[QE-users] Fermi energy and position of dirac point in 2D electronic band structure
Steven Best
steven.best at hdr.qut.edu.au
Thu Jun 23 07:39:49 CEST 2022
Hello Lorenzo,
Thanks for your valuable advice.
Kind regards,
Steven
________________________________
From: Lorenzo Paulatto <lorenzo.paulatto at cnrs.fr>
Sent: Wednesday, June 22, 2022 6:44 PM
To: Steven Best <steven.best at hdr.qut.edu.au>; users at lists.quantum-espresso.org <users at lists.quantum-espresso.org>
Subject: Re: [QE-users] Fermi energy and position of dirac point in 2D electronic band structure
Hello Steven,
indeed with a smearing of 0.3eV, it is hard to pinpoint the position of the Ef with a precision of 0.006eV. You can try using a simpler, more symmetric, smearing (like Fermi-Dirac), but if it works it would be mostly by chance. The only definitive solution, is to reduce the smearing and increase the k-points, or to acknowledge that any calculation is approximate and live with it.
hth
On 22/06/2022 10:33, Steven Best wrote:
Hello QE Community,
I have calculated the electronic band structure (without spin orbit coupling) of a 2D organometallic topological insulator: triphenyl-Pb,
reproducing the plot from this paper: Wang, Z., Liu, Z. & Liu, F. Organic topological insulators in organometallic lattices.
Nat Commun 4, 1471 (2013). https://doi.org/10.1038/ncomms2451<https://urldefense.com/v3/__https://doi.org/10.1038/ncomms2451__;!!NVzLfOphnbDXSw!GmfSgrW1aCkyW4A4kavjLXQZvnjiy_TUJbduJAWhGfcKaV3amqG9jfG9wQhascoHiUL125qcbnUbl1NBRLkfdvgLQ0Ao8T4jrCbL$>. I obtain very good agreement.
However, I find that for my calculation there is a small mismatch between the Fermi energy and the position of the dirac point at K.
The mismatch is approximately 0.006 eV with the Fermi energy higher.
I thought this mismatch could be a consequence of the metallic smearing used in the calculation.
The reported contribution to the total energy from the smearing is -TS = -0.00570874 Ry = -0.07767136 eV.
I have used 0.3 eV marzari-vanderbilt smearing in the calculations.
Is this reasoning correct? What other contributions can cause the mismatch?
Thanks,
Steven Best
PhD Student,
School of Chemistry and Physics, Queensland University of Technology, Brisbane, Australia
Below are my input files (QE version 6.3):
###########################################################################################################
# pw.x scf calculation
&CONTROL
calculation = 'scf',
max_seconds = 72000,
verbosity = 'high',
restart_mode = 'from_scratch',
wf_collect = .T.,
nstep = 200,
tstress = .true.,
tprnfor = .true.,
outdir = './',
prefix = 'SCF_triphenyl_Pb_OM_inf_2D_sheet_NONplanar_0.3eV_t304a',
etot_conv_thr = 1.0d-6,
forc_conv_thr = 1.0d-5,
pseudo_dir = './pseudo'
/
&SYSTEM
ibrav = 12,
A = 12.305661, B = 12.305661, C = 20.0, cosAB = 0.5,
nat = 32, ntyp = 3, ! C=18, H=12, Pb=2
ecutwfc = 60.0, ecutrho = 480.0,
occupations = 'smearing', smearing = 'marzari-vanderbilt', degauss = 0.02205,
/
&ELECTRONS
electron_maxstep = 100,
conv_thr = 1.0d-8,
mixing_mode = 'plain',
mixing_beta = 0.4, mixing_ndim = 8,
diagonalization = 'david'
/
&IONS
ion_dynamics = 'bfgs'
/
ATOMIC_SPECIES
Pb 207.2 Pb.pbe-dn-kjpaw_psl.0.2.2.UPF
H 1.008 H.pbe-kjpaw_psl.1.0.0.UPF
C 12.011 C.pbe-n-kjpaw_psl.1.0.0.UPF
ATOMIC_POSITIONS (angstrom)
C 1.887951458 1.089922558 9.614560235
C 1.897161739 2.478716980 9.795131247
C 3.058056895 3.149174969 10.201826686
C 3.094519107 0.403062014 9.798882538
C 4.255445582 1.073514486 10.205501492
C 4.264620685 2.462307471 10.386022641
C 4.954605459 6.434598051 10.203602904
C 4.954765288 7.775193715 9.796929960
C 6.152653343 5.732466782 10.385695674
C 6.152988872 8.476869452 9.614145680
C 7.351027374 7.774685777 9.796148892
C 7.350891338 6.434112052 10.202892391
C 8.040607478 2.462414124 10.385502375
C 8.049072424 1.074051311 10.201623729
C 9.210124709 0.403787071 9.795016930
C 9.247909382 3.148856515 10.204584582
C 10.408959312 2.478560082 9.798036472
C 10.417476033 1.090183030 9.614153988
H 0.998237207 3.074868116 9.635193425
H 2.991811789 4.226209592 10.358631992
H 3.160769651 -0.673988810 9.642207163
H 3.988739061 5.954004099 10.362184021
H 3.989028106 8.256228576 9.638913669
H 5.154406664 0.477394068 10.365382031
H 7.149446547 0.478191613 10.358631345
H 8.316631087 5.953081922 10.360913089
H 8.316906000 8.255223371 9.637391566
H 9.143302088 -0.672828642 9.635510075
H 9.314642621 4.225484042 10.364079361
H 11.308571967 3.074480176 9.641154739
Pb 0.000000000 0.000000000 8.851674686
Pb 6.152648942 3.552431083 11.147874419
K_POINTS (automatic)
15 15 1 0 0 0
###########################################################################################################
# pw.x bands calculation
&CONTROL
calculation = 'bands',
max_seconds = 108000,
verbosity = 'high',
restart_mode = 'from_scratch',
wf_collect = .T.,
nstep = 200,
tstress = .true.,
tprnfor = .true.,
outdir = './',
prefix = 'SCF_triphenyl_Pb_OM_inf_2D_sheet_NONplanar_0.3eV_t304a',
etot_conv_thr = 1.0d-6,
forc_conv_thr = 1.0d-5,
pseudo_dir = './pseudo'
/
&SYSTEM
ibrav = 12,
A = 12.305661, B = 12.305661, C = 20.0, cosAB = 0.5,
nat = 32, ntyp = 3, ! C=18, H=12, Pb=2
ecutwfc = 60.0, ecutrho = 480.0,
occupations = 'smearing', smearing = 'marzari-vanderbilt', degauss = 0.02205,
/
&ELECTRONS
electron_maxstep = 100,
conv_thr = 1.0d-8,
mixing_mode = 'plain',
mixing_beta = 0.4, mixing_ndim = 8,
diagonalization = 'david'
/
&IONS
ion_dynamics = 'bfgs'
/
ATOMIC_SPECIES
Pb 207.2 Pb.pbe-dn-kjpaw_psl.0.2.2.UPF
H 1.008 H.pbe-kjpaw_psl.1.0.0.UPF
C 12.011 C.pbe-n-kjpaw_psl.1.0.0.UPF
ATOMIC_POSITIONS (angstrom)
C 1.887951458 1.089922558 9.614560235
C 1.897161739 2.478716980 9.795131247
C 3.058056895 3.149174969 10.201826686
C 3.094519107 0.403062014 9.798882538
C 4.255445582 1.073514486 10.205501492
C 4.264620685 2.462307471 10.386022641
C 4.954605459 6.434598051 10.203602904
C 4.954765288 7.775193715 9.796929960
C 6.152653343 5.732466782 10.385695674
C 6.152988872 8.476869452 9.614145680
C 7.351027374 7.774685777 9.796148892
C 7.350891338 6.434112052 10.202892391
C 8.040607478 2.462414124 10.385502375
C 8.049072424 1.074051311 10.201623729
C 9.210124709 0.403787071 9.795016930
C 9.247909382 3.148856515 10.204584582
C 10.408959312 2.478560082 9.798036472
C 10.417476033 1.090183030 9.614153988
H 0.998237207 3.074868116 9.635193425
H 2.991811789 4.226209592 10.358631992
H 3.160769651 -0.673988810 9.642207163
H 3.988739061 5.954004099 10.362184021
H 3.989028106 8.256228576 9.638913669
H 5.154406664 0.477394068 10.365382031
H 7.149446547 0.478191613 10.358631345
H 8.316631087 5.953081922 10.360913089
H 8.316906000 8.255223371 9.637391566
H 9.143302088 -0.672828642 9.635510075
H 9.314642621 4.225484042 10.364079361
H 11.308571967 3.074480176 9.641154739
Pb 0.000000000 0.000000000 8.851674686
Pb 6.152648942 3.552431083 11.147874419
K_POINTS (crystal_b)
4
0.0 0.0 0.0 30 ! Gamma
0.666666667 0.333333333 0.0 30 ! K
0.5 0.5 0.0 30 ! M
0.0 0.0 0.0 30 ! Gamma
###########################################################################################################
# post-processing bands.x
&bands
outdir = './'
prefix = 'SCF_triphenyl_Pb_OM_inf_2D_sheet_NONplanar_0.3eV_t304a',
filband = 't304c_triphenyl_Pb_OM_inf_2D_sheet_NONp_0.3eV_kpath1.bands.dat',
lsym = .true.
/
###########################################################################################################
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--
Dr. Lorenzo Paulatto
IdR @ IMPMC - CNRS UMR 7590 & Sorbonne Université
phone: +33 (0)1 442 79822 / skype: paulatz
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