{
"cells": [
{
"cell_type": "markdown",
"id": "f2d4dcef",
"metadata": {},
"source": [
"## Calculation of electron-phonon matrix elements including quadrupoles from first principle\n",
"Author: S. Ponce (v1, 10/27/2024)
\n",
"Revision: S. Tiwari (v1.2, 10/29/2024)
\n",
"\n",
"We interpolate the electron-phonon matrix elements $|g_{nm\\nu}(\\mathbf{k,q})|$ using EPW and compare the results matrix elements computed with direct DFPT calculations.\n",
"\n",
"Below we define constants that will remain all accross the calculations\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "295a5af1",
"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",
"1\n",
"https://raw.githubusercontent.com/PseudoDojo/ONCVPSP-PBE-FR-PDv0.4/master/Si/Si.upf\n",
"https://raw.githubusercontent.com/PseudoDojo/ONCVPSP-PBE-FR-PDv0.4/master/Si/Si_r.upf\n",
"pseudo found at pseudodojo : ONCVPSP-PBE-FR-PDv0.4/Si_r.upf\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n"
]
}
],
"source": [
"import os\n",
"import EPWpy\n",
"from EPWpy import EPWpy\n",
"from EPWpy.plotting import plot_bands\n",
"from EPWpy.plotting import plot_g\n",
"\n",
"silicon=EPWpy.EPWpy({'prefix':'\\'si\\'','restart_mode':'\\'from_scratch\\'','ibrav':2,'nat':2,'calculation':'\\'scf\\'',\n",
" 'atomic_species':['Si'],'mass':[28.0855],\n",
" 'atoms':['Si','Si'],'ntyp':1,'pseudo':['Si.upf'],'ecutwfc':'40','ecutrho':'160',\n",
" 'celldm(1)':'10.262','verbosity':'\\'high\\'','pseudo_auto':True, \n",
" },env='mpirun')\n",
"\n",
"silicon.run_serial = True\n",
"silicon.verbosity = 2\n"
]
},
{
"cell_type": "markdown",
"id": "cdc1c3d1",
"metadata": {},
"source": [
"### Self-consistent field (SCF) calculations\n",
"\n",
"Here we perform the self-consistent field calculation to obtain the electron charge density of silicon in the ground state. The calculation consists of three separate steps:\n",
"1. Apply the method `scf` to the object `silicon`. This step specifies runtime parameters for an SCF calculation on siicon \n",
"2. Based on the properties defined at step 1 as well as other properties that are set by default within EPWpy, the method `prepare` creates the input file needed by QE\n",
"3. The method `run` applied to the object `silicon` instructs QE to perform the SCF calculation"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "ca1c2189",
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"parallelization chosen: -nk 2\n",
"-- -- -- -- -- -- -- -- -- -- -- Calculation: scf -- -- -- -- -- -- -- -- -- -- -- \n",
"on 1: running: mpirun -np 4 /mnt/storage/sabya/For_video/epwpy/build/q-e-EPW-5.9s/bin/pw.x -nk 2 -in scf.in > scf.out\n",
"Running scf |████████████████████████████████████████| in 2.0s (1.16/s) \n",
"\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n"
]
}
],
"source": [
"silicon.scf(electrons={'conv_thr':'1E-13'},kpoints={'kpoints':[[4,4,4]], 'kpoints_type':'automatic'}, name='scf')\n",
"silicon.prepare(0,type_run='scf')\n",
"silicon.run(4, parallelization='-nk 2')"
]
},
{
"cell_type": "markdown",
"id": "a705bdd2",
"metadata": {},
"source": [
"### Band structure calculation\n",
"\n",
"In this step, we compute the band structure of silicon along some high-symmetry lines in the Brillouin zone.\n",
"\n",
"This calculation is not strictly necessary to compute the mobility, but it is useful to understand the electronic structure of the system under consideration.\n",
"\n",
"Also in this case, we use **three instructions** to specify runtime parameters, prepare the input file, and execute the QE calculation."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "6d16a983",
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-- -- -- -- -- -- -- -- -- -- -- Calculation: bs -- -- -- -- -- -- -- -- -- -- -- \n",
"on 1: running: mpirun -np 4 /mnt/storage/sabya/For_video/epwpy/build/q-e-EPW-5.9s/bin/pw.x -nk 2 -nt 2 -in bs.in > bs.out\n",
"Running bs |████████████████████████████████████████| in 4.5s (0.35/s) \n",
"\n",
"-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n"
]
}
],
"source": [
"silicon.scf(control={'calculation':'\\'bands\\''},system={'nbnd':12},electrons={'conv_thr':'1E-11'},\n",
" kpoints={'kpoints':[['0.5', '0.5', '0.5', '20'],\n",
" ['0.0','0.0','0.0','20'],\n",
" ['0.0','0.5','0.5','20']],\n",
" 'kpoints_type':'{crystal_b}'},\n",
" name='bs')\n",
"silicon.prepare(type_run='bs')\n",
"silicon.run(4,type_run='bs')"
]
},
{
"cell_type": "markdown",
"id": "2ce7b068",
"metadata": {},
"source": [
"### Band structure plot\n",
"\n",
"We now plot the electronic band structure computed at the previous step. The zero of the energy axis is set to the value specified manually via `ef0`.\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "983d506b",
"metadata": {},
"outputs": [
{
"data": {
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\n",
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