[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

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.quantum-espresso.org/pipermail/users/attachments/20200614/cd4694c1/attachment.html>


More information about the users mailing list