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<font face="Courier New, Courier, monospace">Dear QE users,<br>
<br>
I'm trying to calculate electron-phonon coefficient and the
critical superconducting temperature of Pb(111). As an
introduction I've done the [PHonon/examples/example03] (bulk Al),
and I've reproduced the results successfully. However, in case of
Pb(111), I can't get Tc for the system. I only get "NaN". I
understand that, this is often a result of imaginary components in
the dynamical matrices, thus I've been redoing the calculations
with different sets of parameters, however, to no avail. <br>
<br>
In scf I've been changing:<br>
<br>
1. ecutwfc, and ecutrho (current values 80, and 650 Ry,
respectively)<br>
2. conv_thr (currently 1.0d-14)<br>
3. k-point mesh (currently 36x36x1)<br>
4. Pb pseudopotentials (currently Pb.rel-pbe-n-nc.UPF, previously
Pb.rel-pbe-dn-rrkjus_psl.0.2.2.UPF)<br>
5. Slab thickness (6-12 layers)<br>
<br>
In ph I've been testing:<br>
<br>
1. tr2_ph (currently 1.0d-16, and </font><font face="Courier New,
Courier, monospace"><font face="Courier New, Courier, monospace"><font
face="Courier New, Courier, monospace">up to </font></font><font
face="Courier New, Courier, monospace"><font face="Courier New,
Courier, monospace"><font face="Courier New, Courier,
monospace">1.0d-17</font></font></font> with </font><font
face="Courier New, Courier, monospace"><font face="Courier New,
Courier, monospace">Pb.rel-pbe-dn-rrkjus_psl.0.2.2.UPF</font></font><font
face="Courier New, Courier, monospace"><font face="Courier New,
Courier, monospace">)<br>
2. electron_phonon (interpolated, and simple)<br>
3. q mesh (form 2x2x1 to 6x6x1)<br>
<br>
As a first step I've done the vc-relax, to relax the lattice
constant of the slab. Next I perform relaxation with SOC
included (etot_conv_thr, and forc_conv_thr= both 1.0d-6). Next I
do the scf run e.g.:<br>
<br>
--------------------------------------------------------<br>
<i> &system</i><i><br>
</i><i> ibrav= 4, </i><i><br>
</i><i> a=3.503660834</i><i><br>
</i><i> c=40</i><i><br>
</i><i> nat= 6, ntyp= 1,</i><i><br>
</i><i> ecutwfc =80.0,</i><i><br>
</i><i> ecutrho = 650, </i><i><br>
</i><i> occupations='smearing', smearing='mv', degauss=0.05</i><i><br>
</i><i> lspinorb=.true., noncolin=.true.,
starting_spin_angle=.true., starting_magnetization=0.0,</i><i><br>
</i><i> la2F = .true.,</i><i><br>
</i><i> nbnd = 48 </i><i><br>
</i><i>/</i><i><br>
</i><i> &electrons</i><i><br>
</i><i> mixing_mode = 'plain'</i><i><br>
</i><i> mixing_beta = 0.5</i><i><br>
</i><i> conv_thr = 1.0d-14</i><i><br>
</i><i> /</i><i><br>
</i><i> ATOMIC_SPECIES</i><i><br>
</i><i> Pb 207.2 Pb.rel-pbe-n-nc.UPF</i><i><br>
</i><i>ATOMIC_POSITIONS angstrom</i><i><br>
</i><i>Pb 0.000000000 0.000000000 19.078230578</i><i><br>
</i><i>Pb 0.000000000 0.000000000 27.596055131</i><i><br>
</i><i>Pb 1.751830417 1.011419906 16.119173776</i><i><br>
</i><i>Pb 1.751830417 1.011419906 24.874997245</i><i><br>
</i><i>Pb 3.503661844 2.022839813 13.398232981</i><i><br>
</i><i>Pb 3.503661844 2.022839813 21.915874849</i><i><br>
</i><i>K_POINTS automatic</i><i><br>
</i><i>36 36 1 0 0 0</i><br>
</font></font><font face="Courier New, Courier, monospace"><font
face="Courier New, Courier, monospace">--------------------------------------------------------<br>
<br>
this is followed by ph.x run:<br>
</font></font><br>
<font face="Courier New, Courier, monospace"><font face="Courier
New, Courier, monospace"><font face="Courier New, Courier,
monospace"><font face="Courier New, Courier, monospace">--------------------------------------------------------<br>
</font></font><i>&inputph</i><i><br>
</i><i> outdir='Files/',</i><i><br>
</i><i> prefix='QE'</i><i><br>
</i><i> fildvscf='aldv',</i><i><br>
</i><i> tr2_ph = 1.0d-16</i><i><br>
</i><i> amass(1) = 207.2</i><i><br>
</i><i> fildyn = 'Pb.dyn'</i><i><br>
</i><i> alpha_mix=0.2</i><i><br>
</i><i> electron_phonon='interpolated',</i><i><br>
</i><i> el_ph_sigma=0.005, </i><i><br>
</i><i> el_ph_nsigma=10,</i><i><br>
</i><i> trans=.true.,</i><i><br>
</i><i> ldisp=.true.</i><i><br>
</i><i> nq1 = 6, nq2 = 6, nq3 = 1</i><i><br>
</i><i> nogg = .true.</i><i><br>
</i><i> asr = .true.</i><i><br>
</i><i>/</i><br>
</font></font><font face="Courier New, Courier, monospace"><font
face="Courier New, Courier, monospace">--------------------------------------------------------<br>
<br>
Next are q2r.x, <br>
<br>
</font></font><br>
<font face="Courier New, Courier, monospace"><font face="Courier
New, Courier, monospace"><font face="Courier New, Courier,
monospace"><font face="Courier New, Courier, monospace">--------------------------------------------------------<br>
</font></font><i>&input</i><i><br>
</i><i> fildyn = 'Pb.dyn'</i><i><br>
</i><i> zasr = 'crystal'</i><i><br>
</i><i> flfrc = 'Pb.q661.fc'</i><i><br>
</i><i> la2F=.true.</i><i><br>
</i><i>/</i><br>
</font></font><font face="Courier New, Courier, monospace"><font
face="Courier New, Courier, monospace">--------------------------------------------------------<br>
<br>
matdyn.x,<br>
<br>
</font></font><br>
<font face="Courier New, Courier, monospace"><font face="Courier
New, Courier, monospace"><font face="Courier New, Courier,
monospace"><font face="Courier New, Courier, monospace"><font
face="Courier New, Courier, monospace"><font face="Courier
New, Courier, monospace">--------------------------------------------------------</font></font></font></font><br>
<i>&input</i><i><br>
</i><i> asr= 'simple'</i><i><br>
</i><i> flfrc = 'Pb.q661.fc', flfrq='Pb.q661.freq',
la2F=.true., dos=.true.</i><i><br>
</i><i> fldos='phonon.dos', nk1=60, nk2=60, nk3=1, ndos=50</i><i><br>
</i><i> /</i></font></font><br>
<font face="Courier New, Courier, monospace"><font face="Courier
New, Courier, monospace"><font face="Courier New, Courier,
monospace"><font face="Courier New, Courier, monospace"><font
face="Courier New, Courier, monospace"><font face="Courier
New, Courier, monospace"><font face="Courier New,
Courier, monospace"><font face="Courier New, Courier,
monospace">--------------------------------------------------------<br>
<br>
</font></font></font></font></font></font>and lambda.x
<br>
</font></font><br>
<font face="Courier New, Courier, monospace"><font face="Courier
New, Courier, monospace"><font face="Courier New, Courier,
monospace"><font face="Courier New, Courier, monospace"><font
face="Courier New, Courier, monospace"><font face="Courier
New, Courier, monospace"><font face="Courier New,
Courier, monospace"><font face="Courier New, Courier,
monospace">--------------------------------------------------------<br>
</font></font></font></font></font></font><i>5 0.12
1 ! emax (something more than highest phonon mode in THz),
degauss, smearing method </i><i><br>
</i><i> 7</i><i><br>
</i><i> 1 0.0000000 0.0000000 0.0000000 1.00</i><i><br>
</i><i> 2 0.1666667 0.0962250 0.0000000 6.00</i><i><br>
</i><i> 3 0.3333333 0.1924501 0.0000000 6.00</i><i><br>
</i><i> 4 0.5000000 0.2886751 0.0000000 3.00</i><i><br>
</i><i> 5 0.1666667 0.2886751 0.0000000 6.00</i><i><br>
</i><i> 6 0.3333333 0.3849002 0.0000000 12.00</i><i><br>
</i><i> 7 0.3333333 0.5773503 0.0000000 2.00</i><i><br>
</i><i>elph_dir/elph.inp_lambda.1 </i><i><br>
</i><i>elph_dir/elph.inp_lambda.2 </i><i><br>
</i><i>elph_dir/elph.inp_lambda.3 </i><i><br>
</i><i>elph_dir/elph.inp_lambda.4 </i><i><br>
</i><i>elph_dir/elph.inp_lambda.5 </i><i><br>
</i><i>elph_dir/elph.inp_lambda.6 </i><i><br>
</i><i>elph_dir/elph.inp_lambda.7 </i><i><br>
</i><i>0.10</i> <br>
</font></font><font face="Courier New, Courier, monospace"><font
face="Courier New, Courier, monospace"><font face="Courier New,
Courier, monospace"><font face="Courier New, Courier,
monospace"><font face="Courier New, Courier, monospace"><font
face="Courier New, Courier, monospace"><font
face="Courier New, Courier, monospace"><font
face="Courier New, Courier, monospace">--------------------------------------------------------<br>
</font></font></font></font></font></font><br>
The parameters I've used are relatively high in comparison to
the Pb fcc example given by S. Poncé in 2018. Output of ph.x
lacks negative frequencies, and DOS seems also fine:<br>
<br>
<i> # Frequency[cm^-1] DOS PDOS</i><i><br>
</i><i> 0.0000000000E+00 0.0000000000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00</i><i><br>
</i><i> 1.4306338313E+00 3.8122112950E-03 6.3283E-04
6.3953E-04 6.3336E-04 6.3251E-04 6.4093E-04 6.3306E-04</i><i><br>
</i><i> 2.8612676626E+00 6.7934053704E-03 1.1376E-03
1.1328E-03 1.1244E-03 1.1215E-03 1.1385E-03 1.1386E-03</i><i><br>
</i><i> 4.2919014939E+00 9.5022844921E-03 1.6112E-03
1.5734E-03 1.5628E-03 1.5658E-03 1.5730E-03 1.6162E-03</i><i><br>
</i><i> 5.7225353252E+00 1.2941007092E-02 2.2167E-03
2.1293E-03 2.1167E-03 2.1337E-03 2.1145E-03 2.2302E-03<br>
<br>
</i><i>...</i><br>
<br>
Also matdyn.x produces "lambda" file with:<br>
<br>
<i> Broadening 0.0050 lambda 1.7637 dos(Ef) 21.5379
omega_ln [K] 49.4388</i><i><br>
</i><i> Broadening 0.0100 lambda 1.7028 dos(Ef) 21.2277
omega_ln [K] 49.7600</i><i><br>
</i><i> Broadening 0.0150 lambda 1.6783 dos(Ef) 21.0885
omega_ln [K] 49.5935</i><i><br>
</i><i> Broadening 0.0200 lambda 1.6881 dos(Ef) 21.1817
omega_ln [K] 49.4624</i><i><br>
</i><i> Broadening 0.0250 lambda 1.7060 dos(Ef) 21.3799
omega_ln [K] 49.3380</i><i><br>
</i><i> Broadening 0.0300 lambda 1.7218 dos(Ef) 21.5945
omega_ln [K] 49.1667</i><i><br>
</i><i> Broadening 0.0350 lambda 1.7335 dos(Ef) 21.7888
omega_ln [K] 48.9500</i><i><br>
</i><i> Broadening 0.0400 lambda 1.7414 dos(Ef) 21.9474
omega_ln [K] 48.7041</i><i><br>
</i><i> Broadening 0.0450 lambda 1.7466 dos(Ef) 22.0647
omega_ln [K] 48.4423</i><i><br>
</i><i> Broadening 0.0500 lambda 1.7499 dos(Ef) 22.1428
omega_ln [K] 48.1738</i><br>
<br>
so shouldn't Tc be just a product of substitution into McMillan
formula using </font></font><font face="Courier New, Courier,
monospace"><font face="Courier New, Courier, monospace"><font
face="Courier New, Courier, monospace"><font face="Courier
New, Courier, monospace">values of omega_ln and </font></font></font></font><font
face="Courier New, Courier, monospace"><font face="Courier New,
Courier, monospace"><font face="Courier New, Courier, monospace"><font
face="Courier New, Courier, monospace"><font face="Courier
New, Courier, monospace"><font face="Courier New, Courier,
monospace">lambda</font></font><font face="Courier New,
Courier, monospace"><font face="Courier New, Courier,
monospace">?<br>
<br>
</font></font><font face="Courier New, Courier, monospace"><font
face="Courier New, Courier, monospace">Regards,<br>
Maciej Szary</font></font><i><font face="Courier New,
Courier, monospace"><font face="Courier New, Courier,
monospace"><i><br>
</i></font></font></i></font></font></font></font>
<pre class="moz-signature" cols="72">--
Research Assistant,
Institute of Physics,
Poznan University of Technology
Piotrowo 3A, 61-138 Poznan</pre>
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