Dear elk developers and useres
I have some questions, please help me to know:
1-please tell me about the approximation framework of linear optical (task 121) and nonlinear optical (task 125) calculations in the current version of elk code. is it RPA (random phase approximation) or IPA (independent particle approximation)?
2- what is the main difference between RPA and IPA?
3- as you know the excitonic effects can change the linear spectra, especially in gap region. can you tell me about the variation of nonlinear spectra in the presence of excitonic effects. is there any enhancement? if yes, at lower energies or higher energies. the nonlinear spectra shifts to lower energies or higher one?
BEST REGARDS
THANKS
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RPA: refer to https://en.wikipedia.org/wiki/Random_phase_approximation
IPA: refer to PRB_1993v48p11705_Nonlinear optical response of semiconductors in the IPA
Task 121: refer to Physica Scripta T109 170 (2004).
Excitonic effects: refer to PRB_2011v84p085404_Excitonic effects in the optical properties of a SiC sheet and nanotubes
Good luck
Lan
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But i think both linear and nonlinear optical calculations use same approximation, since both use same basis and same elements of polarization matrix, (i.e., both tasks 121 and 125 are based on tasks 0 and 120). therefore if task 121 is RPA, task 125 should be RPA, too. please give me a clear explanation.
thanks
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task 120 calculated the matrix elements of the grad operator. It can be shown that in q-->0 limit the head of the kohn-sham response function \chi_0 can be calculated using these matrix elements.
task 121 calcultes the the limean optical response within RPA. This uses the matrix elements calculated in task 120.
task 125 calcukates the second order response also within RPA.
For linear and non-linear optics with in RPA see:
Physica Scripta T109, 128 (2004)
Excitonic efffects can be included using the TD-DFT within linear response regime or using BSE (this is very expensive). For including excitons in linear response use
task
300
fxctype
210
gmaxrf
0.0
Excitonic effects in NLO are not present with in the elk code.
For details see:
Phys. Rev. Lett. 107, 186401 (2011)
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Dear sharma
thanks for your response, but I still have some problems:
The nonlinear formula are developed within Independent Particle Approximation (IPA) by sipe and ghahramani, but you say it is calculated within Random Phase Approximation (RPA). I cannot solve this puzzle. Is there any difference between thses approximations? If yes, why you use RPA instead of IPA.
thanks
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Dear sharma
I think the RPA required the inclusion of local-field effects that is more complicated. For a discussion of the different approximation see PRB 71, 195209 (2005) section II.C and II.D.
thanks
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RPA can also be done without local field effects. That is what 121 does. If you want RPA with LFE do a TDDFT calcukation with
fxctype
0
gmaxrf
0
in SHG LFE are not included and only bubble diagrams are summed and and hence one could say it is RPA. However, IPA also involves not taking e-h interaction into account. I would still say that everything that is calculated from \chi_0 with fxc=0 is RPA.
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THANKS A LOT.
Excuse me I have another question:
Recent articles have shown that excitonic effects can be important also for the xhi^2 (see for instance PRB 89, 081102 (2014) or PRB 82, 235201(2010) ), do you think that also in this case excitonic effects could enhanced some part of the xhi^2, for example the low frequency ones?
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
Dear elk developers and useres
I have some questions, please help me to know:
1-please tell me about the approximation framework of linear optical (task 121) and nonlinear optical (task 125) calculations in the current version of elk code. is it RPA (random phase approximation) or IPA (independent particle approximation)?
2- what is the main difference between RPA and IPA?
3- as you know the excitonic effects can change the linear spectra, especially in gap region. can you tell me about the variation of nonlinear spectra in the presence of excitonic effects. is there any enhancement? if yes, at lower energies or higher energies. the nonlinear spectra shifts to lower energies or higher one?
BEST REGARDS
THANKS
RPA: refer to https://en.wikipedia.org/wiki/Random_phase_approximation
IPA: refer to PRB_1993v48p11705_Nonlinear optical response of semiconductors in the IPA
Task 121: refer to Physica Scripta T109 170 (2004).
Excitonic effects: refer to PRB_2011v84p085404_Excitonic effects in the optical properties of a SiC sheet and nanotubes
Good luck
Lan
Dear Lan
thanks for your consideration
have a nice day
But i think both linear and nonlinear optical calculations use same approximation, since both use same basis and same elements of polarization matrix, (i.e., both tasks 121 and 125 are based on tasks 0 and 120). therefore if task 121 is RPA, task 125 should be RPA, too. please give me a clear explanation.
thanks
task 120 calculated the matrix elements of the grad operator. It can be shown that in q-->0 limit the head of the kohn-sham response function \chi_0 can be calculated using these matrix elements.
task 121 calcultes the the limean optical response within RPA. This uses the matrix elements calculated in task 120.
task 125 calcukates the second order response also within RPA.
For linear and non-linear optics with in RPA see:
Physica Scripta T109, 128 (2004)
Excitonic efffects can be included using the TD-DFT within linear response regime or using BSE (this is very expensive). For including excitons in linear response use
task
300
fxctype
210
gmaxrf
0.0
Excitonic effects in NLO are not present with in the elk code.
For details see:
Phys. Rev. Lett. 107, 186401 (2011)
Dear sharma
thanks for your response, but I still have some problems:
The nonlinear formula are developed within Independent Particle Approximation (IPA) by sipe and ghahramani, but you say it is calculated within Random Phase Approximation (RPA). I cannot solve this puzzle. Is there any difference between thses approximations? If yes, why you use RPA instead of IPA.
thanks
Dear sharma
I think the RPA required the inclusion of local-field effects that is more complicated. For a discussion of the different approximation see PRB 71, 195209 (2005) section II.C and II.D.
thanks
RPA can also be done without local field effects. That is what 121 does. If you want RPA with LFE do a TDDFT calcukation with
fxctype
0
gmaxrf
0
in SHG LFE are not included and only bubble diagrams are summed and and hence one could say it is RPA. However, IPA also involves not taking e-h interaction into account. I would still say that everything that is calculated from \chi_0 with fxc=0 is RPA.
THANKS A LOT.
Excuse me I have another question:
Recent articles have shown that excitonic effects can be important also for the xhi^2 (see for instance PRB 89, 081102 (2014) or PRB 82, 235201(2010) ), do you think that also in this case excitonic effects could enhanced some part of the xhi^2, for example the low frequency ones?