ELPH SELFEN BAND STOP KP: Difference between revisions
Add ELPH_SELFEN_BAND_STOP_KP tag documentation |
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{{TAGDEF|ELPH_SELFEN_BAND_STOP_KP|[integer]|-1}} | {{TAGDEF|ELPH_SELFEN_BAND_STOP_KP|[integer]|-1}} | ||
Description: Index of the last k' band included in the electron self-energy sum; -1 uses all bands up to {{TAG|ELPH_NBANDS}}, and -2 activates automatic determination based on energy conservation. | Description: Index of the last <math>k'</math> band included in the electron self-energy sum; -1 uses all bands up to {{TAG|ELPH_NBANDS}}, and -2 activates automatic determination based on energy conservation. | ||
{{Available|6. | {{Available|6.6.0}} | ||
---- | ---- | ||
The Fan-Migdal self-energy involves a sum over intermediate scattering states at k' = k + q: | The Fan-Migdal self-energy involves a sum over intermediate scattering states at <math>k' = k + q</math>: | ||
:<math>\Sigma^{\text{FM}}_{n\mathbf{k}}(T) = \frac{1}{N_q}\sum_{m\nu\mathbf{q}} |g_{mn\mathbf{k},\nu\mathbf{q}}|^2 \left[\frac{\cdots}{\varepsilon_{n\mathbf{k}} - \varepsilon_{m\mathbf{k}+\mathbf{q}} \pm \omega_{\nu\mathbf{q}} + i\delta}\right]</math> | :<math>\Sigma^{\text{FM}}_{n\mathbf{k}}(T) = \frac{1}{N_q}\sum_{m\nu\mathbf{q}} |g_{mn\mathbf{k},\nu\mathbf{q}}|^2 \left[\frac{\cdots}{\varepsilon_{n\mathbf{k}} - \varepsilon_{m\mathbf{k}+\mathbf{q}} \pm \omega_{\nu\mathbf{q}} + i\delta}\right]</math> | ||
{{TAG|ELPH_SELFEN_BAND_START_KP}} and {{TAG|ELPH_SELFEN_BAND_STOP_KP}} control the range of band indices m (at k') included in this sum. | {{TAG|ELPH_SELFEN_BAND_START_KP}} and {{TAG|ELPH_SELFEN_BAND_STOP_KP}} control the range of band indices <math>m</math> (at <math>k'</math>) included in this sum. | ||
This is distinct from {{TAG|ELPH_SELFEN_BAND_START}} and {{TAG|ELPH_SELFEN_BAND_STOP}}, which select the bands | This is distinct from {{TAG|ELPH_SELFEN_BAND_START}} and {{TAG|ELPH_SELFEN_BAND_STOP}}, which select the bands <math>v</math> at <math>k</math>for which the self-energy is computed. | ||
The following values are accepted: | The following values are accepted: | ||
* <code>-1</code> (default): include all bands up to {{TAG|ELPH_NBANDS}}. | * <code>-1</code> (default): include all bands up to {{TAG|ELPH_NBANDS}}. | ||
* <code>-2</code>: determine the upper bound automatically from energy conservation. Only k' bands whose eigenvalues fall within ±ω<sub>max</sub> of the target k bands are included, where ω<sub>max</sub> is the maximum phonon energy. This can significantly reduce the cost when {{TAG|ELPH_NBANDS}} is large. | * <code>-2</code>: determine the upper bound automatically from energy conservation. Only <math>k'</math> bands whose eigenvalues fall within ±ω<sub>max</sub> of the target <math>k</math> bands are included, where ω<sub>max</sub> is the maximum phonon energy. This can significantly reduce the cost when {{TAG|ELPH_NBANDS}} is large. | ||
* Positive integer: use the specified band index as the upper bound. | * Positive integer: use the specified band index as the upper bound. | ||
Latest revision as of 14:02, 10 July 2026
ELPH_SELFEN_BAND_STOP_KP = [integer]
Default: ELPH_SELFEN_BAND_STOP_KP = -1
Description: Index of the last [math]\displaystyle{ k' }[/math] band included in the electron self-energy sum; -1 uses all bands up to ELPH_NBANDS, and -2 activates automatic determination based on energy conservation.
| Mind: Available as of VASP 6.6.0 |
The Fan-Migdal self-energy involves a sum over intermediate scattering states at [math]\displaystyle{ k' = k + q }[/math]:
- [math]\displaystyle{ \Sigma^{\text{FM}}_{n\mathbf{k}}(T) = \frac{1}{N_q}\sum_{m\nu\mathbf{q}} |g_{mn\mathbf{k},\nu\mathbf{q}}|^2 \left[\frac{\cdots}{\varepsilon_{n\mathbf{k}} - \varepsilon_{m\mathbf{k}+\mathbf{q}} \pm \omega_{\nu\mathbf{q}} + i\delta}\right] }[/math]
ELPH_SELFEN_BAND_START_KP and ELPH_SELFEN_BAND_STOP_KP control the range of band indices [math]\displaystyle{ m }[/math] (at [math]\displaystyle{ k' }[/math]) included in this sum. This is distinct from ELPH_SELFEN_BAND_START and ELPH_SELFEN_BAND_STOP, which select the bands [math]\displaystyle{ v }[/math] at [math]\displaystyle{ k }[/math]for which the self-energy is computed.
The following values are accepted:
-1(default): include all bands up to ELPH_NBANDS.-2: determine the upper bound automatically from energy conservation. Only [math]\displaystyle{ k' }[/math] bands whose eigenvalues fall within ±ωmax of the target [math]\displaystyle{ k }[/math] bands are included, where ωmax is the maximum phonon energy. This can significantly reduce the cost when ELPH_NBANDS is large.- Positive integer: use the specified band index as the upper bound.
Setting both ELPH_SELFEN_BAND_START_KP and ELPH_SELFEN_BAND_STOP_KP to -2 is recommended when a large number of bands is required for convergence but most of them lie far from the relevant energy window.