{ "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 3.158441e+01 6.529925e+00\n", " * time: 0.005012989044189453\n", " 1 3.075073e+01 6.204884e+00\n", " * time: 0.02259206771850586\n", " 2 2.384565e+01 6.900158e+00\n", " * time: 0.04505801200866699\n", " 3 2.128919e+01 9.843236e+00\n", " * time: 0.06493806838989258\n", " 4 2.018377e+01 9.144052e+00\n", " * time: 0.08582115173339844\n", " 5 1.893492e+01 1.021940e+01\n", " * time: 0.10528802871704102\n", " 6 1.403439e+01 5.227915e+00\n", " * time: 0.12463808059692383\n", " 7 1.011977e+01 1.590490e+00\n", " * time: 0.15041399002075195\n", " 8 9.348949e+00 1.183203e+00\n", " * time: 0.1669330596923828\n", " 9 9.015211e+00 6.558213e-01\n", " * time: 0.18684601783752441\n", " 10 8.834260e+00 5.404419e-01\n", " * time: 0.20301198959350586\n", " 11 8.661745e+00 6.066365e-01\n", " * time: 0.21939921379089355\n", " 12 8.507849e+00 7.603904e-01\n", " * time: 0.23871803283691406\n", " 13 8.424249e+00 5.384395e-01\n", " * time: 0.2515990734100342\n", " 14 8.360487e+00 6.086083e-01\n", " * time: 0.26422810554504395\n", " 15 8.294354e+00 6.111526e-01\n", " * time: 0.27623414993286133\n", " 16 8.231355e+00 5.778194e-01\n", " * time: 0.2897810935974121\n", " 17 8.182206e+00 3.512043e-01\n", " * time: 0.35185909271240234\n", " 18 8.139180e+00 3.605274e-01\n", " * time: 0.36698102951049805\n", " 19 8.114362e+00 2.690385e-01\n", " * time: 0.37894320487976074\n", " 20 8.090753e+00 3.617133e-01\n", " * time: 0.39075708389282227\n", " 21 8.063628e+00 3.784565e-01\n", " * time: 0.40259408950805664\n", " 22 8.042975e+00 4.132328e-01\n", " * time: 0.4145979881286621\n", " 23 8.035295e+00 6.769483e-01\n", " * time: 0.4265320301055908\n", " 24 8.007101e+00 2.451503e-01\n", " * time: 0.4390590190887451\n", " 25 7.983448e+00 3.981588e-01\n", " * time: 0.45063114166259766\n", " 26 7.948248e+00 3.615840e-01\n", " * time: 0.4624199867248535\n", " 27 7.912236e+00 2.997334e-01\n", " * time: 0.4745349884033203\n", " 28 7.874021e+00 1.940306e-01\n", " * time: 0.48646020889282227\n", " 29 7.849063e+00 2.490011e-01\n", " * time: 0.4983952045440674\n", " 30 7.830412e+00 1.608276e-01\n", " * time: 0.5144321918487549\n", " 31 7.819493e+00 3.117066e-01\n", " * time: 0.5260941982269287\n", " 32 7.812808e+00 4.556886e-01\n", " * time: 0.5385231971740723\n", " 33 7.809314e+00 4.468907e-01\n", " * time: 0.5503671169281006\n", " 34 7.798518e+00 3.331207e-01\n", " * time: 0.5623400211334229\n", " 35 7.774004e+00 3.206037e-01\n", " * time: 0.5744590759277344\n", " 36 7.749812e+00 3.385668e-01\n", " * time: 0.5860781669616699\n", " 37 7.738444e+00 3.758820e-01\n", " * time: 0.5978569984436035\n", " 38 7.732835e+00 3.319419e-01\n", " * time: 0.6095490455627441\n", " 39 7.715152e+00 2.167460e-01\n", " * time: 0.6221082210540771\n", " 40 7.701509e+00 1.572975e-01\n", " * time: 0.6351540088653564\n", " 41 7.695084e+00 2.799058e-01\n", " * time: 0.6480941772460938\n", " 42 7.684083e+00 2.292058e-01\n", " * time: 0.7040841579437256\n", " 43 7.673713e+00 1.905271e-01\n", " * time: 0.7198870182037354\n", " 44 7.665272e+00 1.519861e-01\n", " * time: 0.7359151840209961\n", " 45 7.659671e+00 1.091244e-01\n", " * time: 0.7511610984802246\n", " 46 7.655865e+00 1.740893e-01\n", " * time: 0.7630951404571533\n", " 47 7.655305e+00 2.404561e-01\n", " * time: 0.7750611305236816\n", " 48 7.651406e+00 1.465628e-01\n", " * time: 0.7904829978942871\n", " 49 7.651069e+00 1.717657e-01\n", " * time: 0.8024301528930664\n", " 50 7.647354e+00 1.367918e-01\n", " * time: 0.8144631385803223\n", " 51 7.643276e+00 1.150762e-01\n", " * time: 0.8261480331420898\n", " 52 7.642837e+00 1.533728e-01\n", " * time: 0.8413150310516357\n", " 53 7.640802e+00 1.504505e-01\n", " * time: 0.8530540466308594\n", " 54 7.638910e+00 1.012863e-01\n", " * time: 0.8687491416931152\n", " 55 7.638536e+00 1.618244e-01\n", " * time: 0.880620002746582\n", " 56 7.636860e+00 9.836260e-02\n", " * time: 0.8962421417236328\n", " 57 7.636789e+00 1.669978e-01\n", " * time: 0.9077601432800293\n", " 58 7.636011e+00 1.747419e-01\n", " * time: 0.9195291996002197\n", " 59 7.634030e+00 1.117289e-01\n", " * time: 0.9313950538635254\n", " 60 7.630807e+00 6.890239e-02\n", " * time: 0.9467902183532715\n", " 61 7.629135e+00 9.575292e-02\n", " * time: 0.9588930606842041\n", " 62 7.627555e+00 8.994076e-02\n", " * time: 0.9720280170440674\n", " 63 7.625488e+00 5.338541e-02\n", " * time: 0.9894599914550781\n", " 64 7.625127e+00 7.262604e-02\n", " * time: 1.0024471282958984\n", " 65 7.624339e+00 5.492033e-02\n", " * time: 1.045790195465088\n", " 66 7.623521e+00 5.575755e-02\n", " * time: 1.061622142791748\n", " 67 7.623088e+00 6.203352e-02\n", " * time: 1.0735511779785156\n", " 68 7.622127e+00 5.924829e-02\n", " * time: 1.0891871452331543\n", " 69 7.621472e+00 2.904818e-02\n", " * time: 1.1050782203674316\n", " 70 7.621003e+00 4.336102e-02\n", " * time: 1.117004156112671\n", " 71 7.620444e+00 4.070069e-02\n", " * time: 1.1290581226348877\n", " 72 7.620383e+00 8.000880e-02\n", " * time: 1.144928216934204\n", " 73 7.620274e+00 6.530196e-02\n", " * time: 1.1573781967163086\n", " 74 7.619809e+00 6.272210e-02\n", " * time: 1.1708860397338867\n", " 75 7.619484e+00 5.758136e-02\n", " * time: 1.1828231811523438\n", " 76 7.619142e+00 5.606010e-02\n", " * time: 1.1949050426483154\n", " 77 7.618864e+00 4.618268e-02\n", " * time: 1.2071380615234375\n", " 78 7.618336e+00 4.077179e-02\n", " * time: 1.2189970016479492\n", " 79 7.617988e+00 4.958259e-02\n", " * time: 1.2307190895080566\n", " 80 7.617845e+00 4.203126e-02\n", " * time: 1.2429661750793457\n", " 81 7.617545e+00 4.210287e-02\n", " * time: 1.254892110824585\n", " 82 7.617344e+00 2.124653e-02\n", " * time: 1.2704792022705078\n", " 83 7.617246e+00 4.418489e-02\n", " * time: 1.2823851108551025\n", " 84 7.617027e+00 3.055669e-02\n", " * time: 1.2980060577392578\n", " 85 7.616882e+00 3.383558e-02\n", " * time: 1.3104500770568848\n", " 86 7.616689e+00 2.833114e-02\n", " * time: 1.327991008758545\n", " 87 7.616596e+00 3.499899e-02\n", " * time: 1.3413481712341309\n", " 88 7.616593e+00 3.264173e-02\n", " * time: 1.3771851062774658\n", " 89 7.616522e+00 2.592447e-02\n", " * time: 1.3891031742095947\n", " 90 7.616405e+00 4.241944e-02\n", " * time: 1.4010791778564453\n", " 91 7.616319e+00 3.687591e-02\n", " * time: 1.4128060340881348\n", " 92 7.616162e+00 3.262028e-02\n", " * time: 1.4243831634521484\n", " 93 7.615949e+00 2.230139e-02\n", " * time: 1.4361050128936768\n", " 94 7.615927e+00 4.021824e-02\n", " * time: 1.4479191303253174\n", " 95 7.615858e+00 5.021080e-02\n", " * time: 1.4597342014312744\n", " 96 7.615690e+00 3.264359e-02\n", " * time: 1.4713711738586426\n", " 97 7.615613e+00 3.229184e-02\n", " * time: 1.4830760955810547\n", " 98 7.615436e+00 2.663123e-02\n", " * time: 1.4988842010498047\n", " 99 7.615249e+00 1.706134e-02\n", " * time: 1.5144309997558594\n", " 100 7.615131e+00 1.558290e-02\n", " * time: 1.5300052165985107\n", " 101 7.615088e+00 3.960597e-02\n", " * time: 1.541923999786377\n", " 102 7.614951e+00 2.573776e-02\n", " * time: 1.5571980476379395\n", " 103 7.614847e+00 2.211328e-02\n", " * time: 1.569031000137329\n", " 104 7.614744e+00 2.184947e-02\n", " * time: 1.580848217010498\n", " 105 7.614706e+00 3.118701e-02\n", " * time: 1.5924930572509766\n", " 106 7.614583e+00 2.225687e-02\n", " * time: 1.6084351539611816\n", " 107 7.614444e+00 3.721184e-02\n", " * time: 1.6203851699829102\n", " 108 7.614270e+00 2.238069e-02\n", " * time: 1.6362311840057373\n", " 109 7.614136e+00 3.332699e-02\n", " * time: 1.6495351791381836\n", " 110 7.613996e+00 3.047618e-02\n", " * time: 1.6624751091003418\n", " 111 7.613852e+00 2.431327e-02\n", " * time: 1.6754281520843506\n", " 112 7.613679e+00 3.551999e-02\n", " * time: 1.7102580070495605\n", " 113 7.613513e+00 2.328950e-02\n", " * time: 1.7221720218658447\n", " 114 7.613490e+00 4.512833e-02\n", " * time: 1.7338461875915527\n", " 115 7.613388e+00 4.183490e-02\n", " * time: 1.7461740970611572\n", " 116 7.613230e+00 2.065543e-02\n", " * time: 1.761625051498413\n", " 117 7.613047e+00 2.239544e-02\n", " * time: 1.7735559940338135\n", " 118 7.612909e+00 3.036614e-02\n", " * time: 1.785431146621704\n", " 119 7.612740e+00 1.804457e-02\n", " * time: 1.7971811294555664\n", " 120 7.612726e+00 5.013613e-02\n", " * time: 1.8088171482086182\n", " 121 7.612510e+00 4.108673e-02\n", " * time: 1.8241770267486572\n", " 122 7.612388e+00 3.100265e-02\n", " * time: 1.8399240970611572\n", " 123 7.612273e+00 3.618959e-02\n", " * time: 1.8522601127624512\n", " 124 7.612139e+00 4.680698e-02\n", " * time: 1.863948106765747\n", " 125 7.611903e+00 2.270899e-02\n", " * time: 1.879164218902588\n", " 126 7.611732e+00 2.316536e-02\n", " * time: 1.8907160758972168\n", " 127 7.611678e+00 4.431792e-02\n", " * time: 1.90214204788208\n", " 128 7.611507e+00 3.821697e-02\n", " * time: 1.9172132015228271\n", " 129 7.611307e+00 3.305492e-02\n", " * time: 1.9324150085449219\n", " 130 7.611202e+00 5.913222e-02\n", " * time: 1.9448540210723877\n", " 131 7.610937e+00 3.714063e-02\n", " * time: 1.9600050449371338\n", " 132 7.610834e+00 4.066158e-02\n", " * time: 1.973717212677002\n", " 133 7.610721e+00 3.380214e-02\n", " * time: 1.9908959865570068\n", " 134 7.610424e+00 3.130255e-02\n", " * time: 2.003547191619873\n", " 135 7.610233e+00 3.079234e-02\n", " * time: 2.040894031524658\n", " 136 7.610069e+00 2.612226e-02\n", " * time: 2.0601181983947754\n", " 137 7.609930e+00 2.650606e-02\n", " * time: 2.079094171524048\n", " 138 7.609803e+00 1.910044e-02\n", " * time: 2.094766139984131\n", " 139 7.609730e+00 3.099989e-02\n", " * time: 2.1066830158233643\n", " 140 7.609633e+00 3.299785e-02\n", " * time: 2.1182310581207275\n", " 141 7.609497e+00 2.455384e-02\n", " * time: 2.12986421585083\n", " 142 7.609379e+00 3.025385e-02\n", " * time: 2.145726203918457\n", " 143 7.609237e+00 1.065880e-02\n", " * time: 2.161553144454956\n", " 144 7.609107e+00 1.687673e-02\n", " * time: 2.173441171646118\n", " 145 7.609083e+00 2.562332e-02\n", " * time: 2.1851260662078857\n", " 146 7.608934e+00 2.855580e-02\n", " * time: 2.196895122528076\n", " 147 7.608820e+00 1.760804e-02\n", " * time: 2.2124030590057373\n", " 148 7.608657e+00 1.998861e-02\n", " * time: 2.223755121231079\n", " 149 7.608605e+00 2.835028e-02\n", " * time: 2.235621213912964\n", " 150 7.608461e+00 2.620076e-02\n", " * time: 2.2516682147979736\n", " 151 7.608396e+00 4.002600e-02\n", " * time: 2.2631471157073975\n", " 152 7.608276e+00 3.675353e-02\n", " * time: 2.2749290466308594\n", " 153 7.608185e+00 3.570448e-02\n", " * time: 2.286708116531372\n", " 154 7.608020e+00 2.730947e-02\n", " * time: 2.299337148666382\n", " 155 7.607962e+00 4.760897e-02\n", " * time: 2.3125171661376953\n", " 156 7.607782e+00 2.783927e-02\n", " * time: 2.3298439979553223\n", " 157 7.607659e+00 2.816178e-02\n", " * time: 2.3674161434173584\n", " 158 7.607546e+00 3.266044e-02\n", " * time: 2.384275197982788\n", " 159 7.607407e+00 2.782225e-02\n", " * time: 2.39614200592041\n", " 160 7.607286e+00 1.697699e-02\n", " * time: 2.4114601612091064\n", " 161 7.607168e+00 2.324873e-02\n", " * time: 2.4230501651763916\n", " 162 7.607131e+00 4.170998e-02\n", " * time: 2.4354031085968018\n", " 163 7.607051e+00 3.509715e-02\n", " * time: 2.446927070617676\n", " 164 7.606945e+00 3.507676e-02\n", " * time: 2.458728075027466\n", " 165 7.606803e+00 3.277189e-02\n", " * time: 2.474316120147705\n", " 166 7.606683e+00 2.995915e-02\n", " * time: 2.4860000610351562\n", " 167 7.606528e+00 3.020213e-02\n", " * time: 2.5013771057128906\n", " 168 7.606507e+00 4.120695e-02\n", " * time: 2.512902021408081\n", " 169 7.606481e+00 2.714590e-02\n", " * time: 2.5243802070617676\n", " 170 7.606357e+00 2.121519e-02\n", " * time: 2.536015033721924\n", " 171 7.606268e+00 2.347918e-02\n", " * time: 2.54746413230896\n", " 172 7.606117e+00 2.037599e-02\n", " * time: 2.5633931159973145\n", " 173 7.606072e+00 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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": "1.7.1" }, "kernelspec": { "name": "julia-1.7", "display_name": "Julia 1.7.1", "language": "julia" } }, "nbformat": 4 }