{ "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": "0.3842999767139144" }, "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: 16%|██▌ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 34%|█████▌ | ETA: 0:00:01\u001b[K\rDiagonalising Hamiltonian kblocks: 53%|████████▌ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 78%|████████████▌ | ETA: 0:00:00\u001b[K\rDiagonalising Hamiltonian kblocks: 97%|███████████████▌| 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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