |  ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks:  37%|█████▉          |  ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks:  42%|██████▊         |  ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks:  48%|███████▋        |  ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks:  53%|████████▌       |  ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks:  60%|█████████▋      |  ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks:  66%|██████████▋     |  ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks:  73%|███████████▋    |  ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks:  79%|████████████▊   |  ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks:  84%|█████████████▍  |  ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks:  90%|██████████████▍ |  ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks:  95%|███████████████▏|  ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 100%|████████████████| Time: 0:00:02\u001b[K\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=80}",
      "image/png": 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      ]
     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "cell_type": "code",
   "source": [
    "using Plots\n",
    "\n",
    "n_bands = 8\n",
    "ρ0 = guess_density(basis)  # Just dummy, has no meaning in this model\n",
    "p = plot_bandstructure(basis, ρ0, n_bands, εF=εF, kline_density=10)\n",
    "ylims!(p, (-5, 6))"
   ],
   "metadata": {},
   "execution_count": 4
  }
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