{ "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", "atoms = [Si, Si]\n", "positions = [ones(3)/8, -ones(3)/8]\n", "lattice = Si.lattice_constant / 2 .* [[0 1 1.]; [1 0 1.]; [1 1 0.]];" ], "metadata": {}, "execution_count": 1 }, { "cell_type": "markdown", "source": [ "Next we build the rather simple model and discretize it with moderate `Ecut`:" ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "model = Model(lattice, atoms, positions; terms=[Kinetic(), AtomicLocal()])\n", "basis = PlaneWaveBasis(model, Ecut=10.0, kgrid=(2, 2, 2));" ], "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": "0.4017310500215955" }, "metadata": {}, "execution_count": 3 } ], "cell_type": "code", "source": [ "ham = Hamiltonian(basis)\n", "eigres = diagonalize_all_kblocks(DFTK.lobpcg_hyper, ham, 6)\n", "εF = DFTK.compute_occupation(basis, eigres.λ).εF" ], "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 -> U and K -> Γ -> L -> W -> X\n", "\rDiagonalising Hamiltonian kblocks: 14%|██▎ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 36%|█████▊ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 57%|█████████▏ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 79%|████████████▋ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 100%|████████████████| Time: 0:00:00\u001b[K\n" ] }, { "output_type": "execute_result", "data": { "text/plain": "Plot{Plots.GRBackend() n=18}", "image/png": 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