The Kelvin Formula for Thermopower

Abstract

Thermoelectrics are important in physics, engineering, and material science due to their useful applications and inherent theoretical difficulty, especially in strongly correlated materials. Here we reexamine the framework for calculating the thermopower, inspired by ideas of Lord Kelvin from 1854. We find an approximate but concise expression, which we term as the Kelvin formula for the the Seebeck coefficient. According to this formula, the Seebeck coefficient is given as the particle number $N$ derivative of the entropy $\Sigma$, at constant volume $V$ and temperature $T$, $S_{\text{Kelvin}}=\frac{1}{q_e}\{\frac{\partial \Sigma }{\partial N}{\}}_{V,T}$. This formula is shown to be competitive compared to other approximations in various contexts including strongly correlated systems. We finally connect to a recent thermopower calculation for non-Abelian fractional quantum Hall states, where we point out that the Kelvin formula is exact.

6 pages, 2 figures

References in corpus (6)

• Thermopower as a Possible Probe of Non-Abelian Quasiparticle Statistics in Fractional Quantum Hall Liquids
• Unified electronic phase diagram for hole-doped high-Tc cuprates
• Mottness in High-Temperature Copper-Oxide Superconductors
• Strong Correlations Produce the Curie-Weiss Phase of Na${}_x$CoO${}_2$
• Thermoelectric effects in a strongly correlated model for Na${}_x$CoO${}_2$
• Finite temperature properties of the triangular lattice t-J model, applications to Na${}_x$CoO${}_2$

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