{ "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": "0.3842999761497365" }, "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: 0:00:17\u001b[K\rDiagonalising Hamiltonian kblocks: 5%|▉ | ETA: 0:00:05\u001b[K\rDiagonalising Hamiltonian kblocks: 10%|█▋ | ETA: 0:00:04\u001b[K\rDiagonalising Hamiltonian kblocks: 14%|██▎ | ETA: 0:00:03\u001b[K\rDiagonalising Hamiltonian kblocks: 17%|██▊ | ETA: 0:00:03\u001b[K\rDiagonalising Hamiltonian kblocks: 21%|███▎ | ETA: 0:00:03\u001b[K\rDiagonalising Hamiltonian kblocks: 26%|████▏ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 32%|█████ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 36%|█████▊ | 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: 50%|████████ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 55%|████████▉ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 61%|█████████▊ | 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": "1.5.3" }, "kernelspec": { "name": "julia-1.5", "display_name": "Julia 1.5.3", "language": "julia" } }, "nbformat": 4 }