[QE-users] Born charges of PbS

[Vahid Askarpour]

Dear QE Community,

I have calculated the Born charges using the PHONON code for PbS. The only non-zero elements are the diagonal ones and are 4.122 and -4.168, respectively.

In the zstar_eu.f90, Born charges consist of two terms as seen below: a part due to polarization calculation (dynamic) and the other is zv (static) which is the z_valence according to read_upf_v2.f90.

 do ipol = 1, 3
     do na = 1, nat
        zstareu (ipol, ipol, na) = zstareu (ipol, ipol, na) + zv (ityp ( na) )
     enddo
  enddo

The zv values for Pb and S are 14 and 6 given in the PSP. If we subtract zv from the Born charges, we get the term due to polarization: -9.878 and -10.168. These values seem too large because of the argument below.

To estimate the polarization term, I reduce the alat by 1% and relax the atoms. This shifts the atoms from the unstrained position. I calculate the Bader charges for the unstrained and the strained cases. The change in the Bader charge is related to the atomic displacement. I have also tried keeping alat fixed and moving the atoms by 1%.

For unstrained PbS, the Bader charges are 12.998 and 7.001. 
For the strained PbS, they are 13.004 and 6.995.

So a ~1% change in atomic positions results in a +/-0.006 change in Bader charge. From this calculation, I expect the contribution from polarization to be u(dZ/du), where u is interatomic distance, which amount to +0.6 for Pb and -0.6 for S.

The contribution from polarization I get (0.6 and -0.6) are quite different from the those of the PHONON code (-9.878 and -10.168). I am assuming that the code is correct and my logic is flawed. I would appreciate any thoughts you may have on this discrepancy.

Thank you,
Vahid


Vahid Askarpour
Department of physics and atmospheric science
Dalhousie University
Halifax, NS
Canada