{ "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": [ { "output_type": "execute_result", "data": { "text/plain": "3×3 Matrix{Float64}:\n 0.0 5.13061 5.13061\n 5.13061 0.0 5.13061\n 5.13061 5.13061 0.0" }, "metadata": {}, "execution_count": 1 } ], "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=(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": "0.3842999767139458" }, "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; occupation_threshold=0).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: 12%|██ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 31%|█████ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 47%|███████▌ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 66%|██████████▌ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 84%|█████████████▌ | 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=48}", "image/png": 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