Transport coefficients including electron-phonon scattering - Revision history

Mani: /* Thermoelectric coefficients and the ZT figure of merit */ Add OUTCAR output example and accumulator reference

2025-02-26T12:49:15Z

Thermoelectric coefficients and the ZT figure of merit: Add OUTCAR output example and accumulator reference

← Older revision		Revision as of 12:49, 26 February 2025
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	The conductivity <math>\sigma</math>, Seebeck coefficient <math>S</math> and the electronic contribution to the thermal conductivity <math>\kappa_e</math> are reported in the {{FILE\|OUTCAR}} file.		The conductivity <math>\sigma</math>, Seebeck coefficient <math>S</math> and the electronic contribution to the thermal conductivity <math>\kappa_e</math> are reported in the {{FILE\|OUTCAR}} file.
			Here is an example output where these values are reported for the different [[ELPH_SELFEN_TEMPS \| temperatures ]] in a small table for each [[Electron-phonon accumulators \| accumulator]]:
			<pre>
			Transport for self-energy accumulator N= 1
			T K mu eV sigma S/m mob cm^2/(V.s) seebeck μV/K peltier μV kappa_e W/(m.K)
			0.00000000 9.79452083 153.09934046 95.55902268 0.00000000 0.00000000 0.00000000 Gauss-Legendre grids
			100.00000000 9.80301003 149.76360902 93.48293224 228.06843439 22806.84343939 0.00040952 Gauss-Legendre grids
			200.00000000 9.82655169 134.56767701 83.98822174 377.34590243 75469.18048584 0.00077142 Gauss-Legendre grids
			300.00000000 9.86137412 125.22459498 78.15905958 476.66107679 142998.32303627 0.00106949 Gauss-Legendre grids
			400.00000000 9.90446361 117.64008575 73.42946205 548.72555653 219490.22261143 0.00131031 Gauss-Legendre grids
			500.00000000 9.95389195 108.91505893 67.98526987 604.60014228 302300.07113882 0.00147236 Gauss-Legendre grids
			</pre>
	The lattice thermal conductivity <math>\kappa_l</math> can be computed with an external package such as [https://phonopy.github.io/phono3py/ phono3py].		The lattice thermal conductivity <math>\kappa_l</math> can be computed with an external package such as [https://phonopy.github.io/phono3py/ phono3py].

Mani: Add accumulator info

2025-02-26T11:49:29Z

Add accumulator info

← Older revision		Revision as of 11:49, 26 February 2025
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	{{TAGBL\|TRANSPORT_NEDOS}} = 501		{{TAGBL\|TRANSPORT_NEDOS}} = 501
	{{TAGBL\|ELPH_SELFEN_TEMPS}} = 0 100 200 300 400 500		{{TAGBL\|ELPH_SELFEN_TEMPS}} = 0 100 200 300 400 500

			The final output of the code is reported for each combination of computational parameters using the concept of [[Electron-phonon accumulators \| electron-phonon accumulators]].

	== Conductivity for metals ==		== Conductivity for metals ==
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	* [[Bandgap renormalization due to electron-phonon coupling\|Band-structure renormalization]]		* [[Bandgap renormalization due to electron-phonon coupling\|Band-structure renormalization]]
	* [[Electron-phonon potential from supercells]]		* [[Electron-phonon potential from supercells]]
			* [[Electron-phonon accumulators]]
	* {{FILE\|phelel_params.hdf5}}		* {{FILE\|phelel_params.hdf5}}
	* [[Electron-phonon interactions from Monte-Carlo sampling]]		* [[Electron-phonon interactions from Monte-Carlo sampling]]

	[[Category:Electron-phonon interactions]][[Category:Howto]]		[[Category:Electron-phonon interactions]][[Category:Howto]]

Huebsch: /* Related tags and articles */

2025-02-05T08:00:31Z

Mani: Add related tags and articles

2025-01-20T15:16:35Z

Add related tags and articles

← Older revision		Revision as of 15:16, 20 January 2025
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	Because the Seebeck coefficient <math>S</math> and electronic contribution to the thermal conductivity <math>\kappa_e</math> depend on the first and second momentum of the transport function, a larger number of points ({{TAG\|TRANSPORT_NEDOS}}) is often required to obtain an accurate integration of these transport quantities than for the conductivity or mobility.		Because the Seebeck coefficient <math>S</math> and electronic contribution to the thermal conductivity <math>\kappa_e</math> depend on the first and second momentum of the transport function, a larger number of points ({{TAG\|TRANSPORT_NEDOS}}) is often required to obtain an accurate integration of these transport quantities than for the conductivity or mobility.

			== Related tags and articles ==
			* [[Bandgap renormalization due to electron-phonon coupling\|Bandstructure renormalization]]
			* [[Electron-phonon potential from supercells]]
			* {{FILE\|phelel_params.hdf5}}
			* [[Electron-phonon interactions from Monte-Carlo sampling]]

	[[Category:Electron-phonon interactions]][[Category:Howto]]		[[Category:Electron-phonon interactions]][[Category:Howto]]

Mani: Add availability notice

2025-01-20T14:47:55Z

Add availability notice

← Older revision		Revision as of 14:47, 20 January 2025
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	As such, it is instructive to start by computing the transport coefficients in the constant-relaxation-time approximation (CRTA).		As such, it is instructive to start by computing the transport coefficients in the constant-relaxation-time approximation (CRTA).
	This gives us an idea of the <b>k</b>-point density required to obtain a precise value.		This gives us an idea of the <b>k</b>-point density required to obtain a precise value.
			{{Available\|6.5.0}}

	The most basic {{FILE\|INCAR}} to compute the transport coefficients is		The most basic {{FILE\|INCAR}} to compute the transport coefficients is

Mani: Remove mention of ELPH_ISMEAR=-24

2024-12-19T12:38:10Z

Remove mention of ELPH_ISMEAR=-24

← Older revision		Revision as of 12:38, 19 December 2024
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	# for the determination of the chemical potential		# for the determination of the chemical potential
	~~{{TAGBL\|EFERMI_NEDOS}} = 501 # number of integration points for {{TAG\|ELPH_ISMEAR}} = -24~~		{{TAGBL\|ELPH_ISMEAR}} = -15 # smearing method
	{{TAGBL\|ELPH_ISMEAR}} = -24 # smearing method

	# for the computation of transport coefficients		# for the computation of transport coefficients

Mani: Add categories and remove elphon release banner

2024-12-18T14:16:34Z

Add categories and remove elphon release banner

← Older revision		Revision as of 14:16, 18 December 2024
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	~~{{elph release}}~~

	In the framework of the linearized Boltzmann equations, we can compute a few electronic transport observables.		In the framework of the linearized Boltzmann equations, we can compute a few electronic transport observables.
	The transport coefficients can be evaluated rather straightforwardly under the approximation of the constant relaxation time.		The transport coefficients can be evaluated rather straightforwardly under the approximation of the constant relaxation time.
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	Because the Seebeck coefficient <math>S</math> and electronic contribution to the thermal conductivity <math>\kappa_e</math> depend on the first and second momentum of the transport function, a larger number of points ({{TAG\|TRANSPORT_NEDOS}}) is often required to obtain an accurate integration of these transport quantities than for the conductivity or mobility.		Because the Seebeck coefficient <math>S</math> and electronic contribution to the thermal conductivity <math>\kappa_e</math> depend on the first and second momentum of the transport function, a larger number of points ({{TAG\|TRANSPORT_NEDOS}}) is often required to obtain an accurate integration of these transport quantities than for the conductivity or mobility.

			[[Category:Electron-phonon interactions]][[Category:Howto]]

Mani: /* Thermoelectric coefficients and the ZT figure of merit */ add temperature to figure of merit

2024-12-18T13:29:43Z

Thermoelectric coefficients and the ZT figure of merit: add temperature to figure of merit

← Older revision		Revision as of 13:29, 18 December 2024
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	== Thermoelectric coefficients and the ZT figure of merit ==		== Thermoelectric coefficients and the ZT figure of merit ==

	The ZT figure of merit is given as a function of the transport coefficients		The ZT figure of merit is given as a function of the transport coefficients and the absolute temperature, <math>T</math>:
	::<math>ZT=\frac{\sigma S^2}{\kappa_e+\kappa_l}</math>		::<math>ZT=\frac{\sigma S^2 T}{\kappa_e+\kappa_l}</math>

	~~Both the~~ conductivity <math>\sigma</math>, Seebeck coefficient <math>S</math> and the electronic contribution to the thermal conductivity <math>\kappa_e</math> are reported in the {{FILE\|OUTCAR}} file.		The conductivity <math>\sigma</math>, Seebeck coefficient <math>S</math> and the electronic contribution to the thermal conductivity <math>\kappa_e</math> are reported in the {{FILE\|OUTCAR}} file.
	The lattice thermal conductivity <math>\kappa_l</math> can be computed with an external package such as [https://phonopy.github.io/phono3py/ phono3py].		The lattice thermal conductivity <math>\kappa_l</math> can be computed with an external package such as [https://phonopy.github.io/phono3py/ phono3py].

	Because the Seebeck coefficient <math>S</math> and electronic contribution to the thermal conductivity <math>\kappa_e</math> depend on the first and second momentum of the transport function, a larger number of points ({{TAG\|TRANSPORT_NEDOS}}) is often required to obtain an accurate integration of these transport quantities than for the conductivity or mobility.		Because the Seebeck coefficient <math>S</math> and electronic contribution to the thermal conductivity <math>\kappa_e</math> depend on the first and second momentum of the transport function, a larger number of points ({{TAG\|TRANSPORT_NEDOS}}) is often required to obtain an accurate integration of these transport quantities than for the conductivity or mobility.

Miranda.henrique at 09:18, 17 October 2024

2024-10-17T09:18:02Z

← Older revision		Revision as of 09:18, 17 October 2024
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	#run electron-phonon calculation		#run electron-phonon calculation
	~~{{TAGBL\|ELPH_RUN}} = .TRUE.~~
	{{TAGBL\|ELPH_MODE}} = TRANSPORT		{{TAGBL\|ELPH_MODE}} = TRANSPORT

	# for the determination of the chemical potential		# for the determination of the chemical potential
	{{TAGBL\|EFERMI_NEDOS}} = ~~101~~ # number of integration points for {{TAG\|ELPH_ISMEAR}} = -24		{{TAGBL\|EFERMI_NEDOS}} = 501 # number of integration points for {{TAG\|ELPH_ISMEAR}} = -24
	{{TAGBL\|ELPH_ISMEAR}} = -24 # smearing method		{{TAGBL\|ELPH_ISMEAR}} = -24 # smearing method

	# for the computation of transport coefficients		# for the computation of transport coefficients
	{{TAGBL\|TRANSPORT_NEDOS}} = ~~101~~		{{TAGBL\|TRANSPORT_NEDOS}} = 501
	{{TAGBL\|ELPH_SELFEN_TEMPS}} = 0 100 200 300 400 500		{{TAGBL\|ELPH_SELFEN_TEMPS}} = 0 100 200 300 400 500

Miranda.henrique: /* Conductivity for metals */

2024-10-01T15:09:19Z

Conductivity for metals

← Older revision		Revision as of 15:09, 1 October 2024
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	Conductivity <math>\sigma_{\alpha\beta}</math> relates the current to the applied electric field		Conductivity <math>\sigma_{\alpha\beta}</math> relates the current to the applied electric field
	::<math> J_\alpha = \sigma_{\alpha\beta} E_\beta</math>		::<math> J_\alpha = \sigma_{\alpha\beta} E_\beta</math>
			<!--The conductivity is computed from the Onsager coefficient
	The conductivity is computed from the Onsager coefficient

	::<math> \quad \sigma = \mathcal{L}_{11} </math>		::<math> \quad \sigma = \mathcal{L}_{11} </math>
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	\mathcal{T}(\epsilon)=\frac{e^2}{V N} \sum_{\mathbf{k}n} \tau_{\mathbf{k}n} \mathbf{v}_{\mathbf{k}n} \otimes \mathbf{v}_{\mathbf{k}n} \delta(\epsilon-\epsilon_{\mathbf{k}n}) </math>		\mathcal{T}(\epsilon)=\frac{e^2}{V N} \sum_{\mathbf{k}n} \tau_{\mathbf{k}n} \mathbf{v}_{\mathbf{k}n} \otimes \mathbf{v}_{\mathbf{k}n} \delta(\epsilon-\epsilon_{\mathbf{k}n}) </math>

	with <math>V</math> the volume of the lattice, and N the number of k-point in the full Brillouin zone.		with <math>V</math> the volume of the lattice, and N the number of k-point in the full Brillouin zone.-->

	=== Constant relaxation-time approximation ===		=== Constant relaxation-time approximation ===
	The constant relaxation time is often a good approximation for metals because the density of states often changes little around the Fermi level.		The constant relaxation time is often a good approximation for metals because the density of states often changes little around the Fermi level.

← Older revision		Revision as of 09:18, 17 October 2024
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	#run electron-phonon calculation		#run electron-phonon calculation
	~~{{TAGBL\|ELPH_RUN}} = .TRUE.~~
	{{TAGBL\|ELPH_MODE}} = TRANSPORT		{{TAGBL\|ELPH_MODE}} = TRANSPORT

	# for the determination of the chemical potential		# for the determination of the chemical potential
	{{TAGBL\|EFERMI_NEDOS}} = ~~101~~ # number of integration points for {{TAG\|ELPH_ISMEAR}} = -24		{{TAGBL\|EFERMI_NEDOS}} = 501 # number of integration points for {{TAG\|ELPH_ISMEAR}} = -24
	{{TAGBL\|ELPH_ISMEAR}} = -24 # smearing method		{{TAGBL\|ELPH_ISMEAR}} = -24 # smearing method

	# for the computation of transport coefficients		# for the computation of transport coefficients
	{{TAGBL\|TRANSPORT_NEDOS}} = ~~101~~		{{TAGBL\|TRANSPORT_NEDOS}} = 501
	{{TAGBL\|ELPH_SELFEN_TEMPS}} = 0 100 200 300 400 500		{{TAGBL\|ELPH_SELFEN_TEMPS}} = 0 100 200 300 400 500

← Older revision		Revision as of 08:00, 5 February 2025
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	== Related tags and articles ==		== Related tags and articles ==
	* [[Bandgap renormalization due to electron-phonon coupling\|~~Bandstructure~~ renormalization]]		* [[Bandgap renormalization due to electron-phonon coupling\|Band-structure renormalization]]
	* [[Electron-phonon potential from supercells]]		* [[Electron-phonon potential from supercells]]
	* {{FILE\|phelel_params.hdf5}}		* {{FILE\|phelel_params.hdf5}}