[Wannier] confusion on conductivity tensor calculation

Giovanni Pizzi giovanni.pizzi at epfl.ch
Thu Jul 6 15:49:54 CEST 2017


Hi,

When I was speaking of convergence issues, I was not thinking to the preliminary DFT computation, but mainly to the convergence with the dense grid in BoltzWann - the calculation includes a derivative of a Fermi-Dirac distribution, that is a Dirac-delta in the zero-temperature limit. Smearing (of the TDF, in BoltzWann) can help but I think will give an incorrect result in practice.

Also, the Seebeck coefficient calculation requires to invert a matrix, and at low temperature with the chemical potential in the electronic gap, one risks to ask the code to invert a matrix with basically zero eigenvalues, which is also a problem.

Giovanni

--
Giovanni Pizzi
Theory and Simulation of Materials and MARVEL, EPFL
http://people.epfl.ch/giovanni.pizzi
http://nccr-marvel.ch/en/people/profile/giovanni-pizzi

On 25 Jun 2017, at 05:23, Jun Liu <jun.physics at gmail.com<mailto:jun.physics at gmail.com>> wrote:

Dear Prof. Giovanni,

Thank you very much for your help. I do need to see how conductivity changes across the three cases I mentioned under T=2K. But I should be satisfied with the trend of change if the results look reasonable at higher T. I have submitted jobs for T=50K and see how they will work out (still not finished yet).

Could you please elaborate on what you mean by numerical and convergence issues? I think I should have at least reached K-points and ENCUT convergence.

Thanks,

Sincerely,
Jun

On Thu, Jun 15, 2017 at 12:24 PM, Giovanni Pizzi <giovanni.pizzi at epfl.ch<mailto:giovanni.pizzi at epfl.ch>> wrote:
Dear Jun,
You are working in the range of temperatures 2-10 K. Is this expected? Such low temperatures are very hard to work with in the code, because of numerical and convergence issues.

If you work at higher temperature, is the result better?

Also, remember that by changing the strain you will change the energy position of the bands (as basically all materials have non-zero deformation potentials) and therefore you cannot really compare values at the same exact chemical potential mu. E.g. it is possible that when you get close to zero, it is because at that strain there’s no band close to the chemical potential (and since you are at low T, you need bands really close). Changing strain, bands enter in the region.

I suggest that you start by T>50K (and without boltz_tdf_smr_fixed_en_width) and you compare the whole plots in a chemical potential range, and once you understand the behaviour you go down in temperature, potentially putting back some smearing in the TDF, to check also if you are converged enough. Note however that the TDF smearing while probably needed at low T, might introduce some errors in the final results.

Hope this helps,

Giovanni



--
Giovanni Pizzi
Theory and Simulation of Materials and MARVEL, EPFL
http://people.epfl.ch/giovanni.pizzi
http://nccr-marvel.ch/en/people/profile/giovanni-pizzi

On 31 May 2017, at 18:42, Jun Liu <jun.physics at gmail.com<mailto:jun.physics at gmail.com>> wrote:

Dear wannier users,

I would like to ask whether the following input for conductivity tensor calculation looks ok.

num_bands =   128  ! set to NBANDS by VASP
 num_wann =   88
 begin projections
 Mo:d    ! 20
 Te:p    ! 24
 end projections

###########BoltzWann ############
boltzwann = true
kmesh = 400 400 400
boltz_relax_time = 0.001
boltz_mu_min = 7.95123782                       #ef-def
boltz_mu_max = 8.35123782
boltz_mu_step = 0.04
boltz_temp_min = 2
boltz_temp_max = 10
boltz_temp_step = 2
boltz_tdf_energy_step=0.01
boltz_tdf_smr_fixed_en_width = 0.01
boltz_tdf_smr_type = gauss
boltz_calc_also_dos = true
boltz_dos_energy_min = 5.0
boltz_dos_energy_max = 15.0
boltz_dos_energy_step = 0.01
#################################

write_hr = .true.
# Bandstructure
 restart = plot
 bands_plot = true
 begin kpoint_path
....
 end kpoint_path
 bands_num_points 100 # bands_plot_format gnuplot


spinors = .true.

begin unit_cell_cart
     3.4716802     0.0000000     0.0000000  /*this and the next line changes*/
     0.0000000     6.3666750     0.0000000  /*accordingly for different cases*/
     0.0000000     0.0000000    13.8452386
end unit_cell_cart

begin atoms_cart
...
end atoms_cart

mp_grid =    12     6     3  /*this line differs from each case*/

begin kpoints
...
end kpoints

This input returns reasonable result (in that the conductivity tensor is nearly diagonal for orthorhombic structure). But if I compare results across different cases, they differ too much under as small as 0.5% lattice constant change. More details are given below.

I tried to calculate the conductivity tensor with postw90.x with version 2.1. I tried it on three cases related with slight elongation along a or b directions defining an orthorhombic structure on the original lattice. The resulting conductivity tensor differs by nearly 100% for a 0.5% lattice constant change, which cannot be right. To give you some numbers, the following shows different sigma_x,x scanned under different chemical potentials for different lattice structures, (other components of sigma are suppressed for brevity but the whole sigma matrix does show a diagonal feature expected for an orthorhombic structure.)

For the base structure (a,b,c)
    mu                      T                          sigma_x,x
   7.963542580       2.000000000      0.4228380355E-05
   7.963542580       4.000000000      0.6146815602E-01
   7.963542580       6.000000000       1.261398051
   7.963542580       8.000000000       5.250207712
   7.963542580       10.00000000       11.71261179

For the elongated structure along a by 0.5%
    mu                      T                          sigma_x,x
   7.962242580       2.000000000      0.5201871790E-03
   7.962242580       4.000000000      0.6688530829
   7.962242580       6.000000000       6.051666588
   7.962242580       8.000000000       16.35207686
   7.962242580       10.00000000       27.52636769

For the elongated structure along b by 0.5%
    mu                      T                          sigma_x,x
   7.951237820       2.000000000       332.9039665<tel:%28332%29%20903-9665>
   7.951237820       4.000000000       363.9745377
   7.951237820       6.000000000       287.1196636
   7.951237820       8.000000000       228.9187157<tel:%28228%29%20918-7157>
   7.951237820       10.00000000       188.4869745

Any idea on how to check the calculation? Thanks all very much for your insightful help!

Sincerely,
Jun

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