Scissor MoS2

[Ehsanulazim]

Hi,

I am following a tutorial "Yambo tutorial: Quasiparticles in the GW approximation"(https://enccs.github.io/max-coe-worksho ... tutorials/) and I finished all of the processes. I am little bit confused about how to pick up scissor value from the calculation and use it in KfnQP_E or XfnQP_E. For example, in MoS2 the GW approximated values are:

Code: Select all

# Vxc  =Slater exchange(X)+Perdew & Zunger(C)
# Vnlxc=Hartree-Fock
#
#    K-point            Band               Eo [eV]            E-Eo [eV]          Sc|Eo [eV]
#
         7                 13                 0.000000          -0.025774           0.543987
         7                 14                 1.858370           3.496193          -0.417555
# 

Here, Eo comes from DFT (KS energies) and E is the corrected energy (yambo) which we can find as
E=(Eo+E-Eo)=(0 - 0.025774) = - 0.025774 (for K-point 7 and Band 13)
E=(Eo+E-Eo)=(1.858370 + 3.496193) = 5.354563 (for K-point 7 and Band 14)
Based on the above info band gap of MoS2 from DFT is (1.858370 - 0) = 1.858370 ev and after GW approximation corrected band gap is (5.354563 - (- 0.025774)) = 5.380337 ev
However, I am confused about the Sc|Eo, what this value corresponds and what value I can insert as the scissor value (1st column) in KfnQP_E or XfnQP_E in the followings based on the above info (e.g, the MoS2 case)
In BSE framework

Code: Select all

%KfnQP_E				
0.000000|1.000000|1.000000|		
%

RPA response is

Code: Select all

%XfnQP_E			
0.000000|1.000000|1.000000|		
%

Kind Regards
Ehsanul Azim
Masters Student
Mechanical Engineering
University of Texas Rio Grande Valley

[Daniele Varsano]

Dear Ehsanul,

Sc|Eo is the self energy calculated at the KS energy value.
Scissor and stretching can be extracted by plotting the E_qp vs E_ks. In this way you can verify that the scissor approximation holds: the scissor is evaluated from the band corrections while the conduction/valence stretching parameter can be evaluated via a linear fit.

Here, you can find the procedure using yambo-py:
https://yambo-code.eu/wiki/index.php/Ya ... structures

Here, using gnuplot:
https://yambo-code.eu/wiki/index.php/GW ... 21_version

Best,
Daniele

[Ehsanulazim]

Hi Dr. Daniele,

Thanks for your suggestions.

As you said "the scissor is evaluated from the band corrections". For the MoS2 example, is my scissor shift (0.543987-(-0.417555))=0.961542 OK? Lets say, valance bands and conduction bands slope x and y respectively,

Code: Select all

# Vxc  =Slater exchange(X)+Perdew & Zunger(C)
# Vnlxc=Hartree-Fock
#
#    K-point            Band               Eo [eV]            E-Eo [eV]          Sc|Eo [eV]
#
         7                 13                 0.000000          -0.025774           0.543987
         7                 14                 1.858370           3.496193          -0.417555
#

Code: Select all

valence bands:
slope:     x
conduction bands:
slope:     y
scissor list (shift,c,v): [shift, y, x]
scissor list (shift,c,v): [0.961542, y, x]

Kind Regards
Ehsanul Azim
Masters Student
Mechanical Engineering
University of Texas Rio Grande Valley

[Daniele Varsano]

Dear Ehsanul,
the scissor value is given by gap_GW - gap_KS,
in your example, is 3.52 eV i.e. the GW correction to the gap.

To find the stretching parameters, you need to evaluate the GW energies for a number of bands and k points and perform a linear fit of the E_qp vs E_ks on the valence and conduction energies respectively, which means for Eks < 0 and E_ks > 0. It is not possible to evaluate them if you calculated the corrections for two points only.

Best,

Daniele

[Quxiao]

Dear Daniele:
I know that parameters KfnQP_E and XfnQP_E represent the scissor operator, but I want to know more about how it affects the dielectric function. Or is there a clear expression of parameters KfnQP_E and XfnQP_E, and related articles to explain it. For example, KfnQP_E represents the correction of E_c-E_v, and XfnQP_E represents what is modified, is it W? Or other physical quantities?
Or are they the same physical quantity, but given two names in different processes? One is identified in the BSE module, and the other is identified in the computational RPA?
Thanks for your help！
Best wishes
Quxiao

[Daniele Varsano]

Dear Quixiao,

the two variable have the same meaning, ie. to shift up conduction bands. KfnQP_E it is used in the construction of the BSE kernel, while XfnQP_E for the calculation of the independent particle response function (needed to calculate W). In a standard GW/BSE calculation, QP correction are considered in BSE and not in W unless you aim to eigenvalue GW self-consistency,

Best,
Daniele

[Quxiao]

Dear Daniele：
Thank you very much for your help. I understand it through your answer.
I want to ask another question. A2y is abinit to yambo, p2y is pwscf to yambo, so what does e2y mean?
I clicked the link about this introduction for e2y on the yambo website, but it was invalid, so I want to ask you.
Best wishes！
Quxiao

[Daniele Varsano]

Der Quxiao,

this is a converter from the etsf file format using the etsf_io library and it is meant for interoperability among different codes.

https://www.etsf.eu/software/interoperability
https://github.com/ElectronicStructureL ... ibetsf_io/

Best,
Daniele