[QE-users] Lambda ad Tc for Pb(111)
Maciej Szary
maciej.szary at put.poznan.pl
Sun Jun 14 15:50:59 CEST 2020
Dear QE users,
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.
In scf I've been changing:
1. ecutwfc, and ecutrho (current values 80, and 650 Ry, respectively)
2. conv_thr (currently 1.0d-14)
3. k-point mesh (currently 36x36x1)
4. Pb pseudopotentials (currently Pb.rel-pbe-n-nc.UPF, previously
Pb.rel-pbe-dn-rrkjus_psl.0.2.2.UPF)
5. Slab thickness (6-12 layers)
In ph I've been testing:
1. tr2_ph (currently 1.0d-16, and up to 1.0d-17 with
Pb.rel-pbe-dn-rrkjus_psl.0.2.2.UPF)
2. electron_phonon (interpolated, and simple)
3. q mesh (form 2x2x1 to 6x6x1)
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.:
--------------------------------------------------------
/ &system//
// ibrav= 4, //
// a=3.503660834//
// c=40//
// nat= 6, ntyp= 1,//
// ecutwfc =80.0,//
// ecutrho = 650, //
// occupations='smearing', smearing='mv', degauss=0.05//
// lspinorb=.true., noncolin=.true.,
starting_spin_angle=.true., starting_magnetization=0.0,//
// la2F = .true.,//
// nbnd = 48 //
/////
// &electrons//
// mixing_mode = 'plain'//
// mixing_beta = 0.5//
// conv_thr = 1.0d-14//
// ///
// ATOMIC_SPECIES//
// Pb 207.2 Pb.rel-pbe-n-nc.UPF//
//ATOMIC_POSITIONS angstrom//
//Pb 0.000000000 0.000000000 19.078230578//
//Pb 0.000000000 0.000000000 27.596055131//
//Pb 1.751830417 1.011419906 16.119173776//
//Pb 1.751830417 1.011419906 24.874997245//
//Pb 3.503661844 2.022839813 13.398232981//
//Pb 3.503661844 2.022839813 21.915874849//
//K_POINTS automatic//
//36 36 1 0 0 0/
--------------------------------------------------------
this is followed by ph.x run:
--------------------------------------------------------
/&inputph//
// outdir='Files/',//
// prefix='QE'//
// fildvscf='aldv',//
// tr2_ph = 1.0d-16//
// amass(1) = 207.2//
// fildyn = 'Pb.dyn'//
// alpha_mix=0.2//
// electron_phonon='interpolated',//
// el_ph_sigma=0.005, //
// el_ph_nsigma=10,//
// trans=.true.,//
// ldisp=.true.//
// nq1 = 6, nq2 = 6, nq3 = 1//
// nogg = .true.//
// asr = .true.//
////
--------------------------------------------------------
Next are q2r.x,
--------------------------------------------------------
/&input//
// fildyn = 'Pb.dyn'//
// zasr = 'crystal'//
// flfrc = 'Pb.q661.fc'//
// la2F=.true.//
////
--------------------------------------------------------
matdyn.x,
--------------------------------------------------------
/&input//
// asr= 'simple'//
// flfrc = 'Pb.q661.fc', flfrq='Pb.q661.freq', la2F=.true., dos=.true.//
// fldos='phonon.dos', nk1=60, nk2=60, nk3=1, ndos=50//
// //
--------------------------------------------------------
and lambda.x
--------------------------------------------------------
/5 0.12 1 ! emax (something more than highest phonon mode in THz),
degauss, smearing method //
// 7//
// 1 0.0000000 0.0000000 0.0000000 1.00//
// 2 0.1666667 0.0962250 0.0000000 6.00//
// 3 0.3333333 0.1924501 0.0000000 6.00//
// 4 0.5000000 0.2886751 0.0000000 3.00//
// 5 0.1666667 0.2886751 0.0000000 6.00//
// 6 0.3333333 0.3849002 0.0000000 12.00//
// 7 0.3333333 0.5773503 0.0000000 2.00//
//elph_dir/elph.inp_lambda.1 //
//elph_dir/elph.inp_lambda.2 //
//elph_dir/elph.inp_lambda.3 //
//elph_dir/elph.inp_lambda.4 //
//elph_dir/elph.inp_lambda.5 //
//elph_dir/elph.inp_lambda.6 //
//elph_dir/elph.inp_lambda.7 //
//0.10/
--------------------------------------------------------
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:
/ # Frequency[cm^-1] DOS PDOS//
// 0.0000000000E+00 0.0000000000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00//
// 1.4306338313E+00 3.8122112950E-03 6.3283E-04 6.3953E-04
6.3336E-04 6.3251E-04 6.4093E-04 6.3306E-04//
// 2.8612676626E+00 6.7934053704E-03 1.1376E-03 1.1328E-03
1.1244E-03 1.1215E-03 1.1385E-03 1.1386E-03//
// 4.2919014939E+00 9.5022844921E-03 1.6112E-03 1.5734E-03
1.5628E-03 1.5658E-03 1.5730E-03 1.6162E-03//
// 5.7225353252E+00 1.2941007092E-02 2.2167E-03 2.1293E-03
2.1167E-03 2.1337E-03 2.1145E-03 2.2302E-03
//.../
Also matdyn.x produces "lambda" file with:
/ Broadening 0.0050 lambda 1.7637 dos(Ef) 21.5379 omega_ln
[K] 49.4388//
// Broadening 0.0100 lambda 1.7028 dos(Ef) 21.2277 omega_ln
[K] 49.7600//
// Broadening 0.0150 lambda 1.6783 dos(Ef) 21.0885 omega_ln
[K] 49.5935//
// Broadening 0.0200 lambda 1.6881 dos(Ef) 21.1817 omega_ln
[K] 49.4624//
// Broadening 0.0250 lambda 1.7060 dos(Ef) 21.3799 omega_ln
[K] 49.3380//
// Broadening 0.0300 lambda 1.7218 dos(Ef) 21.5945 omega_ln
[K] 49.1667//
// Broadening 0.0350 lambda 1.7335 dos(Ef) 21.7888 omega_ln
[K] 48.9500//
// Broadening 0.0400 lambda 1.7414 dos(Ef) 21.9474 omega_ln
[K] 48.7041//
// Broadening 0.0450 lambda 1.7466 dos(Ef) 22.0647 omega_ln
[K] 48.4423//
// Broadening 0.0500 lambda 1.7499 dos(Ef) 22.1428 omega_ln
[K] 48.1738/
so shouldn't Tc be just a product of substitution into McMillan formula
using values of omega_ln and lambda?
Regards,
Maciej Szary//
//
--
Research Assistant,
Institute of Physics,
Poznan University of Technology
Piotrowo 3A, 61-138 Poznan
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