{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Calculation of polarons\n",
"\n",
"Author: J. Lafuente-Bartolome' (v1, XX/01/2024)
\n",
"Revision: F. Giustino (v1.1, 07/23/2024)
\n",
"Revision: S. Tiwari (v1.2, 09/30/2024)
\n",
"\n",
"\n",
"In this notebook, we perform calculations of polarons. The theory and computational method are described in [Phys. Rev. Lett. **122**, 246403 (2019)](https://doi.org/10.1103/PhysRevLett.122.246403) and [Phys. Rev. B **99**, 235139 (2019)](https://doi.org/10.1103/PhysRevB.99.235139). \n",
"\n",
"Electrons and phonons are computed with Quantum ESPRESSO (QE), maximally-localized Wannier functions are computed with Wannier90, and polarons are computed with EPW. "
]
},
{
"cell_type": "markdown",
"metadata": {
"jp-MarkdownHeadingCollapsed": true
},
"source": [
"## Theory\n",
"\n",
"Here, we briefly present the main concepts and equations that are solved by EPW to obtain polaron formation energy, wavefunction, and atomic displacements.\n",
"\n",
"The ground state wave function $\\psi(\\mathbf{r})$ and atomic displacements $\\Delta \\tau_{\\kappa\\alpha p}$ of the polarons are found by minimizing the total energy functional\n",
"of an excess electron added to a crystal. This minimization problem translates into the solution of the following coupled system of equations:\n",
"$$\n",
" \\hat{H}_{\\mathrm{KS}}^{0} \\, \\psi(\\mathbf{r})\n",
" +\n",
" \\sum_{\\kappa\\alpha p} \\frac{\\partial V_{\\mathrm{KS}}^{0}}{\\partial \\tau_{\\kappa \\alpha p}}\n",
" \\Delta \\tau_{\\kappa \\alpha p} \\, \\psi(\\mathbf{r})\n",
" =\n",
" \\varepsilon \\, \\psi(\\mathbf{r}) ~,\n",
"$$\n",
"$$\n",
" \\Delta \\tau_{\\kappa \\alpha p}\n",
" =\n",
" -\\sum_{\\kappa'\\alpha' p'} (C^{0})^{-1}_{\\kappa\\alpha p,\\kappa'\\alpha'p'}\n",
" \\int d\\mathbf{r} \\, \\frac{\\partial V_{\\mathrm{KS}}^{0}}{\\partial \\tau_{\\kappa'\\alpha'p'}}\n",
" \\, |\\psi(\\mathbf{r})|^2 ~.\n",
"$$\n",
"In these expressions, $\\tau_{\\kappa\\alpha p}$ represents the Cartesian coordinate\n",
"of atom $\\kappa$ in unit cell $p$ along the direction $\\alpha$, $C^{0}_{\\kappa\\alpha p,\\kappa'\\alpha'p'}$ is the matrix of interatomic force constants, and $\\hat{H}_{\\mathrm{KS}}^{0}$ and $V_{\\mathrm{KS}}^{0}$ represent the Kohn-Sham Hamiltonian and the self-consistent potential, respectively. The superscript $^{0}$ indicates that these quantities are evaluated in the ground state without extra electron. The integral is performed over a Born-Von Karman supercell of the crystal containing $N_p$ unit cells. We will refer to $\\varepsilon$ as the polaron eigenvalue.\n",
"\n",
"By expanding the polaron wave function in terms of the single-particle Kohn-Sham states \n",
"$\\psi_{n\\mathbf{k}}$ with eigenvalues $\\varepsilon_{n\\mathbf{k}}$:\n",
"$$\n",
" \\psi(\\mathbf{r}) = \\frac{1}{\\sqrt{N_p}}\n",
" \\sum_{n\\mathbf{k}} A_{n\\mathbf{k}} \\psi_{n\\mathbf{k}} ~,\n",
"$$\n",
"and the atomic displacements in terms of the phonon eigenmodes $e_{\\kappa\\alpha,\\nu}(\\mathbf{q})$ with frequencies $\\omega_{\\mathbf{q}\\nu}$:\n",
"$$\n",
" \\Delta\\tau_{\\kappa\\alpha p } = -\\frac{2}{N_p}\n",
" \\sum_{\\mathbf{q}\\nu} B^{*}_{\\mathbf{q}\\nu} \n",
" \\left( \\frac{\\hbar}{2M_\\kappa \\omega_{\\mathbf{q}\\nu}} \\right)^{1/2}\n",
" e_{\\kappa\\alpha,\\nu}(\\mathbf{q}) \\, e^{i\\mathbf{q}\\cdot\\mathbf{R}_p},\n",
"$$\n",
"where $M_\\kappa$ is the mass of the atom $\\kappa$ and $\\mathbf{R}_p$ is the lattice vector of the unit cell $p$, we can transform the first two equations into a coupled set of equations for the expansion coefficients in reciprocal space:\n",
"$$\n",
" \\frac{2}{N_p} \\sum_{\\mathbf{q}m\\nu} B_{\\mathbf{q}\\nu}\n",
" \\, g_{mn\\nu}^{*}(\\mathbf{k},\\mathbf{q}) \\, A_{m\\mathbf{k+q}}\n",
" =\n",
" (\\varepsilon_{n\\mathbf{k}}-\\varepsilon) A_{n\\mathbf{k}} ~,\n",
"$$\n",
"$$\n",
" B_{\\mathbf{q}\\nu} = \\frac{1}{N_p}\n",
" \\sum_{mn\\mathbf{k}} A^{*}_{m\\mathbf{k+q}}\n",
" \\frac{g_{mn\\nu}(\\mathbf{k},\\mathbf{q})}{\\hbar\\omega_{\\mathbf{q}\\nu}} A_{n\\mathbf{k}} ~.\n",
"$$\n",
"The polaron formation energy $\\Delta E_{f}$, defined as the energy required to trap \n",
"a conduction band state with eigenvalue $\\varepsilon_{\\mathrm{CBM}}$ into a localized polaron, can be obtained from the expansion coefficients that solve the coupled set of equations by:\n",
"$$\n",
" \\label{eq:eq3}\n",
" \\Delta E_{f}\n",
" =\n",
" \\frac{1}{N_p} \\sum_{n\\mathbf{k}} |A_{n\\mathbf{k}}|^2\n",
" (\\varepsilon_{n\\mathbf{k}}-\\varepsilon_{\\mathrm{CBM}})\n",
" -\n",
" - \\frac{1}{N_p} \\sum_{\\mathbf{q}\\nu} |B_{\\mathbf{q}\\nu}|^2 \\hbar\\omega_{\\mathbf{q}\\nu} ~.\n",
"$$\n",
"We will refer to the first and second terms on the right hand side as the electron and phonon parts of the formation energy, respectively.\n",
"\n",
"From these expressions, we observe that\n",
"the necessary ingredients to solve the polaron equations\n",
"are the Kohn-Sham eigenvalues,\n",
"phonon frequencies,\n",
"and electron-phonon matrix elements on the $\\mathbf{k}$- and $\\mathbf{q}$-grids\n",
"corresponding to the equivalent Born-Von Karman supercell \n",
"in which the first two equations are defined.\n",
"In order to obtain the formation energy of an isolated polaron,\n",
"we will need to solve the coupled set of equations in increasingly denser grids\n",
"and extrapolate the results to the infinite supercell limit."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Set up working environment"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Load required modules:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import scipy.interpolate\n",
"import matplotlib.pyplot as plt\n",
"from mpl_toolkits.mplot3d import Axes3D\n",
"from matplotlib.ticker import MultipleLocator,FormatStrFormatter\n",
"import os\n",
"from EPWpy import EPWpy\n",
"from EPWpy.plotting import plot_wannier\n",
"from EPWpy.plotting import plot_polaron\n",
"from EPWpy.utilities import EPW_util"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Set paths to relevant directories:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# Set prefix\n",
"prefix='lif'"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Set the number of cores to be used in the calculations:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Maximum number of cores to be used: 4\n"
]
}
],
"source": [
"# Maximum number of cores to be used\n",
"cores = 4\n",
"print('Maximum number of cores to be used:', cores)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Define general calculation parameters to be used throughout the workflow:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" \n",
" \n",
" -*#*- ...............- \n",
" .+*= .+%*-=%%: .=#*- -===============-:.\n",
" :*%=*%%- *%* #%* :+%+-%%+ .:. -=. :==-. \n",
" -%S -%%*: :#%. -%%-. -##: #%* -=. :==- \n",
" .. .%S: +%%%%*. :*%%%#= %%= -=. :==- \n",
" :=#%%*- .#S- .. .%%= :*#*: -=. :==- \n",
" -%S:.=#%%*==%# *%%=::=##-+%%. . .=-. :==- .= \n",
" :%%- .-+++: -+##*=. =%S :-::==: .==- --.\n",
" *%# #%+ -=--:. .----:. \n",
" :%%- -%S. \n",
" .-=*####SS%#########: -###########*+: +#######= =%SS####+::. \n",
" =+#**%SSSSSSSSSSSSSSSS= =SSSSSSSSSSSSSSS= #SSSSSSS*. +SSSSSSSS%%%%- \n",
" *%% =SSS.. .SSS= SSS=. .:+SSS+ -SSS:. .-::. .SSS+. #%* \n",
" #%#. =SSS. *S# *S%: SSS= %SS%. .SSS= #SSS%. :SSS: =%#. \n",
" *%%: =SSS#*#SSS- SSS= .+SSS+. %SS*.=SSSSS+ +SS%.:+%+ \n",
" +%%:=SSSSSSSSS- SSSSSSSSSSSSS=. +SSS:SSS%SSS:%SS*-#%= \n",
" ....#S==SSS:..SSS: =+- SSS%######+=. -SSS%SS%.#SS%SSS==%%=. \n",
" .:+##%%#*- =SSS. ::. :SSS. SSS=. SSSSSS:..SSSSSS: :*%%%*=- \n",
" #%+. -+#SSS*+++++++*SSS: .=+SSS#++++: %SSSS+. =SSSS%. :-+#%%+ \n",
" #%* .SSSSSSSSSSSSSSSSSS: *SSSSSSSSSSS. +SSS%. %SSS*. . .%%= \n",
" =%S :::::::::::::::::. .:::::::::. :::. :::. =+=-.#%+ \n",
" -%S: =+===#S: \n",
" ==*------------------------------=========+++++++++++++++++++++++========++-+## \n",
" =+++++++++++*******++++++++++++++++========------------------==========+++++++- \n",
"-- -- -- -- -- -- -- -- -- -- -- -- Structure Info -- -- -- -- -- -- -- -- -- -- -- -- -- \n",
"2\n",
"https://raw.githubusercontent.com/PseudoDojo/ONCVPSP-PBE-FR-PDv0.4/master/Li/Li.upf\n",
"https://raw.githubusercontent.com/PseudoDojo/ONCVPSP-PBE-FR-PDv0.4/master/Li/Li_r.upf\n",
"https://raw.githubusercontent.com/PseudoDojo/ONCVPSP-PBE-FR-PDv0.4/master/Li/Li-sp_r.upf\n",
"https://raw.githubusercontent.com/PseudoDojo/ONCVPSP-PBE-FR-PDv0.4/master/Li/Li-d_r.upf\n",
"https://raw.githubusercontent.com/PseudoDojo/ONCVPSP-PBE-FR-PDv0.4/master/Li/Li-s_r.upf\n",
"pseudo found at pseudodojo : ONCVPSP-PBE-FR-PDv0.4/Li-s_r.upf\n",
"https://raw.githubusercontent.com/PseudoDojo/ONCVPSP-PBE-FR-PDv0.4/master/F/F.upf\n",
"https://raw.githubusercontent.com/PseudoDojo/ONCVPSP-PBE-FR-PDv0.4/master/F/F_r.upf\n",
"pseudo found at pseudodojo : ONCVPSP-PBE-FR-PDv0.4/F_r.upf\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"sh: 1: module: not found\n"
]
},
{
"data": {
"text/plain": [
"32512"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lif=EPWpy.EPWpy({'prefix':'\\''+prefix+'\\'',\n",
" 'restart_mode':'\\'from_scratch\\'',\n",
" 'calculation':'\\'scf\\'',\n",
" 'ibrav':2,\n",
" 'nat':2,\n",
" 'ntyp':2,\n",
" 'atomic_species':['Li', 'F'],\n",
" 'atomic_pos':np.array([[0.0, 0.0, 0.0], [-0.5, 0.5, 0.5]]), # in alat\n",
" 'mass':[6.941, 18.9984],\n",
" 'atoms':['Li', 'F'],\n",
" 'ecutwfc':'80',\n",
" 'celldm(1)':'7.67034',\n",
" 'verbosity':'\\'high\\'',\n",
" 'pseudo_auto':True},\n",
" env='mpirun',\n",
" system='lif')\n",
"lif.run_serial = True\n",
"lif.env = 'mpirun'\n",
"#'pseudo_dir':'\\''+str(pseudo)+'\\''},\n",
"\n",
"# Print relevant info\n",
"os.system('module list')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Workflow\n",
"\n",
"We will consider a hole polaron in LiF as an example."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Preliminary scf, ph, and nscf calculations"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-- -- -- -- -- -- -- -- -- -- -- Calculation: scf -- -- -- -- -- -- -- -- -- -- -- \n",
"Running scf |████████████████████████████████████████| in 2.9s (0.64/s) \n",
"\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n"
]
}
],
"source": [
"# Prepare scf input file\n",
"lif.scf(electrons={'conv_thr':'1.0d-12'}, kpoints={'kpoints':[[6, 6, 6]]}, name='scf')\n",
"lif.prepare(type_run='scf')\n",
"\n",
"# Run scf calculation\n",
"lif.run(4)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-- -- -- -- -- -- -- -- -- -- -- Calculation: ph -- -- -- -- -- -- -- -- -- -- -- \n",
"Running ph |████████████████████████████████████████| in 1:22.7 (0.02/s) \n",
"\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n"
]
}
],
"source": [
"# Prepare ph input file\n",
"lif.ph(phonons={'nq1':3,\n",
" 'nq2':3,\n",
" 'nq3':3})\n",
"\n",
"# Run ph calculation\n",
"lif.prepare(type_run='ph')\n",
"lif.run(4,type_run='ph')"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-- -- -- -- -- -- -- -- -- -- -- Calculation: nscf -- -- -- -- -- -- -- -- -- -- -- \n",
"Running nscf |████████████████████████████████████████| in 12.5s (0.11/s) \n",
"\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n"
]
}
],
"source": [
"# Prepare nscf input file\n",
"lif.nscf(system={'nbnd':15},kpoints={'grid':[6, 6, 6],'kpoints_type': 'crystal'})\n",
"lif.prepare(type_run='nscf')\n",
"# Run nscf calculation\n",
"lif.run(4,type_run='nscf')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Coarse mesh epw calculations"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"obtaining nscf and ph attributes\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- Info -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n",
"Based on previous pw and ph calculations some parameters are set below\n",
"lpolar: .true. (related to epsil in ph)\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n",
"(4, 3)\n",
"[51, 51, 51]\n"
]
}
],
"source": [
"# Prepare epw input for coarse mesh calculation\n",
"lif.reset()\n",
"lif.epw(epwin={'proj':['\\'F : p\\''],\n",
" 'wannier_plot':'.true.',\n",
" 'band_plot':'.true.',\n",
" 'filkf':'\\'./path.kpt\\'',\n",
" 'filqf':'\\'./path.kpt\\'',\n",
" 'num_iter':500,\n",
" 'epbwrite':'.false.',\n",
" 'nbndsub':'3',\n",
" 'bands_skipped':'\\'exclude_bands = 1:2, 6:15\\'',\n",
" 'wannier_plot':'.true.',\n",
" 'wannier_plot_supercell':'6, 6, 6',\n",
" 'lpolar':'.true.',\n",
" 'eig_read':'.false.',\n",
" 'wannierize':'.true.'},\n",
" name='epw1')\n",
"# Generate filkf if needed\n",
"\n",
"W=[0.5,0.75,0.25]\n",
"L=[0.0,0.5,0.0]\n",
"G=[0.0,0.0,0.0]\n",
"X=[0.5,0.5,0.0]\n",
"K=[0.375,0.75,0.375]\n",
"sympoints=[W,L,G,X,W,K]\n",
"#\n",
"lif.filkf(path=sympoints, length=[41, 41, 41, 41, 41], name='path.kpt')\n",
"\n",
"#\n",
"lif.prepare(type_run='epw1') "
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"/mnt/storage/sabya/For_video/epwpy/build/q-e-EPW-5.9s/bin\n",
"-- -- -- -- -- -- -- -- -- -- -- Calculation: epw1 -- -- -- -- -- -- -- -- -- -- -- \n",
"Running epw1 |████████████████████████████████████████| in 48.9s (0.03/s) \n",
"\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n"
]
}
],
"source": [
"print(lif.code)\n",
"\n",
"#lif.env='mpirun -np 4'\n",
"lif.run(4,type_run='epw1')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Wannier function plots"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Notebook initialized with png backend.\n",
"Positive isosurface contour set to: 0.76612 (10% of max value: 7.6612)\n"
]
},
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Specify the path to your .cube file\n",
"cube_file = f'{lif.prefix}/epw/lif_00001.cube'\n",
"# Read .cube file\n",
"Data = EPW_util.read_cube_file(cube_file, 4.0) #Cube file and bonds\n",
"Data['in_notebook']=True # Telling the plotter that you want to see in notebook mode\n",
"Data['backend']='png' # Backend can be png or ipy (which gives an interactive widget)\n",
"Data['verbosity'] = 1 # Telling if extra stuff needs to be printed (set to > 2 for printing)\n",
"# Plot the isosurface and atomic positions\n",
"L = plot_wannier.plot_isosurface_from_cube_file(Data)\n",
"L"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Interpolation to fine mesh and solution of polaron equations"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"obtaining nscf and ph attributes\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- Warning -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n",
"Refreshing EPW input (remove refresh from epw_save.json if not needed)\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- Info -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n",
"Based on previous pw and ph calculations some parameters are set below\n",
"lpolar: .true. (related to epsil in ph)\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n"
]
}
],
"source": [
"# Prepare epw input for fine mesh interpolation and polaron calculation\n",
"lif.epw(epwin={'bands_skipped':'\\'exclude_bands = 1:2, 6:15\\'',\n",
" 'nbndsub':3,\n",
" 'plrn':'.true.',\n",
" 'restart_plrn':'.false.',\n",
" 'type_plrn':1,\n",
" 'init_plrn':1,\n",
" 'init_sigma_plrn':1.0,\n",
" 'niter_plrn':500,\n",
" 'conv_thr_plrn':1.0E-4,\n",
" 'ethrdg_plrn':1.0E-6,\n",
" 'adapt_ethrdg_plrn':'.true.',\n",
" 'init_ethrdg_plrn':1.0E-4,\n",
" 'nethrdg_plrn':20,\n",
" 'io_lvl_plrn':0,\n",
" 'nkf1':6,\n",
" 'nkf2':6,\n",
" 'nkf3':6,\n",
" 'nqf1':6,\n",
" 'nqf2':6,\n",
" 'nqf3':6,\n",
" 'lpolar':'.true.',\n",
" 'eig_read':'.false.'},\n",
" name='epw2')\n",
"\n",
"#\n",
"lif.prepare(1,type_run='epw2')"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-- -- -- -- -- -- -- -- -- -- -- Calculation: epw2 -- -- -- -- -- -- -- -- -- -- -- \n",
"Running epw2 |████████████████████████████████████████| in 5.7s (0.27/s) \n",
"\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n"
]
}
],
"source": [
"# Run\n",
"lif.run(4,type_run='epw2')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Visualization and post-processing"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-- -- -- -- -- -- -- -- -- -- -- -- -- Warning -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n",
"Refreshing EPW input (remove refresh from epw_save.json if not needed)\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- Info -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n",
"Based on previous pw and ph calculations some parameters are set below\n",
"lpolar: .true. (related to epsil in ph)\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"cp: cannot stat '../path.kpt': No such file or directory\n"
]
}
],
"source": [
"# Prepare epw input for postprocessing calculation\n",
"lif.epw(epwin={'bands_skipped':'\\'exclude_bands = 1:2, 6:15\\'',\n",
" 'plrn':'.true.',\n",
" 'restart_plrn':'.true.',\n",
" 'type_plrn':1,\n",
" 'cal_psir_plrn':'.true.',\n",
" 'step_wf_grid_plrn':4,\n",
" 'interp_Ank_plrn':'.true.',\n",
" 'interp_Bqu_plrn':'.true.',\n",
" 'filkf':'\\'../path.kpt\\'',\n",
" 'filqf':'\\'../path.kpt\\'',\n",
" 'nkf1':6,\n",
" 'nkf2':6,\n",
" 'nkf3':6,\n",
" 'nqf1':6,\n",
" 'nqf2':6,\n",
" 'nqf3':6,\n",
" 'eig_read':'.false.',\n",
" 'lpolar':'.true.'},\n",
" name='epw3')\n",
"lif.prepare(1,type_run='epw3')"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-- -- -- -- -- -- -- -- -- -- -- Calculation: epw3 -- -- -- -- -- -- -- -- -- -- -- \n",
"Running epw3 |████████████████████████████████████████| in 4.9s (0.32/s) \n",
"\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n"
]
}
],
"source": [
"# Run post-processing\n",
"lif.run(4,type_run='epw3')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plot polaron wave function\n",
"\n",
"Using EPWpy we can visualize polarons, where arrows show the displacements and the isosurface shows the polaron wave function. Below we plot the hole polaron wavefunction in LiF (Li in red and F in blue)."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"['-12.1769074', '0.0000000', '12.1769074']\n",
"['0.0000000', '12.1769074', '12.1769074']\n",
"['-12.1769074', '12.1769074', '0.0000000']\n",
"432\n",
"Notebook initialized with png backend.\n"
]
},
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Plot polaron wavefunction in real space\n",
"Data=EPW_util.read_psir_plrn(f'./{lif.prefix}/epw/psir_plrn.xsf')\n",
"Data['in_notebook']=True # Telling the plotter that you want to see in notebook mode\n",
"Data['backend']='png' # Backend can be png or ipy (which gives an interactive widget)\n",
"plot_polaron.plot_psir_plrn(Data)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plot expansion coefficients"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
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