What is measured when measuring a thermoelectric coefficient?

Kamran Behnia

doi:10.5802/crphys.100

What is measured when measuring a thermoelectric coefficient?
[Que mesure-t-on en mesurant un coefficient thermoélectrique ?]

Kamran Behnia ¹

¹ Laboratoire de Physique et d’Etude de Matériaux (CNRS-Sorbonne University), ESPCI Paris, PSL University, 10 Rue Vauquelin, 75005 Paris, France

Comptes Rendus. Physique, Volume 23 (2022) no. S2, pp. 25-40.

corrigé par Corrigendum: What is measured when measuring a thermoelectric coefficient?

Résumé
Abstract

Dans un solide contenant des électrons itinérants, un gradient thermique génère un champ électrique. En présence d’un champ magnétique (ou une courbure de Berry) ce champ électrique a une composante transverse. Ces deux effets sont connus sous le nom de coefficients de Seebeck et de Nernst. Callen a soutenu, en 1948 que l’effet Seebeck quantifie l’entropie portée par un flux de particules chargées en l’absence de gradient thermique. De même, la conductivité de Nernst quantifie l’entropie portée par un flux de flux magnétique en l’absence de gradient thermique. Cet article résume une approche aux phénomènes thermoélectriques dans laquelle leur amplitude approximative est donnée par des constantes fondamentales et des longueur caractéristiques qui dépendent du matériau. Par conséquent, la connaissance de ces échelles de longueur permet de prédire l’amplitude du signal mesuré. Plus précisément, la conductivité de Nernst dans les métaux varie avec le carré du libre parcours moyen. Sa composante anormale dans les solides magnétiques est proportionnelle au carré de la longueur magnétique fictive. Dans l’état normal d’un supraconducteur, les paires de Cooper éphémères génèrent un signal qui évolue avec le carré de la longueur de cohérence supraconductrice. En dessous de la température critique, se signal devient celui produit par les vortex mobiles du supraconducteur en question.

A thermal gradient generates an electric field in any solid hosting mobile electrons. In presence of a finite magnetic field (or Berry curvature) this electric field has a transverse component. These are known as Seebeck and Nernst coefficients. As Callen argued, back in 1948, the Seebeck effect quantifies the entropy carried by a flow of charged particles in absence of thermal gradient. Similarly, the Nernst conductivity, $α_{x y}$ , quantifies the entropy carried by a flow of magnetic flux in absence of thermal gradient. The present paper summarizes a picture in which the rough amplitude of the thermoelectric response is given by fundamental units and material-dependent length scales. Therefore, knowledge of material-dependent length scales allows predicting the amplitude of the signal measured by experiments. Specifically, the Nernst conductivity scales with the square of the mean-free-path in metals. Its anomalous component in magnets scales with the square of the fictitious magnetic length. Ephemeral Cooper pairs in the normal state of a superconductor generate a signal, which scales with the square of the superconducting coherence length and smoothly evolves to the signal produced by mobile vortices below the critical temperature.

Reçu le : 2021-12-06
Révisé le : 2022-01-27
Accepté le : 2022-02-01
Première publication : 2022-03-23
Publié le : 2023-06-19

DOI : 10.5802/crphys.100

Keywords: Thermoelectricity, correlated electrons, topological materials
Mot clés : Thermoélectricité, électrons corrélés, matériaux topologiques

Affiliations des auteurs :

Kamran Behnia ¹

¹ Laboratoire de Physique et d’Etude de Matériaux (CNRS-Sorbonne University), ESPCI Paris, PSL University, 10 Rue Vauquelin, 75005 Paris, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {What is measured when measuring a thermoelectric coefficient?},
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Kamran Behnia. What is measured when measuring a thermoelectric coefficient?. Comptes Rendus. Physique, Volume 23 (2022) no. S2, pp. 25-40. doi : 10.5802/crphys.100. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.100/

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