{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Graphene band structure"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "This example plots the band structure of graphene, a 2D material. 2D band structures are not supported natively (yet), so we manually build a custom path in reciprocal space."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n     Energy            log10(ΔE)   log10(Δρ)   Diag\n",
      "---   ---------------   ---------   ---------   ----\n",
      "  1   -11.15669255813                   -0.60    5.9\n",
      "  2   -11.16022783936       -2.45       -1.30    1.4\n",
      "  3   -11.16040828074       -3.74       -2.32    4.6\n",
      "  4   -11.16041666136       -5.08       -3.05    4.9\n",
      "  5   -11.16041695702       -6.53       -3.33    5.3\n",
      "\rDiagonalising Hamiltonian kblocks:   5%|▊               |  ETA: 0:00:10\u001b[K\rDiagonalising Hamiltonian kblocks:   7%|█▏              |  ETA: 0:00:08\u001b[K\rDiagonalising Hamiltonian kblocks:   9%|█▌              |  ETA: 0:00:07\u001b[K\rDiagonalising Hamiltonian kblocks:  12%|█▉              |  ETA: 0:00:06\u001b[K\rDiagonalising Hamiltonian kblocks:  14%|██▎             |  ETA: 0:00:06\u001b[K\rDiagonalising Hamiltonian kblocks:  16%|██▋             |  ETA: 0:00:05\u001b[K\rDiagonalising Hamiltonian kblocks:  21%|███▍            |  ETA: 0:00:05\u001b[K\rDiagonalising Hamiltonian kblocks:  26%|████▏           |  ETA: 0:00:04\u001b[K\rDiagonalising Hamiltonian kblocks:  28%|████▌           |  ETA: 0:00:04\u001b[K\rDiagonalising Hamiltonian kblocks:  33%|█████▎          |  ETA: 0:00:04\u001b[K\rDiagonalising Hamiltonian kblocks:  37%|██████          |  ETA: 0:00:03\u001b[K\rDiagonalising Hamiltonian kblocks:  42%|██████▊         |  ETA: 0:00:03\u001b[K\rDiagonalising Hamiltonian kblocks:  49%|███████▉        |  ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks:  53%|████████▌       |  ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks:  56%|████████▉       |  ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks:  58%|█████████▎      |  ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks:  63%|██████████      |  ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks:  70%|███████████▏    |  ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks:  74%|███████████▉    |  ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks:  79%|████████████▋   |  ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks:  84%|█████████████▍  |  ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks:  88%|██████████████▏ |  ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks:  93%|██████████████▉ |  ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks:  95%|███████████████▎|  ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks:  98%|███████████████▋|  ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 100%|████████████████| Time: 0:00:04\u001b[K\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=69}",
      "image/png": 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     "metadata": {},
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   ],
   "cell_type": "code",
   "source": [
    "using DFTK\n",
    "using Unitful\n",
    "using UnitfulAtomic\n",
    "using LinearAlgebra\n",
    "\n",
    "# Define the convergence parameters (these should be increased in production)\n",
    "L = 20  # height of the simulation box\n",
    "kgrid = [6, 6, 1]\n",
    "Ecut = 15\n",
    "temperature = 1e-3\n",
    "\n",
    "# Define the geometry and pseudopotential\n",
    "a = 4.66  # lattice constant\n",
    "a1 = a*[1/2,-sqrt(3)/2, 0]\n",
    "a2 = a*[1/2, sqrt(3)/2, 0]\n",
    "a3 = L*[0  , 0        , 1]\n",
    "lattice = [a1 a2 a3]\n",
    "C1 = [1/3,-1/3,0.0]  # in reduced coordinates\n",
    "C2 = -C1\n",
    "positions = [C1, C2]\n",
    "C = ElementPsp(:C, psp=load_psp(\"hgh/pbe/c-q4\"))\n",
    "atoms = [C, C]\n",
    "\n",
    "# Run SCF\n",
    "model = model_PBE(lattice, atoms, positions; temperature)\n",
    "basis = PlaneWaveBasis(model; Ecut, kgrid)\n",
    "scfres = self_consistent_field(basis)\n",
    "\n",
    "# Choose the points of the band diagram, in reduced coordinates (in the (b1,b2) basis)\n",
    "Γ  = [0, 0, 0]\n",
    "K  = [ 1, 1, 0]/3\n",
    "Kp = [-1, 2, 0]/3\n",
    "M  = (K + Kp)/2\n",
    "kpath_coords = [Γ, K, M, Γ]\n",
    "kpath_names  = [\"Γ\", \"K\", \"M\", \"Γ\"]\n",
    "\n",
    "# Build the path manually for now\n",
    "kline_density = 20\n",
    "function build_path(k1, k2)\n",
    "    target_Δk = 1/kline_density  # the actual Δk is |k2-k1|/npt\n",
    "    npt = ceil(Int, norm(model.recip_lattice * (k2-k1)) / target_Δk)\n",
    "    [k1 + t * (k2-k1) for t in range(0, 1, length=npt)]\n",
    "end\n",
    "kcoords = []\n",
    "for i = 1:length(kpath_coords)-1\n",
    "    append!(kcoords, build_path(kpath_coords[i], kpath_coords[i+1]))\n",
    "end\n",
    "klabels = Dict(zip(kpath_names, kpath_coords))\n",
    "\n",
    "# Plot the bands\n",
    "band_data = compute_bands(basis, kcoords; scfres.ρ)\n",
    "DFTK.plot_band_data(band_data; scfres.εF, klabels)"
   ],
   "metadata": {},
   "execution_count": 1
  }
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