What is measured when measuring a thermoelectric coefficient?

TL;DR

This paper reviews how thermoelectric coefficients like Seebeck and Nernst are fundamentally linked to entropy transport and material length scales, providing a predictive framework for experimental measurements across different materials.

Contribution

It offers a unified picture connecting thermoelectric responses to fundamental units and material-dependent length scales, enhancing understanding and prediction of experimental signals.

Findings

Nernst conductivity scales with the square of the mean-free-path in metals.

Anomalous Nernst response in magnets scales with the square of the magnetic length.

Superconducting fluctuations produce signals scaling with the coherence length.

Abstract

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, $\alpha_{xy}$, 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.