{ "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": "0.3842999767138786" }, "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: 0:00:16\u001b[K\rDiagonalising Hamiltonian kblocks: 8%|█▎ | ETA: 0:00:03\u001b[K\rDiagonalising Hamiltonian kblocks: 14%|██▎ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 20%|███▏ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 26%|████▏ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 33%|█████▎ | ETA: 0:00:02\u001b[K\rDiagonalising Hamiltonian kblocks: 39%|██████▎ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 46%|███████▎ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 52%|████████▍ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 59%|█████████▍ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 66%|██████████▋ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 75%|████████████ | ETA: 0:00:00\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: 93%|███████████████ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 99%|███████████████▉| ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 100%|████████████████| Time: 0:00:01\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 }