{ "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": "0.38429997671376526" }, "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: 1%|▏ | ETA: 0:00:30\u001b[K\rDiagonalising Hamiltonian kblocks: 7%|█ | ETA: 0:00:07\u001b[K\rDiagonalising Hamiltonian kblocks: 12%|█▉ | ETA: 0:00:04\u001b[K\rDiagonalising Hamiltonian kblocks: 16%|██▋ | ETA: 0:00:04\u001b[K\rDiagonalising Hamiltonian kblocks: 20%|███▏ | ETA: 0:00:03\u001b[K\rDiagonalising Hamiltonian kblocks: 25%|████ | ETA: 0:00:03\u001b[K\rDiagonalising Hamiltonian kblocks: 29%|████▊ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 35%|█████▋ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 40%|██████▍ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 46%|███████▎ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 51%|████████▏ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 57%|█████████ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 62%|█████████▉ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 66%|██████████▋ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 72%|███████████▌ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 77%|████████████▍ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 82%|█████████████ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 87%|█████████████▉ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 92%|██████████████▊ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 96%|███████████████▎| 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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"\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ] }, "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", "ρspin0 = nothing\n", "p = plot_bandstructure(basis, ρ0, ρspin0, n_bands, εF=εF, kline_density=10)\n", "ylims!(p, (-5, 6))" ], "metadata": {}, "execution_count": 4 } ], "nbformat_minor": 3, "metadata": { "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.6.0" }, "kernelspec": { "name": "julia-1.6", "display_name": "Julia 1.6.0", "language": "julia" } }, "nbformat": 4 }