{ "cells": [ { "cell_type": "markdown", "source": [ "# Gross-Pitaevskii equation with external magnetic field" ], "metadata": {} }, { "cell_type": "markdown", "source": [ "We solve the 2D Gross-Pitaevskii equation with a magnetic field.\n", "This is similar to the\n", "previous example (Gross-Pitaevskii equation in one dimension),\n", "but with an extra term for the magnetic field.\n", "We reproduce here the results of https://arxiv.org/pdf/1611.02045.pdf Fig. 10" ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "using DFTK\n", "using StaticArrays\n", "using Plots" ], "metadata": {}, "execution_count": 1 }, { "cell_type": "markdown", "source": [ "Unit cell. Having one of the lattice vectors as zero means a 2D system" ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "a = 15\n", "lattice = a .* [[1 0 0.]; [0 1 0]; [0 0 0]];" ], "metadata": {}, "execution_count": 2 }, { "cell_type": "markdown", "source": [ "Confining scalar potential, and magnetic vector potential" ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "pot(x, y, z) = ((x - a/2)^2 + (y - a/2)^2)/2\n", "ω = .6\n", "Apot(x, y, z) = ω * @SVector [y - a/2, -(x - a/2), 0]\n", "Apot(X) = Apot(X...);" ], "metadata": {}, "execution_count": 3 }, { "cell_type": "markdown", "source": [ "Parameters" ], "metadata": {} }, { "outputs": [], "cell_type": "code", "source": [ "Ecut = 20 # Increase this for production\n", "η = 500\n", "C = η/2\n", "α = 2\n", "n_electrons = 1; # Increase this for fun" ], "metadata": {}, "execution_count": 4 }, { "cell_type": "markdown", "source": [ "Collect all the terms, build and run the model" ], "metadata": {} }, { "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Iter Function value Gradient norm \n", " 0 3.186678e+01 9.383155e+00\n", " * time: 0.0016548633575439453\n", " 1 2.763206e+01 4.860778e+00\n", " * time: 0.006888866424560547\n", " 2 1.885185e+01 4.280055e+00\n", " * time: 0.012089967727661133\n", " 3 1.288344e+01 2.940758e+00\n", " * time: 0.01645803451538086\n", " 4 1.194721e+01 2.801569e+00\n", " * time: 0.019794940948486328\n", " 5 1.089841e+01 1.770251e+00\n", " * time: 0.023251056671142578\n", " 6 1.011533e+01 1.271781e+00\n", " * time: 0.026489973068237305\n", " 7 9.340925e+00 1.162382e+00\n", " * time: 0.030128002166748047\n", " 8 8.725210e+00 6.931441e-01\n", " * time: 0.033540964126586914\n", " 9 8.467250e+00 4.123209e-01\n", " * time: 0.03746485710144043\n", " 10 8.358130e+00 4.780912e-01\n", " * time: 0.04129290580749512\n", " 11 8.286957e+00 4.688065e-01\n", " * time: 0.04557991027832031\n", " 12 8.272010e+00 6.452613e-01\n", " * time: 0.04852890968322754\n", " 13 8.188374e+00 4.655708e-01\n", " * time: 0.05157303810119629\n", " 14 8.162237e+00 5.967006e-01\n", " * time: 0.05424189567565918\n", " 15 8.085695e+00 7.480522e-01\n", " * time: 0.056715965270996094\n", " 16 8.013657e+00 5.301728e-01\n", " * time: 0.060133934020996094\n", " 17 7.987975e+00 7.962903e-01\n", " * time: 0.1053159236907959\n", " 18 7.929826e+00 6.741991e-01\n", " * time: 0.10892200469970703\n", " 19 7.848895e+00 4.961541e-01\n", " * time: 0.11214494705200195\n", " 20 7.831137e+00 6.316091e-01\n", " * time: 0.11490297317504883\n", " 21 7.818284e+00 5.626819e-01\n", " * time: 0.11750292778015137\n", " 22 7.790311e+00 4.648493e-01\n", " * time: 0.12085604667663574\n", " 23 7.754822e+00 2.852908e-01\n", " * time: 0.12427401542663574\n", " 24 7.730264e+00 3.372240e-01\n", " * time: 0.12671494483947754\n", " 25 7.716068e+00 2.843639e-01\n", " * time: 0.12906289100646973\n", " 26 7.701747e+00 2.010284e-01\n", " * time: 0.13161396980285645\n", " 27 7.700124e+00 2.883239e-01\n", " * time: 0.1341390609741211\n", " 28 7.691607e+00 2.326198e-01\n", " * time: 0.13651299476623535\n", " 29 7.684879e+00 1.332036e-01\n", " * time: 0.13988590240478516\n", " 30 7.682395e+00 2.440068e-01\n", " * time: 0.1424999237060547\n", " 31 7.673349e+00 2.106831e-01\n", " * time: 0.14510488510131836\n", " 32 7.666693e+00 1.711247e-01\n", " * time: 0.14756393432617188\n", " 33 7.665821e+00 2.187834e-01\n", " * time: 0.15007495880126953\n", " 34 7.662436e+00 1.341418e-01\n", " * time: 0.15333986282348633\n", " 35 7.660110e+00 1.645868e-01\n", " * time: 0.15594887733459473\n", " 36 7.659362e+00 2.084078e-01\n", " * time: 0.1585710048675537\n", " 37 7.656457e+00 1.626125e-01\n", " * time: 0.16135597229003906\n", " 38 7.656188e+00 2.102620e-01\n", " * time: 0.16412687301635742\n", " 39 7.652600e+00 1.180453e-01\n", " * time: 0.16776490211486816\n", " 40 7.650010e+00 1.336260e-01\n", " * time: 0.17072606086730957\n", " 41 7.645992e+00 1.265253e-01\n", " * time: 0.17450690269470215\n", " 42 7.644085e+00 1.230184e-01\n", " * time: 0.1774458885192871\n", " 43 7.642765e+00 1.558829e-01\n", " * time: 0.18036198616027832\n", " 44 7.640004e+00 6.930845e-02\n", " * time: 0.184251070022583\n", " 45 7.638946e+00 9.780124e-02\n", " * time: 0.18727707862854004\n", " 46 7.637115e+00 7.337029e-02\n", " * time: 0.19099688529968262\n", " 47 7.635318e+00 5.779216e-02\n", " * time: 0.19481396675109863\n", " 48 7.634469e+00 9.015674e-02\n", " * time: 0.19773197174072266\n", " 49 7.632977e+00 4.968419e-02\n", " * time: 0.2015080451965332\n", " 50 7.632184e+00 5.849560e-02\n", " * time: 0.20448589324951172\n", " 51 7.631207e+00 3.947136e-02\n", " * time: 0.20828986167907715\n", " 52 7.630482e+00 6.061611e-02\n", " * time: 0.21109485626220703\n", " 53 7.629480e+00 4.417135e-02\n", " * time: 0.23879003524780273\n", " 54 7.629195e+00 6.342209e-02\n", " * time: 0.24136900901794434\n", " 55 7.628554e+00 5.408703e-02\n", " * time: 0.24381494522094727\n", " 56 7.627807e+00 5.328629e-02\n", " * time: 0.24652791023254395\n", " 57 7.627642e+00 5.465785e-02\n", " * time: 0.24916386604309082\n", " 58 7.627028e+00 4.686141e-02\n", " * time: 0.2518930435180664\n", " 59 7.626499e+00 5.711766e-02\n", " * time: 0.2545499801635742\n", " 60 7.626113e+00 3.760274e-02\n", " * time: 0.25714802742004395\n", " 61 7.625687e+00 4.041762e-02\n", " * time: 0.2595798969268799\n", " 62 7.625313e+00 4.640540e-02\n", " * time: 0.26212286949157715\n", " 63 7.625045e+00 5.613019e-02\n", " * time: 0.26473402976989746\n", " 64 7.624572e+00 3.153462e-02\n", " * time: 0.2673459053039551\n", " 65 7.624414e+00 8.770346e-02\n", " * time: 0.2699470520019531\n", " 66 7.624001e+00 6.677856e-02\n", " * time: 0.2732388973236084\n", " 67 7.623648e+00 6.925827e-02\n", " * time: 0.2758610248565674\n", " 68 7.622986e+00 4.283296e-02\n", " * time: 0.2793090343475342\n", " 69 7.622691e+00 5.392292e-02\n", " * time: 0.2817220687866211\n", " 70 7.622416e+00 5.525521e-02\n", " * time: 0.2841958999633789\n", " 71 7.621938e+00 4.712146e-02\n", " * time: 0.2868359088897705\n", " 72 7.621588e+00 5.292050e-02\n", " * time: 0.2893838882446289\n", " 73 7.621377e+00 9.317087e-02\n", " * time: 0.2919809818267822\n", " 74 7.621063e+00 6.277133e-02\n", " * time: 0.29491496086120605\n", " 75 7.620276e+00 5.789929e-02\n", " * time: 0.2977108955383301\n", " 76 7.619513e+00 3.276276e-02\n", " * time: 0.3014090061187744\n", " 77 7.618927e+00 4.876947e-02\n", " * time: 0.30429601669311523\n", " 78 7.618346e+00 4.942239e-02\n", " * time: 0.3080019950866699\n", " 79 7.617934e+00 4.279016e-02\n", " * time: 0.310960054397583\n", " 80 7.617496e+00 3.773494e-02\n", " * time: 0.31472206115722656\n", " 81 7.617094e+00 2.405566e-02\n", " * time: 0.3184850215911865\n", " 82 7.617053e+00 5.394157e-02\n", " * time: 0.3213980197906494\n", " 83 7.616967e+00 5.312728e-02\n", " * time: 0.3242359161376953\n", " 84 7.616922e+00 6.436742e-02\n", " * time: 0.32726502418518066\n", " 85 7.616531e+00 6.642598e-02\n", " * time: 0.33019304275512695\n", " 86 7.616523e+00 7.204034e-02\n", " * time: 0.3329908847808838\n", " 87 7.616272e+00 9.439531e-02\n", " * time: 0.33581995964050293\n", " 88 7.615383e+00 4.137449e-02\n", " * time: 0.33868408203125\n", " 89 7.615060e+00 5.195357e-02\n", " * time: 0.3416099548339844\n", " 90 7.614599e+00 5.764841e-02\n", " * time: 0.3444099426269531\n", " 91 7.614263e+00 3.488419e-02\n", " * time: 0.3680250644683838\n", " 92 7.614200e+00 7.111445e-02\n", " * time: 0.37058591842651367\n", " 93 7.613861e+00 4.745466e-02\n", " * time: 0.3739299774169922\n", " 94 7.613758e+00 7.308721e-02\n", " * time: 0.3766360282897949\n", " 95 7.613495e+00 4.235777e-02\n", " * time: 0.37992191314697266\n", " 96 7.613284e+00 5.425698e-02\n", " * time: 0.3826110363006592\n", " 97 7.613238e+00 6.422631e-02\n", " * time: 0.3851280212402344\n", " 98 7.613127e+00 4.979302e-02\n", " * time: 0.3876760005950928\n", " 99 7.612736e+00 4.531421e-02\n", " * time: 0.39010095596313477\n", " 100 7.612289e+00 5.095473e-02\n", " * time: 0.39246296882629395\n", " 101 7.612222e+00 4.808735e-02\n", " * time: 0.39496707916259766\n", " 102 7.611996e+00 6.912635e-02\n", " * time: 0.3975050449371338\n", " 103 7.611706e+00 2.985130e-02\n", " * time: 0.4007599353790283\n", " 104 7.611560e+00 3.449005e-02\n", " * time: 0.4033820629119873\n", " 105 7.611282e+00 5.316134e-02\n", " * time: 0.4059779644012451\n", " 106 7.611116e+00 4.251209e-02\n", " * time: 0.4083578586578369\n", " 107 7.610870e+00 3.447823e-02\n", " * time: 0.411513090133667\n", " 108 7.610586e+00 2.380779e-02\n", " * time: 0.4148590564727783\n", " 109 7.610354e+00 1.604283e-02\n", " * time: 0.4182589054107666\n", " 110 7.610179e+00 2.954325e-02\n", " * time: 0.4208219051361084\n", " 111 7.609994e+00 2.836942e-02\n", " * time: 0.423551082611084\n", " 112 7.609707e+00 3.280260e-02\n", " * time: 0.4263749122619629\n", " 113 7.609551e+00 2.938361e-02\n", " * time: 0.429218053817749\n", " 114 7.609499e+00 5.670751e-02\n", " * time: 0.4321138858795166\n", " 115 7.609390e+00 5.356822e-02\n", " * time: 0.43501996994018555\n", " 116 7.609069e+00 6.140819e-02\n", " * time: 0.43799400329589844\n", " 117 7.608452e+00 3.059866e-02\n", " * time: 0.44161105155944824\n", " 118 7.608039e+00 4.174294e-02\n", " * time: 0.44414806365966797\n", " 119 7.608010e+00 5.065873e-02\n", " * time: 0.4467949867248535\n", " 120 7.607890e+00 3.976398e-02\n", " * time: 0.4495210647583008\n", " 121 7.607477e+00 3.737014e-02\n", " * time: 0.4522089958190918\n", " 122 7.607349e+00 5.343386e-02\n", " * time: 0.4548349380493164\n", " 123 7.606988e+00 5.275236e-02\n", " * time: 0.45735788345336914\n", " 124 7.606985e+00 6.752284e-02\n", " * time: 0.4599778652191162\n", " 125 7.606702e+00 6.529163e-02\n", " * time: 0.46324992179870605\n", " 126 7.606354e+00 3.788633e-02\n", " * time: 0.4666469097137451\n", " 127 7.606143e+00 3.974327e-02\n", " * time: 0.48087000846862793\n", " 128 7.606039e+00 4.722561e-02\n", " * time: 0.4834408760070801\n", " 129 7.605736e+00 4.394593e-02\n", " * time: 0.48592400550842285\n", " 130 7.605403e+00 3.369078e-02\n", " * time: 0.4891970157623291\n", " 131 7.605211e+00 1.990565e-02\n", " * time: 0.4925079345703125\n", " 132 7.605016e+00 2.552495e-02\n", " * time: 0.49509286880493164\n", " 133 7.604825e+00 3.091710e-02\n", " * time: 0.49860191345214844\n", " 134 7.604743e+00 3.957199e-02\n", " * time: 0.5011980533599854\n", " 135 7.604613e+00 2.444005e-02\n", " * time: 0.5041649341583252\n", " 136 7.604571e+00 4.185735e-02\n", " * time: 0.5067319869995117\n", " 137 7.604414e+00 4.031241e-02\n", " * time: 0.5092198848724365\n", " 138 7.604352e+00 4.443359e-02\n", " * time: 0.5117340087890625\n", " 139 7.604118e+00 3.322841e-02\n", " * time: 0.515143871307373\n", " 140 7.603884e+00 3.926253e-02\n", " * time: 0.5178439617156982\n", " 141 7.603753e+00 4.465385e-02\n", " * time: 0.5204100608825684\n", " 142 7.603644e+00 4.676564e-02\n", " * time: 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n_electrons=n_electrons,\n", " terms=terms, spin_polarization=:spinless) # \"spinless electrons\"\n", "basis = PlaneWaveBasis(model; Ecut, kgrid=(1, 1, 1))\n", "scfres = direct_minimization(basis, tol=1e-5) # Reduce tol for production\n", "heatmap(scfres.ρ[:, :, 1, 1], c=:blues)" ], "metadata": {}, "execution_count": 5 } ], "nbformat_minor": 3, "metadata": { "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.7.0" }, "kernelspec": { "name": "julia-1.7", "display_name": "Julia 1.7.0", "language": "julia" } }, "nbformat": 4 }