ELPH SCATTERING APPROX - Revision history

Singraber at 08:05, 24 October 2025

2025-10-24T08:05:34Z

← Older revision		Revision as of 08:05, 24 October 2025
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	== Options to select ==		== Options to select ==
	;{{~~TAGO~~\|ELPH_SCATTERING_APPROX\|CRTA}} - <u>C</u>onstant <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation		;{{TAG\|ELPH_SCATTERING_APPROX\|CRTA}} - <u>C</u>onstant <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation
	:The relaxation time is assumed constant. It needs to be specified via {{TAG\|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.		:The relaxation time is assumed constant. It needs to be specified via {{TAG\|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.
	{{NB\|warning\|While the CRTA can be a reasonable approximation for metals, it will generally fail for insulators.}}		{{NB\|warning\|While the CRTA can be a reasonable approximation for metals, it will generally fail for insulators.}}

	;{{~~TAGO~~\|ELPH_SCATTERING_APPROX\|SERTA}} - <u>S</u>elf-<u>E</u>nergy <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation		;{{TAG\|ELPH_SCATTERING_APPROX\|SERTA}} - <u>S</u>elf-<u>E</u>nergy <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation
	:Computes the relaxation time from the imaginary part of the Fan self-energy, evaluated on the electronic eigenenergy:		:Computes the relaxation time from the imaginary part of the Fan self-energy, evaluated on the electronic eigenenergy:
	:<math>		:<math>
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	</math>		</math>

	;{{~~TAGO~~\|ELPH_SCATTERING_APPROX\|ERTA_LAMDBA}} - <u>E</u>nergy <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation (mean-free path approximation)		;{{TAG\|ELPH_SCATTERING_APPROX\|ERTA_LAMDBA}} - <u>E</u>nergy <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation (mean-free path approximation)
	:Applies an energy-projected weight scaled by mean-free path (where <math>\mu</math> is the [[Chemical_potential_in_electron-phonon_interactions\|chemical potential]]):		:Applies an energy-projected weight scaled by mean-free path (where <math>\mu</math> is the [[Chemical_potential_in_electron-phonon_interactions\|chemical potential]]):
	:<math>		:<math>
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	</math>		</math>
	}}		}}
	;{{~~TAGO~~\|ELPH_SCATTERING_APPROX\|ERTA_TAU }} - <u>E</u>nergy <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation (lifetime approximation)		;{{TAG\|ELPH_SCATTERING_APPROX\|ERTA_TAU }} - <u>E</u>nergy <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation (lifetime approximation)
	:<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} \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)
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	</math>		</math>
	}}		}}
	;{{~~TAGO~~\|ELPH_SCATTERING_APPROX\|MRTA_LAMDBA}} - <u>M</u>omentum <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation (mean-free path approximation)		;{{TAG\|ELPH_SCATTERING_APPROX\|MRTA_LAMDBA}} - <u>M</u>omentum <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation (mean-free path approximation)
	:<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)		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>		</math>

	;{{~~TAGO~~\|ELPH_SCATTERING_APPROX\|MRTA_TAU }} - <u>M</u>omentum <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation (lifetime approximation)		;{{TAG\|ELPH_SCATTERING_APPROX\|MRTA_TAU }} - <u>M</u>omentum <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation (lifetime approximation)
	:<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)		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)

Csheldon: /* Options to select */

2025-10-23T14:28:22Z

Options to select

← Older revision		Revision as of 14:28, 23 October 2025
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	\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]		\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>		</math>
	:~~Here~~, the scattering weight is:		:where <math>{\tau^{\mathrm{SERTA}}_{n\mathbf{k}}}</math> is the relaxation time (or scattering time, or lifetime) for state <math>(n,\mathbf{k})</math>, <math>w_{n\mathbf{k},n'\mathbf{k}'}</math> is the scattering weight, <math>g^{\nu}_{n\mathbf{k},n'\mathbf{k}'}</math> is the electron-phonon coupling matrix element, <math>f_{n\mathbf{k}}</math> is the population of the electronic state (Fermi-Dirac distribution), <math>n_{\nu\mathbf{q}}</math> is the population of the phononic state (Bose-Einstein distribution), <math>\varepsilon_{n\mathbf{k}}</math> is the energy of an electron band, <math>\omega_{\nu\mathbf{q}}</math> is the phonon frequency, and <math>\delta</math> is the Dirac delta function.

			:For SERTA, the scattering weight is:
	:<math>		:<math>
	w_{n\mathbf{k},n'\mathbf{k}'} = 1		w_{n\mathbf{k},n'\mathbf{k}'} = 1
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	;{{TAGO\|ELPH_SCATTERING_APPROX\|ERTA_LAMDBA}} - <u>E</u>nergy <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation (mean-free path approximation)		;{{TAGO\|ELPH_SCATTERING_APPROX\|ERTA_LAMDBA}} - <u>E</u>nergy <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation (mean-free path approximation)
	:Applies an energy-projected weight scaled by mean-free path:		:Applies an energy-projected weight scaled by mean-free path (where <math>\mu</math> is the [[Chemical_potential_in_electron-phonon_interactions\|chemical potential]]):
	:<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}'}\|} \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)

Miranda.henrique: /* Related tags and articles */

2025-10-22T20:25:35Z

Csheldon at 14:14, 20 October 2025

2025-10-20T14:14:47Z

← Older revision		Revision as of 14:14, 20 October 2025
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	==Related tags and articles==		==Related tags and articles==
	* [[Transport coefficients including electron-phonon scattering\|Transport calculations]]		* [[Transport coefficients including electron-phonon scattering\|Transport calculations]]
			* [[Electronic transport coefficients]]
	* [[Electron-phonon accumulators]]		* [[Electron-phonon accumulators]]
	* {{TAG\|ELPH_RUN}}		* {{TAG\|ELPH_RUN}}

Csheldon: /* Options to select */

2025-10-15T13:17:15Z

Options to select

← Older revision		Revision as of 13:17, 15 October 2025
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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\|The formula above is correct and used from the next release of VASP onwards. In VASP 6.5.1, the following formula is used:		{{NB\|warning\|The formula above is correct and used from the next release of VASP onwards. In VASP 6.5.0 and 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\|The formula above is correct and used from the next release of VASP onwards. In VASP 6.5.1, the following formula is used:		{{NB\|warning\|The formula above is correct and used from the next release of VASP onwards. In VASP 6.5.0 and 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\|

Csheldon: /* Options to select */

2025-10-15T13:06:14Z

Options to select

← Older revision		Revision as of 13:06, 15 October 2025
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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\|The formula above is correct and used from ~~vasp 6.5.2~~ onwards. In ~~vasp~~ 6.5.1, the following formula is used:		{{NB\|warning\|The formula above is correct and used from the next release of VASP 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\|The formula above is correct and used from ~~vasp 6.5.2~~ onwards. In ~~vasp~~ 6.5.1, the following formula is used:		{{NB\|warning\|The formula above is correct and used from the next release of VASP 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\|

Csheldon at 12:59, 15 October 2025

2025-10-15T12:59:49Z

← Older revision		Revision as of 12:59, 15 October 2025
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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\|~~As of~~ vasp 6.5.1 ~~this approximation is wrongly implemented. Instead of~~ the formula ~~above what is implemented~~ is:		{{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\|~~As of~~ vasp 6.5.1 ~~this approximation is wrongly implemented. Instead of~~ the formula ~~above what is implemented~~ is:		{{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\|

Miranda.henrique at 12:04, 15 October 2025

2025-10-15T12:04:23Z

← Older revision		Revision as of 12:04, 15 October 2025
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	:Applies an energy-projected weight scaled by mean-free path:		:Applies an energy-projected weight scaled by mean-free path:
	:<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}'}\|} \left\| \frac{\varepsilon_{n'\mathbf{k}'} - \mu}{\varepsilon_{n\mathbf{k}} - \mu} \right\|\right)
	</math>		</math>
	{{NB\|warning\|As of vasp 6.5.1 this approximation is wrongly implemented. ~~It should be~~		{{NB\|warning\|As of vasp 6.5.1 this approximation is wrongly implemented. Instead of the formula above what is implemented is:
	:<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}'}\|} \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}'}\|}\right) \left\| \frac{\varepsilon_{n'\mathbf{k}'} - \mu}{\varepsilon_{n\mathbf{k}} - \mu} \right\|
	</math>		</math>
	}}		}}
	;{{TAGO\|ELPH_SCATTERING_APPROX\|ERTA_TAU }} - <u>E</u>nergy <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation (lifetime approximation)		;{{TAGO\|ELPH_SCATTERING_APPROX\|ERTA_TAU }} - <u>E</u>nergy <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation (lifetime approximation)
	:<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} \left\| \frac{\varepsilon_{n'\mathbf{k}'} - \mu}{\varepsilon_{n\mathbf{k}} - \mu} \right\|\right)
	</math>		</math>
	{{NB\|warning\|As of vasp 6.5.1 this approximation is wrongly implemented. ~~It should be~~		{{NB\|warning\|As of vasp 6.5.1 this approximation is wrongly implemented. Instead of the formula above what is implemented is:
	:<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} \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}\right) \left\| \frac{\varepsilon_{n'\mathbf{k}'} - \mu}{\varepsilon_{n\mathbf{k}} - \mu} \right\|
	</math>		</math>
	}}		}}

Miranda.henrique at 09:29, 3 July 2025

2025-07-03T09:29:25Z

← Older revision		Revision as of 09:29, 3 July 2025
Line 31:		Line 31:
	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\|
	</math>		</math>
	~~<!--~~
	{{NB\|warning\|As of vasp 6.5.1 this approximation is wrongly implemented. It should be		{{NB\|warning\|As of vasp 6.5.1 this approximation is wrongly implemented. It should be
	:<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}'}\|} ~~\cdot~~ \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>
	}}~~-->~~		}}
	;{{TAGO\|ELPH_SCATTERING_APPROX\|ERTA_TAU }} - <u>E</u>nergy <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation (lifetime approximation)		;{{TAGO\|ELPH_SCATTERING_APPROX\|ERTA_TAU }} - <u>E</u>nergy <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation (lifetime approximation)
	:<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\|
	</math>		</math>
	~~<!--~~
	{{NB\|warning\|As of vasp 6.5.1 this approximation is wrongly implemented. It should be		{{NB\|warning\|As of vasp 6.5.1 this approximation is wrongly implemented. It should be
	:<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} \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>
	}}~~-->~~		}}
	;{{TAGO\|ELPH_SCATTERING_APPROX\|MRTA_LAMDBA}} - <u>M</u>omentum <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation (mean-free path approximation)		;{{TAGO\|ELPH_SCATTERING_APPROX\|MRTA_LAMDBA}} - <u>M</u>omentum <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation (mean-free path approximation)
	:<math>		:<math>

Miranda.henrique at 13:25, 30 June 2025

2025-06-30T13:25:02Z

← Older revision		Revision as of 13:25, 30 June 2025
Line 29:		Line 29:
	:Applies an energy-projected weight scaled by mean-free path:		:Applies an energy-projected weight scaled by mean-free path:
	:<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}}\| ~~\cdot~~ \|\mathbf{v}_{n'\mathbf{k}'}\|}\right) ~~\cdot~~ \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\|
	</math>		</math>
			<!--
			{{NB\|warning\|As of vasp 6.5.1 this approximation is wrongly implemented. It should be
			:<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}'}\|} \cdot \left\| \frac{\varepsilon_{n'\mathbf{k}'} - \mu}{\varepsilon_{n\mathbf{k}} - \mu} \right\|\right)
			</math>
			}}-->
	;{{TAGO\|ELPH_SCATTERING_APPROX\|ERTA_TAU }} - <u>E</u>nergy <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation (lifetime approximation)		;{{TAGO\|ELPH_SCATTERING_APPROX\|ERTA_TAU }} - <u>E</u>nergy <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation (lifetime approximation)
	:<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) \cdot \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\|
			</math>
			<!--
			{{NB\|warning\|As of vasp 6.5.1 this approximation is wrongly implemented. It should be
			:<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} \left\| \frac{\varepsilon_{n'\mathbf{k}'} - \mu}{\varepsilon_{n\mathbf{k}} - \mu} \right\|\right)
	</math>		</math>
			}}-->
	;{{TAGO\|ELPH_SCATTERING_APPROX\|MRTA_LAMDBA}} - <u>M</u>omentum <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation (mean-free path approximation)		;{{TAGO\|ELPH_SCATTERING_APPROX\|MRTA_LAMDBA}} - <u>M</u>omentum <u>R</u>elaxation-<u>T</u>ime <u>A</u>pproximation (mean-free path approximation)
	:<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}}\| ~~\cdot~~ \|\mathbf{v}_{n'\mathbf{k}'}\|}\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)
	</math>		</math>

← Older revision		Revision as of 20:25, 22 October 2025
Line 60:		Line 60:
	* [[Electron-phonon accumulators]]		* [[Electron-phonon accumulators]]
	* {{TAG\|ELPH_RUN}}		* {{TAG\|ELPH_RUN}}
			* {{TAG\|ELPH_TRANSPORT}}
			* {{TAG\|ELPH_TRANSPORT_DRIVER}}
	* {{TAG\|TRANSPORT_RELAXATION_TIME}}		* {{TAG\|TRANSPORT_RELAXATION_TIME}}

	[[Category:INCAR tag]][[Category:Electron-phonon_interactions]]		[[Category:INCAR tag]][[Category:Electron-phonon_interactions]]