{ "cells": [ { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "# VV in SiC\n", "\n", "An example of computing Free Induction Decay (FID) and Hahn-echo (HE) with hyperfine couplings from GIPAW for axial and basal divacancies." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import sys\n", "import ase\n", "import pandas as pd\n", "import warnings\n", "import pycce as pc\n", "\n", "np.set_printoptions(suppress=True, precision=5)\n", "warnings.simplefilter(\"ignore\")\n", "\n", "seed = 8805" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Axial kk-VV\n", "First we compute FID and HE for axial divacancy." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Build BathCell from the ground\n", "\n", "One can set up an `BathCell` instance by providing the parameters of the unit cell, or `cell` argument as 3x3 tensor, where each column defines a, b, c unit cell vectors in cartesian coordinates.\n", "\n", "In this tutorial we use the first approach." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "# Set up unit cell with (a, b, c, alpha, beta, gamma)\n", "sic = pc.BathCell(3.073, 3.073, 10.053, 90, 90, 120, 'deg')\n", "# z axis in cell coordinates\n", "sic.zdir = [0, 0, 1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, user has to define positions of atoms in the unit cell.\n", "It is done with `BathCell.add_atoms` function. It takes an unlimited number of arguments, each argument is a tuple. First element of the tuple is the name of the atom, second - list of xyz coordinates either in cell units (if keyword `type='cell'`, default value) or in Angstrom (if keyword `type='angstrom'`). Returns `BathCell.atoms` dictionary, which contains list of coordinates for each type of elements." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "# position of atoms\n", "sic.add_atoms(('Si', [0.00000000, 0.00000000, 0.1880]),\n", " ('Si', [0.00000000, 0.00000000, 0.6880]),\n", " ('Si', [0.33333333, 0.66666667, 0.4380]),\n", " ('Si', [0.66666667, 0.33333333, 0.9380]),\n", " ('C', [0.00000000, 0.00000000, 0.0000]),\n", " ('C', [0.00000000, 0.00000000, 0.5000]),\n", " ('C', [0.33333333, 0.66666667, 0.2500]),\n", " ('C', [0.66666667, 0.33333333, 0.7500]));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Two types of isotopes present in SiC: $^{29}$Si and $^{13}$C. We add this information with the `BathCell.add_isotopes` function. The code knows most of the concentrations, so this step is actually unnecessary. If no isotopes is provided, the natural concentration of common magnetic isotopes is assumed." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "# isotopes \n", "sic.add_isotopes(('29Si', 0.047), ('13C', 0.011))\n", "\n", "# defect position in cell units\n", "vsi_cell = [0, 0, 0.1880]\n", "vc_cell = [0, 0, 0]\n", "\n", "# Generate bath spin positions\n", "atoms = sic.gen_supercell(200, remove=[('Si', vsi_cell),\n", " ('C', vc_cell)],\n", " seed=seed)" ] }, { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "### Read Quantum ESPRESSO output\n", "\n", "**PyCCE** provides a helper function `read_qe` in `pycce.io` module to read hyperfine couplings from Quantum ESPRESSO output. `read_qe` takes from 1 to 3 positional arguments:\n", "\n", "* `pwfile` name of the pw input/output file;\n", "* `hyperfine` name of the gipaw output file containing hyperfine couplings;\n", "* `efg` name of the gipaw output file containing electric field tensor calculations.\n", "\n", "\n", "During its call, `read_qe` will read the cell matrix in pw file and apply it to the coordinates is necessary. However, usually we still need to rotate and translate the Quantum ESPRESSO supercell to allign it with our `BathArray`. To do so we can provide additional keywords arguments `center` and `rotation_matrix`. `center` is the position of (0, 0, 0) point in coordinates of pw file, and `rotation_matrix` is rotation matrix which aligns z-direction of the GIPAW output. This matrix, acting on the (0, 0, 1) in Cartesian coordinates of GIPAW output should produce (a, b, c) vector, alligned with zdirection of the BathCell. Keyword argument `rm_style` shows whether `rotation_matrix` contains coordinates of new basis set as rows (`'row'`, common in physics) or columns (`'col'`, common in math)." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "# Prepare rotation matrix to alling with z axis of generated atoms\n", "# This matrix, acting on the [0, 0, 1] in Cartesian coordinates of GIPAW output\n", "# Should produce [a, b, c] vector, alligned with zdirection of the BathCell\n", "M = np.array([[0, 0, -1],\n", " [0, -1, 0],\n", " [-1, 0, 0]])\n", "\n", "# Position of (0,0,0) point in cell coordinates\n", "center = [0.6, 0.5, 0.5]\n", "# Read GIPAW results\n", "exatoms = pc.read_qe('axial/pw.in',\n", " hyperfine='axial/gipaw.out',\n", " center=center, rotation_matrix=M,\n", " rm_style='col',\n", " isotopes={'C':'13C', 'Si':'29Si'})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`pc.read_qe` produces instance of `BathArray`, with names of bath spins as the most common isotopes of the following elements (if keyword `isotopes` set to `None`) or from the mapping provided by the `isotopes` argument. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Set up CCE Simulator\n", "In this example we set up a bare `Simulator` and add properties of the spin bath later." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "# Setting up CCE calculations\n", "pos = sic.to_cartesian(vsi_cell)\n", "CCE_order = 2\n", "r_bath = 40\n", "r_dipole = 8\n", "B = np.array([0, 0, 500])\n", "\n", "calc = pc.Simulator(1, pos, alpha=[0, 0, 1], beta=[0, 1, 0], magnetic_field=B)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Function `Simulator.read_bath` can be called explicitly to initiallize spin bath.\n", "Additional keyword argument `external_bath` takes instance of `BathArray` with hyperfine couplings read from Quantum Espresso. The program then finds the spins with the same name at the same positions (within the range defined by `error_range` keyword argument) in the total bath and sets their hyperfine couplings.\n", "\n", "Finally, we call `Simulator.generate_clusters` to find the bath spin clusters in the provided bath." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [], "source": [ "calc.read_bath(atoms, r_bath, external_bath=exatoms);\n", "calc.generate_clusters(CCE_order, r_dipole=r_dipole);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### FID with DFT hyperfine couplings\n", "\n", "We provide ``pulses`` argument directly to the compute function instead of during initiallization of the ``Simulator`` object." ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [ "time_space = np.linspace(0, 0.01, 501)\n", "N = 0\n", "\n", "ldft = calc.compute(time_space, pulses=N, as_delay=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### FID with hyperfine couplings from point dipole approximation" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "pdcalc = pc.Simulator(1, pos, alpha=[0, 0, 1], beta=[0, 1, 0], magnetic_field=B,\n", " bath=atoms, r_bath=r_bath, order=CCE_order, r_dipole=r_dipole)\n", "lpd = pdcalc.compute(time_space, pulses=N, as_delay=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the results and and verify that the predictions are significantly different." ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(time_space, lpd.real, label='point dipole')\n", "plt.plot(time_space, ldft.real, label='DFT')\n", "plt.legend()\n", "plt.xlabel('Time (ms)')\n", "plt.ylabel('L');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Hahn-echo comparison\n", "Now we compare the predictions for Hahn-echo signal with different hyperfine couplings." ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "he_time = np.linspace(0, 2.5, 501)\n", "B = np.array([0, 0, 500])\n", "N = 1\n", "\n", "he_ldft = calc.compute(he_time, magnetic_field=B, pulses=N, as_delay=False)\n", "he_lpd = pdcalc.compute(he_time, magnetic_field=B, pulses=N, as_delay=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the results and compare. We observe that electron spin echo modulations differ significantly, while the observed decay is about the same." ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(he_time, he_ldft.real, label='DFT')\n", "plt.plot(he_time, he_lpd.real, label='point dipole')\n", "\n", "plt.legend()\n", "plt.xlabel('Time (ms)')\n", "plt.ylabel('L');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Basal kh-VV in SiC\n", "\n", "The basal divacancy's Hamiltonian includes both D and E terms, which allows for mixing between +1 and -1 spin levels at zero field. \n", "\n", "Thus, either the generalized CCE should be used, or additional perturbational Hamiltonian terms are to be added. Here we consider the generalized CCE framework.\n", "\n", "First, prepare rotation matrix for DFT results. The same supercell was used to compute hyperfine couplings, however z-axis of the electron spin qubit is aligned with Si-C bond, therefore we will need to rotate the DFT supercell accordingly." ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [], "source": [ "# Coordinates of vacancies in cell coordinates (note that Vsi is not located in the first unitcell)\n", "vsi_cell = -np.array([1 / 3, 2 / 3, 0.0620])\n", "vc_cell = np.array([0, 0, 0])\n", "\n", "sic.zdir = [0, 0, 1]\n", "\n", "# Rotation matrix for DFT supercell\n", "R = pc.rotmatrix([0, 0, 1], sic.to_cartesian(vsi_cell - vc_cell))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Total spin bath can be initiallized by simply setting z direction of the `BathCell` object." ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "sic.zdir = vsi_cell - vc_cell\n", "\n", "# Generate bath spin positions\n", "sic.add_isotopes(('29Si', 0.047), ('13C', 0.011))\n", "atoms = sic.gen_supercell(200, remove=[('Si', vsi_cell),\n", " ('C', vc_cell)],\n", " seed=seed)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Read DFT results with `read_qe` function. To rotate in the correct frame we need to apply both changes of basis consequently" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [], "source": [ "M = np.array([[0, 0, -1],\n", " [0, -1, 0],\n", " [-1, 0, 0]])\n", "\n", "# Position of (0,0,0) point in cell coordinates\n", "center = np.array([0.59401, 0.50000, 0.50000])\n", "\n", "# Read GIPAW results\n", "exatoms = pc.read_qe('basal/pw.in',\n", " hyperfine='basal/gipaw.out',\n", " center=center, rotation_matrix=(M.T @ R),\n", " rm_style='col',\n", " isotopes={'C':'13C', 'Si':'29Si'})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To check whether our rotations produced correct results we can find the indexes of the `BathArray` and DFT output with `pc.same_bath_indexes` function. It returns a tuple, containing the indexes of elements in the two `BathArray` instances with the same position and name. First element of the tuple - indexes of first argument, second - of the second. For that we generate supecell with `BathCell` class, containing 100% isotopes, and count the number of found indexes - iut should be equal to the size of DFT supercell." ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "There are 1438 same elements. Size of the DFT supercell is 1438\n" ] } ], "source": [ "# isotopes \n", "sic.add_isotopes(('29Si', 1), ('13C', 1))\n", "allcell = sic.gen_supercell(50, remove=[('Si', vsi_cell),\n", " ('C', vc_cell)],\n", " seed=seed)\n", "\n", "indexes, ext_indexes = pc.same_bath_indexes(allcell, exatoms, 0.2, True)\n", "print(f\"There are {indexes.size} same elements.\"\n", " f\" Size of the DFT supercell is {exatoms.size}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Setting up calculations\n", "Now we can safely setup calculations of coherence function with DFT couplings. We will compare results with or without bath state sampling." ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [], "source": [ "D = 1.334 * 1e6\n", "E = 0.0184 * 1e6\n", "magnetic_field = 0\n", "\n", "calc = pc.Simulator(1, pos, bath=atoms, external_bath=exatoms, D=D, E=E,\n", " magnetic_field=magnetic_field, alpha=0, beta=1,\n", " r_bath=r_bath, order=CCE_order, r_dipole=r_dipole)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The code automatically picks up the two lowest eigenstates of the central spin hamiltonian as qubit states." ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Simulator for center array of size 1.\n", "magnetic field:\n", "array([0., 0., 0.])\n", "\n", "Parameters of cluster expansion:\n", "r_bath: 40\n", "r_dipole: 8\n", "order: 2\n", "\n", "Bath consists of 761 spins.\n", "\n", "Clusters include:\n", "761 clusters of order 1.\n", "1870 clusters of order 2.\n", "\n" ] } ], "source": [ "print(calc)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use the CenterArray, stored in `Simulator.center` attribute, to take a look at the qubit states in the absence of nuclear spin bath." ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 state: [ 0. -1. 0.]; 1 state: [ 0.70711 0. -0.70711]\n" ] } ], "source": [ "calc.center.generate_states()\n", "print(f'0 state: {calc.alpha.real}; 1 state: {calc.beta.real}')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Free Induction Decay (FID)\n", "Now, use the generalized CCE to compute FID of the coherence function at different CCE orders." ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [], "source": [ "N = 0 # Number of pulses\n", "time_space = np.linspace(0, 1, 101) # Time points at which to compute\n", "\n", "orders = [1, 2, 3]\n", "lgen = []\n", "\n", "r_bath = 30\n", "r_dipole = 8\n", "\n", "calc = pc.Simulator(1, pos, bath=atoms, external_bath=exatoms,\n", " D=D, E=E, pulses=N, alpha=0, beta=1,\n", " r_bath=r_bath, r_dipole=r_dipole)" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [], "source": [ "for o in orders:\n", " calc.generate_clusters(o)\n", " l = calc.compute(time_space, method='gcce',\n", " quantity='coherence', as_delay=False)\n", "\n", " lgen.append(np.abs(l))\n", "\n", "lgen = pd.DataFrame(lgen, columns=time_space, index=orders).T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the results do not converge, but rather start to diverge. Bath sampling (setting `nbstates` to some value) will help with that." ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "lgen.plot()\n", "plt.xlabel('Time (ms)')\n", "plt.ylabel('L')\n", "plt.ylim(-0.1, 1.1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note, that this approach is ``nbstates`` times more expensive than the gCCE, therefore the following calculation will take a couple of minutes." ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [], "source": [ "orders = [1, 2]\n", "lgcce = []\n", "\n", "r_bath = 30\n", "r_dipole = 6\n", "\n", "for o in orders:\n", " calc.generate_clusters(o)\n", "\n", " l = calc.compute(time_space, nbstates=30, seed=seed,\n", " method='gcce',\n", " quantity='coherence', as_delay=False)\n", "\n", " lgcce.append(np.abs(l))\n", "\n", "lgcce = pd.DataFrame(lgcce, columns=time_space, index=orders).T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Compare the two results\n", "The gCCE results are converged at 1st order. Note that we used only a small number of bath states (30), thus the calculations are not converged with respect to the number of bath states. Calculations with higher number of bath states (~100) will produce correct results." ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(lgen, color='black', ls=':')\n", "plt.plot(lgcce)\n", "\n", "plt.xlabel('Time (ms)')\n", "plt.ylabel('L')\n", "plt.ylim(-0.1, 1.1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Hahn-echo decay\n", "\n", "Using the similar procedure to the one used for FID, we can compute the Hahn-echo decay." ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [], "source": [ "r_bath = 40\n", "r_dipole = 8\n", "order = 2\n", "N = 1 # Number of pulses\n", "\n", "calc = pc.Simulator(1, pos, bath=atoms, external_bath=exatoms,\n", " pulses=N, D=D, E=E, alpha=-1, beta=0,\n", " r_bath=r_bath, order=order, r_dipole=r_dipole)" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [], "source": [ "ts = np.linspace(0, 4, 101) # time points (in ms)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [], "source": [ "helgen = calc.compute(ts, method='gcce', quantity='coherence')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note the number of nbstates leads to significantly increased time of the calculation. The interface to mpi implementation is provided with keywords `parallel` (general) or `parallel_states`(bath state sampling run-specific). However it requires `mpi4py` installed and a run on several cores." ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [], "source": [ "helgcce = calc.compute(time_space, nbstates=30, seed=seed,\n", " method='gcce', quantity='coherence')" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(ts, helgcce, label='gCCE with mean field')\n", "plt.plot(ts, helgen, label='gCCE')\n", "\n", "plt.legend()\n", "plt.xlabel('Time (ms)')\n", "plt.ylabel('L');" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.3" }, "pycharm": { "stem_cell": { "cell_type": "raw", "metadata": { "collapsed": false }, "source": [] } } }, "nbformat": 4, "nbformat_minor": 4 }