ELPH SCATTERING APPROX: Difference between revisions
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w_{n\mathbf{k},n'\mathbf{k}'} = \left(1 - \frac{\mathbf{v}_{n\mathbf{k}} \cdot \mathbf{v}_{n'\mathbf{k}'}}{|\mathbf{v}_{n\mathbf{k}}| |\mathbf{v}_{n'\mathbf{k}'}|} \left| \frac{\varepsilon_{n'\mathbf{k}'} - \mu}{\varepsilon_{n\mathbf{k}} - \mu} \right|\right) | w_{n\mathbf{k},n'\mathbf{k}'} = \left(1 - \frac{\mathbf{v}_{n\mathbf{k}} \cdot \mathbf{v}_{n'\mathbf{k}'}}{|\mathbf{v}_{n\mathbf{k}}| |\mathbf{v}_{n'\mathbf{k}'}|} \left| \frac{\varepsilon_{n'\mathbf{k}'} - \mu}{\varepsilon_{n\mathbf{k}} - \mu} \right|\right) | ||
</math> | </math> | ||
{{NB|warning| | {{NB|warning|The formula above is correct and used from vasp 6.5.2 onwards. In vasp 6.5.1, the following formula is used: | ||
:<math> | :<math> | ||
w_{n\mathbf{k},n'\mathbf{k}'} = \left(1 - \frac{\mathbf{v}_{n\mathbf{k}} \cdot \mathbf{v}_{n'\mathbf{k}'}}{|\mathbf{v}_{n\mathbf{k}}| |\mathbf{v}_{n'\mathbf{k}'}|}\right) \left| \frac{\varepsilon_{n'\mathbf{k}'} - \mu}{\varepsilon_{n\mathbf{k}} - \mu} \right| | w_{n\mathbf{k},n'\mathbf{k}'} = \left(1 - \frac{\mathbf{v}_{n\mathbf{k}} \cdot \mathbf{v}_{n'\mathbf{k}'}}{|\mathbf{v}_{n\mathbf{k}}| |\mathbf{v}_{n'\mathbf{k}'}|}\right) \left| \frac{\varepsilon_{n'\mathbf{k}'} - \mu}{\varepsilon_{n\mathbf{k}} - \mu} \right| | ||
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w_{n\mathbf{k},n'\mathbf{k}'} = \left(1 - \frac{\mathbf{v}_{n\mathbf{k}} \cdot \mathbf{v}_{n'\mathbf{k}'}}{|\mathbf{v}_{n\mathbf{k}}|^2} \left| \frac{\varepsilon_{n'\mathbf{k}'} - \mu}{\varepsilon_{n\mathbf{k}} - \mu} \right|\right) | w_{n\mathbf{k},n'\mathbf{k}'} = \left(1 - \frac{\mathbf{v}_{n\mathbf{k}} \cdot \mathbf{v}_{n'\mathbf{k}'}}{|\mathbf{v}_{n\mathbf{k}}|^2} \left| \frac{\varepsilon_{n'\mathbf{k}'} - \mu}{\varepsilon_{n\mathbf{k}} - \mu} \right|\right) | ||
</math> | </math> | ||
{{NB|warning| | {{NB|warning|The formula above is correct and used from vasp 6.5.2 onwards. In vasp 6.5.1, the following formula is used: | ||
:<math> | :<math> | ||
w_{n\mathbf{k},n'\mathbf{k}'} = \left(1 - \frac{\mathbf{v}_{n\mathbf{k}} \cdot \mathbf{v}_{n'\mathbf{k}'}}{|\mathbf{v}_{n\mathbf{k}}|^2}\right) \left| \frac{\varepsilon_{n'\mathbf{k}'} - \mu}{\varepsilon_{n\mathbf{k}} - \mu} \right| | w_{n\mathbf{k},n'\mathbf{k}'} = \left(1 - \frac{\mathbf{v}_{n\mathbf{k}} \cdot \mathbf{v}_{n'\mathbf{k}'}}{|\mathbf{v}_{n\mathbf{k}}|^2}\right) \left| \frac{\varepsilon_{n'\mathbf{k}'} - \mu}{\varepsilon_{n\mathbf{k}} - \mu} \right| | ||
Revision as of 12:59, 15 October 2025
ELPH_SCATTERING_APPROX = [string]
Default: ELPH_SCATTERING_APPROX = SERTA MRTA_LAMBDA
Description: Select which type of approximation is used to compute the electron scattering lifetimes due to electron-phonon coupling
| Mind: Available as of VASP 6.5.0 |
There are different approximations to compute the electronic lifetimes due to electron-phonon scattering. Each of these can lead to significantly different transport coefficients. It is possible to select more than one approximation in ELPH_SCATTERING_APPROX. In this case, additional electron-phonon accumulators are created for each scattering approximation.
Options to select
ELPH_SCATTERING_APPROX = CRTA- Constant Relaxation-Time Approximation- The relaxation time is assumed constant. It needs to be specified via TRANSPORT_RELAXATION_TIME. In this case, the computation of electron-phonon matrix elements is skipped entirely, which is a huge performance boost compared to the other relaxation-time approximations.
| Warning: While the CRTA can be a reasonable approximation for metals, it will generally fail for insulators. |
ELPH_SCATTERING_APPROX = SERTA- Self-Energy Relaxation-Time Approximation- Computes the relaxation time from the imaginary part of the Fan self-energy, evaluated on the electronic eigenenergy:
- [math]\displaystyle{ \frac{1}{\tau^{\mathrm{SERTA}}_{n\mathbf{k}}} = \frac{2\pi}{\hbar} \sum_{n'\nu\mathbf{k}'} w_{n\mathbf{k},n'\mathbf{k}'} \, |g^{\nu}_{n\mathbf{k},n'\mathbf{k}'}|^2 \left[ (n_{\nu\mathbf{q}} + 1 - f_{n'\mathbf{k}'}) \, \delta(\varepsilon_{n\mathbf{k}} - \varepsilon_{n'\mathbf{k}'} - \hbar\omega_{\nu\mathbf{q}}) + (n_{\nu\mathbf{q}} + f_{n'\mathbf{k}'}) \, \delta(\varepsilon_{n\mathbf{k}} - \varepsilon_{n'\mathbf{k}'} + \hbar\omega_{\nu\mathbf{q}}) \right] }[/math]
- Here, the scattering weight is:
- [math]\displaystyle{ w_{n\mathbf{k},n'\mathbf{k}'} = 1 }[/math]
ELPH_SCATTERING_APPROX = ERTA_LAMDBA- Energy Relaxation-Time Approximation (mean-free path approximation)- Applies an energy-projected weight scaled by mean-free path:
- [math]\displaystyle{ w_{n\mathbf{k},n'\mathbf{k}'} = \left(1 - \frac{\mathbf{v}_{n\mathbf{k}} \cdot \mathbf{v}_{n'\mathbf{k}'}}{|\mathbf{v}_{n\mathbf{k}}| |\mathbf{v}_{n'\mathbf{k}'}|} \left| \frac{\varepsilon_{n'\mathbf{k}'} - \mu}{\varepsilon_{n\mathbf{k}} - \mu} \right|\right) }[/math]
Warning: The formula above is correct and used from vasp 6.5.2 onwards. In vasp 6.5.1, the following formula is used:
|
ELPH_SCATTERING_APPROX = ERTA_TAU- Energy Relaxation-Time Approximation (lifetime approximation)- [math]\displaystyle{ w_{n\mathbf{k},n'\mathbf{k}'} = \left(1 - \frac{\mathbf{v}_{n\mathbf{k}} \cdot \mathbf{v}_{n'\mathbf{k}'}}{|\mathbf{v}_{n\mathbf{k}}|^2} \left| \frac{\varepsilon_{n'\mathbf{k}'} - \mu}{\varepsilon_{n\mathbf{k}} - \mu} \right|\right) }[/math]
Warning: The formula above is correct and used from vasp 6.5.2 onwards. In vasp 6.5.1, the following formula is used:
|
ELPH_SCATTERING_APPROX = MRTA_LAMDBA- Momentum Relaxation-Time Approximation (mean-free path approximation)- [math]\displaystyle{ w_{n\mathbf{k},n'\mathbf{k}'} = \left(1 - \frac{\mathbf{v}_{n\mathbf{k}} \cdot \mathbf{v}_{n'\mathbf{k}'}}{|\mathbf{v}_{n\mathbf{k}}| |\mathbf{v}_{n'\mathbf{k}'}|}\right) }[/math]
ELPH_SCATTERING_APPROX = MRTA_TAU- Momentum Relaxation-Time Approximation (lifetime approximation)- [math]\displaystyle{ w_{n\mathbf{k},n'\mathbf{k}'} = \left(1 - \frac{\mathbf{v}_{n\mathbf{k}} \cdot \mathbf{v}_{n'\mathbf{k}'}}{|\mathbf{v}_{n\mathbf{k}}|^2}\right) }[/math]