Update format for Postw90 and Appendices.
#1
Conversation
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
qiaojunfeng
requested changes
Feb 13, 2024
|
|
||
| ### `berry_task=kubo`: optical conductivity and joint density of states | ||
|
|
||
| The Kubo-Greenwood formula for the optical conductivity of a crystal in | ||
| the independent-particle approximation reads | ||
|
|
||
| $$\sigma_{\alpha\beta}(\hbar\omega)=\frac{ie^2\hbar}{N_k\Omega_c} |
|
|
||
| ### `berry_task=kubo`: optical conductivity and joint density of states | ||
|
|
||
| The Kubo-Greenwood formula for the optical conductivity of a crystal in | ||
| the independent-particle approximation reads | ||
|
|
||
| $$\sigma_{\alpha\beta}(\hbar\omega)=\frac{ie^2\hbar}{N_k\Omega_c} | ||
| \sum_{\bf k}\sum_{n,m} | ||
| \frac{f_{m{\bf k}}-f_{n{\bf k}}} | ||
| {\varepsilon_{m{\bf k}}-\varepsilon_{n{\bf k}}} | ||
| \frac{\langle\psi_{n{\bf k}}\vert v_\alpha\vert\psi_{m{\bf k}}\rangle | ||
| \langle\psi_{m{\bf k}}\vert v_\beta\vert\psi_{n{\bf k}}\rangle} | ||
| {\varepsilon_{m{\bf k}}-\varepsilon_{n{\bf k}}-(\hbar\omega+i\eta)}.$$ |
| @@ -426,35 +613,50 @@ elements are readily available at the end of a standard MLWF calculation | |||
| with `wannier90`. In particular, $\langle {\bf | |||
| 0}n\vert {\bf r}\vert {\bf R}m\rangle$ can be calculated by Fourier | |||
| transforming the overlap matrices in Eq. (1.7), | |||
| $$\langle u_{n{\bf k}}\vert u_{m{\bf k}+{\bf b}}\rangle.$$ Further | |||
|
|
|||
| $$\langle u_{n{\bf k}}\vert u_{m{\bf k}+{\bf b}}\rangle.$$ | |||
| $$\langle u_{n{\bf k}+{\bf b}_1}\vert | ||
| H_{\bf k}\vert u_{m{\bf k}+{\bf b}_2}\rangle$$ over the *ab-initio* | ||
| H_{\bf k}\vert u_{m{\bf k}+{\bf b}_2}\rangle$$ |
| elements | ||
|
|
||
| $$\langle u_{n{\bf k}}\vert \sigma_\gamma \vert u_{m{\bf k}}\rangle, |
| Sec. [\[sec:boltz2ddir\]](#sec:boltz2ddir){reference-type="ref" | ||
| reference="sec:boltz2ddir"} for the documentation). This is important | ||
| for the evaluation of the Seebeck coefficient. | ||
| !!!Note |
| $\mathrm{\bm{\sigma}}$, the Seebeck coefficient $\mathrm{\bm{S}}$ and | ||
| $\mathrm{\bm{K}}$ are $3\times 3$ tensors, in general. | ||
|
|
||
| !!!Note |
| have to input for its $x$ coordinate $k_x = 0.5 * 2 * \pi / a_{lat}$. As | ||
| a practical example, if $a_{lat}=4$Å, then $k_x = 0.78539816339745$ in | ||
| absolute coordinates in units of 1/Å. | ||
| !!!Note |
| check the date stamp in the first line of the | ||
| ` seedname_geninterp_*.dat` files, or simply delete the | ||
| ` seedname_geninterp_*.dat` files before starting the new calculation. | ||
| !!!Note |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
Update the format. Some table, section in
Postw90were link toWannier90section. I marked as TODO and needs further updated