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Usually the GW Density Functional Theory (DFT) gives larger band gaps in semiconductors compared to the LDA and GGA methods. This seems to be related to the screened potential in GW, but it is not clear to me how.

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  • $\begingroup$ Getting accurate (i.e. matching reality) semiconductor band gaps in any flavor of DFT seems to be hard. Different approaches yield better results for different materials (group IV vs III-V vs II-IV). True understanding may require using all the various potentials and seeing how the different bands change. $\endgroup$ – Jon Custer Jul 1 '15 at 14:29
  • $\begingroup$ My question is more about the band gap being larger in GW case compared to LDA and GGA. Matching experimental values are not our concern here. $\endgroup$ – Hesam Jul 1 '15 at 17:46
  • $\begingroup$ That requires delving deeper in to the nuances of the methods than I have done. Sorry - you've reached my limit! $\endgroup$ – Jon Custer Jul 1 '15 at 22:07
  • $\begingroup$ Consider to spell out acronyms. $\endgroup$ – Qmechanic Sep 27 '19 at 15:25
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The standard DFT (LDA & GGA) could not properly capture the exchange-correlation of a quantum system being investigated, it sort of lacks interaction/quantum property resulting to smaller gaps (inaccurate result in other words).

A better method that will give bigger gaps (closely accurate results/closer to experiments) should be performed. This is why we perform GW approximation.

GW approximation give a more accurate picture of band gaps (larger than LDA & GGA) largely from the nature of its solution. Typically, band gap materials requires solving the non-inhomogeneous differential equation (Time Dependent Schrodinger equation). GW properly handles this by employing a Green's function method. Further solving this we can obtain the:

  1. Dyson's Equation
  2. vertex corrections
  3. polarization function, and the
  4. dynamically screened potential.

None of this is implemented by the standard DFT (LDA & GGA). We could not attribute the accuracy of GW to a certain variable or term but rather to the METHOD.

NOTE:

  1. You may consult the references below regarding the relevant equations.

  2. Interaction/quantum property within exchange-correlation may involve electron-electron interaction, electron screening/shielding, electron-electron repulsion, electron-spin interaction, decoupling, etc.

https://en.wikipedia.org/wiki/GW_approximation

www.tddft.org/bmg/files/seminarios/127407.pdf

benasque.org/2012tddft/talks_contr/049_12benasque_gw.pdf

https://en.wikipedia.org/wiki/Density_functional_theory

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  • $\begingroup$ Question is more about why GW predicts larger gaps not what is GW. This might be related to screened potential in GW. $\endgroup$ – Hesam Jul 23 '15 at 16:02
  • $\begingroup$ Why is it larger is because GW is more accurate than DFT, and its accuracy lies on what GW is not just on the screened potential, it is the WHOLE method of GW that makes it produce larger gap. Anyway, in principle GW DOES NOT only produce larger gaps but smaller gaps as well (depends on the system & points of accuracy), it just so happened that LDA & GGA almost always produce inaccurate smaller gaps that GW produces a more accurate larger gaps. $\endgroup$ – Jones G Jul 25 '15 at 5:31
  • $\begingroup$ In addition, band gaps can be solve more accurately (resulting to larger gaps) with a Green's function method - GW does that. LDA & GGA does not employ that method, in turn, it produces an inaccurate smaller gaps. $\endgroup$ – Jones G Jul 25 '15 at 5:36
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This is probably related to the fact that in GW method the potential is an effective screened potential while there is no screening in the other methods.

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Indeed the screening potential plays an important role in this calculation. Relative to experimental studies GGA and LDA tend to produce significant underestimations of band gap energies. This underestimation can be attributed to the inherent lack of charge derivative discontinuity in these approximations, as discussed in "The effects of copper doping on photocatalytic activity at (101) planes of anatase TiO2: A theoretical study".

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