Thermopower and Entropy: lessons from Sr$_2$RuO$_4$

TL;DR

This study combines electronic structure and dynamical mean-field theory to analyze the thermopower of Sr$_2$RuO$_4$, revealing insights into its crossover from Fermi liquid to incoherent metal and the role of Hund's physics.

Contribution

It provides a detailed theoretical analysis of thermopower in Sr$_2$RuO$_4$, highlighting the entropic origin of its temperature dependence and the impact of Hund's metal behavior.

Findings

Seebeck coefficient aligns with Kelvin formula predictions.

Entropy of spin degrees of freedom is released around room temperature.

High-temperature c-axis thermopower exceeds in-plane thermopower due to interlayer filtering.

Abstract

We calculate the in-plane Seebeck coefficient of Sr$_2$RuO$_4$ within a framework combining electronic structure and dynamical mean-field theory. We show that its temperature-dependence is consistent with entropic considerations embodied in the Kelvin formula, and that it provides a meaningful probe of the crossover out of the Fermi liquid regime into an incoherent metal. This crossover proceeds in two stages: the entropy of spin degrees of freedom is released around room-temperature while orbital degrees of freedom remain quenched up to much higher temperatures. This is confirmed by a direct calculation of the corresponding susceptibilities, and is a hallmark of `Hund's metals'. We also calculate the c-axis thermopower, and predict that it exceeds substantially the in-plane one at high-temperature, a peculiar behaviour which originates from an interlayer 'hole-filtering' mechanism.