GW for 2D or 1D materials

[Dhanjit]

Dear developers,
I am having some confusions while doing GW PPA calculation for low dimensional materials.
In the example of bulk hBN, available in the YAMBO website, while diong the GW/PPA calculation, the term

LongDrXs

is kept as

1.000000 | 1.000000 | 1.000000 |

. Should we keep the same for low dimensional system?
and also, should we keep it same during the static screening for the calculation of BSE?

[Daniele Varsano]

Dear Dhanjit,

being a 2D material, a more meaningful setting it to the direction 1,1,0 i.e. in the plane direction considering your system in the xy plane.
as the direction orthogonal will not play a role.

For the BSE, you can use the same screening you calculated for the GW step.
Next you can calculate the BSE spectrum along the x and y direction separately (BLongdir) in case anysotropy is present in the absorption sepectrum.

Best,
Daniele

[Dhanjit]

Dear Daniele,

Thank you so much for clearing my confusion.

Have a great day.

[Dhanjit]

Dear Daniele,
I have a few more queries

• My system is showing an indirect band gap at DFT level but on GW level it is direct. How should I choose the SCissor parameter for the system?
  (1) Direct band gap (GW)-Indirect band gap (DFT), (2) Diirect band gap (GW)-Diirect band gap (DFT), or something else ?

• In another system, I tried using the QP database from the GW calculation in BS solver. But, I see a very strange behaviour in my optical spectra. The minimum band gap (direct) is aound 3.05 eV, but the first optical spectra is observed at 3.26 eV. Is it because of the allowed/disallowed transitions between some specific orbitals in the CB and VB? Does YAMBO take these into consideration?

• If the system has an indirect band gap in both DFT as well as GW level, then what should we choose as the Scissor parameter: (1) Direct band gap (GW)-Direct band gap (DFT), (2) Indirect band gap (GW)-Indirect band gap (DFT), or something else?

[Daniele Varsano]

Dear Dhanjit,

the way to choose your scissor operator is to fit the Eqp vs E_lda with a linear function plus a constant.
1) if the gap changes its character from indirect to direct, it seems that scissors stretching approximation does not apply.
2) This means that low energy transition are dipole forbidden, so zero or very poor oscillator strength
3) As stated before, you need to find scissor/stretching parameters that approximate the QP band structure when applied to the KS one. If both are indirect, i.e. the band structure shape does not change, it should be irrelevant on where you calculate it as it should be just a constant, plus eventually a stretching parameter to be applied separately to the conduction and valence band.

Best,

Daniele

[Dhanjit]

Dear Daniele,
Thank You very much for your swift reply.

[Dhanjit]

Dear Daniele,
I would like to know how do we define the Fermi level in Yambo? As Yambo shifts the VBM to 0, does it do anything to the Fermi level as well? I have calculated the band structure both with and without the QP correction. In the r_electrons files generated along with the structures say that the Fermi level is at -0.803716 eV. Should we make some changes to the Fermi level as well?

[Daniele Varsano]

Dear Dhanjit,

I'm not sure if I have correctly understood your question and your needs.

If you are dealing with a semiconductor, it is just a matter of convention where you put your zero for the band structure. When you calculate optical spectra
what it is important are the occupation numbers, so a shift in the band structure does not have any effect. In any case, the Ef calcualted by QE is also reported and you can shift all the energies accordingly.

Best,
Daniele

[Dhanjit]

Dear Daniele,
Actually I wanted to know where should the Fermi level be indicated in the graph in the band structure obtained through ypp.
In the r_electrons_bnds file, I get the following

[05.05] Energies & Occupations
==============================

[X] === General ===
[X] Electronic Temperature : 0.000000 0.000000 [eV K]
[X] Bosonic Temperature : 0.000000 0.000000 [eV K]
[X] Finite Temperature mode : no
[X] El. density : 0.16955E+24 [cm-3]
[X] Fermi Level : -0.886417 [eV]

Does it mean that the system has its Ef below the VBM? As VBM is set at zero.

In the pwscf calculation, the Ef is obtained to be at -0.0192 eV and the VBM is well below the Ef.

[Daniele Varsano]

Dear Dhanjit,

the Fermi level indicated in the report it should be the same as the one reported by QE, as it is actually read from the QE database and reported for reference.
Anyway, if you are dealing with a semiconductor, it does not make any difference setting the Ef at the VBM or in the middle of the gap.

Best,
Daniele