ELPH DECOMPOSE - Revision history

Mani: Add information to each kind of matrix element

2025-02-27T11:21:38Z

Add information to each kind of matrix element

← Older revision		Revision as of 11:21, 27 February 2025
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	Each contribution can be included by specifying the associated letter in {{TAG\|ELPH_DECOMPOSE}}.		Each contribution can be included by specifying the associated letter in {{TAG\|ELPH_DECOMPOSE}}.
	We suggest two different combinations to define matrix elements:		We suggest two different combinations to define matrix elements:
	;{{TAGO\|ELPH_DECOMPOSE\|VDPR}}		;{{TAGO\|ELPH_DECOMPOSE\|VDPR}} - "All-electron" (AE) matrix element{{cite\|engel:prb:2022}}{{cite\|chaput:prb:2019}}
	:"All-electron" matrix element{{cite\|engel:prb:2022}}{{cite\|chaput:prb:2019}}		:This is the de-facto standard definition of the electron-phonon matrix element expressed in the language of the PAW method. The AE matrix element can be used in the framework of many-body perturbation theory without any further restrictions. It should also be used if one is not interested in the final observables, but in the values of the matrix elements themselves, for example, to study scattering channels.
	;{{TAGO\|ELPH_DECOMPOSE\|VDQ}}		;{{TAGO\|ELPH_DECOMPOSE\|VDQ}} - "Pseudo" (PS) matrix element{{cite\|engel:prb:2022}}{{cite\|engel:prb:2020}}
	:"Pseudo" matrix element{{cite\|engel:prb:2022}}{{cite\|engel:prb:2020}}		:This matrix element arises naturally from the PAW formulation of the phonon-induced band-structure renormalization in the adiabatic Rayleigh-Schrödinger perturbation theory. It is only really well-defined in this particular context. However, when using this much smoother PS matrix element instead of the AE matrix element, the electron self-energy converges much faster with respect to the number of intermediate states. Despite its definition from an adiabatic theory, we recommend to use the PS matrix element also to compute the [[Bandgap renormalization due to electron-phonon coupling \| non-adiabatic band-structure renormalization]]{{cite\|engel:prb:2022}}. In our experience, the PS matrix element is furthermore well suited to perform [[Transport coefficients including electron-phonon scattering \| transport calculations]], since the difference between AE and PS matrix elements is small for scattering processes close to the Fermi edge. In any case, it is always recommended to compare observables computed with the PS matrix elements against the same observables computed with the AE matrix elements.

	== Available contributions ==		== Available contributions ==

Mani: /* Available contributions */ Add more descriptions

2025-02-27T10:56:34Z

Available contributions: Add more descriptions

← Older revision		Revision as of 10:56, 27 February 2025
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	\rangle		\rangle
	</math>		</math>
			:This term is the pure plane-wave contribution to the total PAW matrix element. If the PAW augmentation region were vanishingly small, this would be the sole contribution.
	;D - Derivative of PAW strength parameters, <math>D_{a, ij}</math>		;D - Derivative of PAW strength parameters, <math>D_{a, ij}</math>
	:<math>		:<math>
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	\rangle		\rangle
	</math>		</math>
			:This contribution stems from the PAW treatment of the electronic Hamiltonian. It is of the same nature as <math>g^{(\text{V})}</math> but is treated in the local basis inside the augmentation region. For a detailed discussion of the PAW strength parameters, we refer to Ref. {{Cite\|kresse:prb:99}}.
	;P - Derivative of PAW projectors, <math>\|\tilde{p}_{ai}\rangle</math>		;P - Derivative of PAW projectors, <math>\|\tilde{p}_{ai}\rangle</math>
	:<math>		:<math>
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	\end{split}		\end{split}
	</math>		</math>
			:This contribution is very similar to <math>g^{(\text{P})}</math>. The only difference is in the Kohn-Sham eigenvalues. While <math>g^{(\text{P})}</math> uses the eigenvalues of both the initial and final state (so <math>\varepsilon_{n \mathbf{k}}</math> and <math>\varepsilon_{m \mathbf{k}'}</math>), <math>g^{(\text{Q})}</math> only uses the eigenvalues of the initial state (<math>\varepsilon_{n \mathbf{k}}</math>).

	==Related tags and articles==		==Related tags and articles==

Mani: /* Related tags and articles */

2025-02-27T06:55:58Z

Mani: Add availability notice

2025-01-17T14:21:28Z

Add availability notice

← Older revision		Revision as of 14:21, 17 January 2025
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	Description: Chooses which contributions to include in the computation of the electron-phonon matrix elements.		Description: Chooses which contributions to include in the computation of the electron-phonon matrix elements.
			{{Available\|6.5.0}}

	----		----

Mani: Add related info and categories

2024-12-19T15:52:31Z

Add related info and categories

← Older revision		Revision as of 15:52, 19 December 2024
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	</math>		</math>

	~~For more details, please refer to Ref.~~{{~~cite~~\|~~engel:prb:2022~~}}~~, and consult our documentation on the~~ [[~~projector~~-~~augmented-wave_formalism~~]].		==Related tags and articles==
			* [[Projector-augmented-wave_formalism]]
			* {{TAG\|ELPH_RUN}}
			* {{TAG\|ELPH_SELFEN_FAN}}
			* {{TAG\|ELPH_SELFEN_DW}}

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

	== References ==		== References ==

Mani: Remove elph release banner

2024-12-18T14:29:52Z

Remove elph release banner

← Older revision		Revision as of 14:29, 18 December 2024
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	~~{{elph_release}}~~
	{{DISPLAYTITLE:ELPH_DECOMPOSE}}		{{DISPLAYTITLE:ELPH_DECOMPOSE}}
	{{TAGDEF\|ELPH_DECOMPOSE\|[string]\|VDPR}}		{{TAGDEF\|ELPH_DECOMPOSE\|[string]\|VDPR}}

Mani: /* Available contributions */ Add R matrix and link to PAW formalism

2024-10-21T16:07:14Z

Available contributions: Add R matrix and link to PAW formalism

← Older revision		Revision as of 16:07, 21 October 2024
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	\tilde{p}_{a j} \|		\tilde{p}_{a j} \|
	\tilde{\psi}_{n \mathbf{k}}		\tilde{\psi}_{n \mathbf{k}}
			\rangle
			</math>
			:with <math>
			R_{a, ij}
			\equiv
			\langle
			\phi_{a i} \|
			\frac{\partial \phi_{a j}}{\partial u_{a}}
			\rangle -
			\langle
			\tilde{\phi}_{a i} \|
			\frac{\partial \tilde{\phi}_{a j}}{\partial u_{a}}
	\rangle		\rangle
	</math>		</math>
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	</math>		</math>

	For more details, please refer to Ref.{{cite\|engel:prb:2022}}.		For more details, please refer to Ref.{{cite\|engel:prb:2022}}, and consult our documentation on the [[projector-augmented-wave_formalism]].

	== References ==		== References ==

Mani: /* Available contributions */ Add more info

2024-10-21T14:00:31Z

Available contributions: Add more info

← Older revision		Revision as of 14:00, 21 October 2024
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	== Available contributions ==		== Available contributions ==

	;V		;V - Derivative of pseudopotential, <math>\tilde{v}</math>
	:<math>		:<math>
	g^{(\text{V})}_{m \mathbf{k}', n \mathbf{k}, a}		g^{(\text{V})}_{m \mathbf{k}', n \mathbf{k}, a}
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	\langle		\langle
	\tilde{\psi}_{m \mathbf{k}'} \|		\tilde{\psi}_{m \mathbf{k}'} \|
	\frac{\partial \~~widetilde~~{v}}{\partial u_{a}} \|		\frac{\partial \tilde{v}}{\partial u_{a}} \|
	\tilde{\psi}_{n \mathbf{k}}		\tilde{\psi}_{n \mathbf{k}}
	\rangle		\rangle
	</math>		</math>
	;D		;D - Derivative of PAW strength parameters, <math>D_{a, ij}</math>
	:<math>		:<math>
	g^{(\text{D})}_{m \mathbf{k}', n \mathbf{k}, a}		g^{(\text{D})}_{m \mathbf{k}', n \mathbf{k}, a}
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	\rangle		\rangle
	</math>		</math>
	;P		;P - Derivative of PAW projectors, <math>\|\tilde{p}_{ai}\rangle</math>
	:<math>		:<math>
	\begin{split}		\begin{split}
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	\end{split}		\end{split}
	</math>		</math>
	;R		;R - Derivative of PAW partial waves, <math>\|\phi_{ai}\rangle</math> and <math>\|\tilde{\phi}_{ai}\rangle</math>
	:<math>		:<math>
	g^{(\text{R})}_{m \mathbf{k}', n \mathbf{k}, a}		g^{(\text{R})}_{m \mathbf{k}', n \mathbf{k}, a}
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	\rangle		\rangle
	</math>		</math>
	;Q		;Q - Derivative of PAW projectors, <math>\|\tilde{p}_{ai}\rangle</math> (different eigenvalues)
	:<math>		:<math>
	\begin{split}		\begin{split}

Mani: /* Available contributions */ Add formulas

2024-10-21T13:41:39Z

Available contributions: Add formulas

@@ Line 18: / Line 18: @@
 ;V
-:<math>g^{(\text{V})}_{m \mathbf{k}', n \mathbf{k}}</math>
+:<math>
 ;D
-:<math>g^{(\text{D})}_{m \mathbf{k}', n \mathbf{k}}</math>
+:<math>
 ;P
-:<math>g^{(\text{P})}_{m \mathbf{k}', n \mathbf{k}}</math>
+:<math>
 ;R
-:<math>g^{(\text{R})}_{m \mathbf{k}', n \mathbf{k}}</math>
+:<math>
 ;Q
-:<math>g^{(\text{Q})}_{m \mathbf{k}', n \mathbf{k}}</math>
+:<math>
 For more details, please refer to Ref.{{cite|engel:prb:2022}}.
 == References ==

Mani: Add Chaput reference

2024-10-18T12:42:39Z

Add Chaput reference

← Older revision		Revision as of 12:42, 18 October 2024
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	We suggest two different combinations to define matrix elements:		We suggest two different combinations to define matrix elements:
	;{{TAGO\|ELPH_DECOMPOSE\|VDPR}}		;{{TAGO\|ELPH_DECOMPOSE\|VDPR}}
	:"All-electron" matrix element{{cite\|engel:prb:2022}}		:"All-electron" matrix element{{cite\|engel:prb:2022}}{{cite\|chaput:prb:2019}}
	;{{TAGO\|ELPH_DECOMPOSE\|VDQ}}		;{{TAGO\|ELPH_DECOMPOSE\|VDQ}}
	:"Pseudo" matrix element{{cite\|engel:prb:2022}}{{cite\|engel:prb:2020}}		:"Pseudo" matrix element{{cite\|engel:prb:2022}}{{cite\|engel:prb:2020}}

← Older revision		Revision as of 06:55, 27 February 2025
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	==Related tags and articles==		==Related tags and articles==
	* [[Projector-augmented-~~wave_formalism~~]]		* [[Projector-augmented-wave formalism]]
	* {{TAG\|ELPH_RUN}}		* {{TAG\|ELPH_RUN}}
	* {{TAG\|ELPH_SELFEN_FAN}}		* {{TAG\|ELPH_SELFEN_FAN}}

← Older revision		Revision as of 12:42, 18 October 2024
Line 11:		Line 11:
	We suggest two different combinations to define matrix elements:		We suggest two different combinations to define matrix elements:
	;{{TAGO\|ELPH_DECOMPOSE\|VDPR}}		;{{TAGO\|ELPH_DECOMPOSE\|VDPR}}
	:"All-electron" matrix element{{cite\|engel:prb:2022}}		:"All-electron" matrix element{{cite\|engel:prb:2022}}{{cite\|chaput:prb:2019}}
	;{{TAGO\|ELPH_DECOMPOSE\|VDQ}}		;{{TAGO\|ELPH_DECOMPOSE\|VDQ}}
	:"Pseudo" matrix element{{cite\|engel:prb:2022}}{{cite\|engel:prb:2020}}		:"Pseudo" matrix element{{cite\|engel:prb:2022}}{{cite\|engel:prb:2020}}