Entropy and Seebeck signals meet on the edges

TL;DR

This study investigates the relationship between electronic entropy and Seebeck signals in zigzag graphene ribbons, revealing their close connection and potential use as spectroscopic probes of electronic energy scales in gapped materials.

Contribution

It demonstrates the correlated behavior of entropy and Seebeck signals in doped graphene ribbons and proposes their measurement as a spectroscopic tool for electronic energy scales.

Findings

Entropy and Seebeck signals develop sharp dip-peak lineshapes in the gap.

The ratio s/𝒮 approaches the elementary charge e at low temperatures.

Measurement of s and 𝒮 can probe electronic energy scales in gapped systems.

Abstract

We explore the electronic entropy per particle $s$ and Seebeck coefficient $\mathcal{S}$ in zigzag graphene ribbons. Pristine and edge-doped ribbons are considered using tight-binding models to inspect the role of edge states in the observed thermal transport properties. As a bandgap opens when the ribbons are doped at one or both edges, due to asymmetric edge potentials, we find that $s$ and $\mathcal{S}$ signals are closely related to each other: both develop sharp dip-peak lineshapes as the chemical potential lies in the gap, while the ratio $s/\mathcal{S}$ exhibits a near constant value equal to the elementary charge $e$ at low temperatures. This constant ratio suggests that $\mathcal{S}$ can be seen as the transport differential entropy per charge, as suggested by some authors. Our calculations also indicate that measurement of $s$ and $\mathcal{S}$ may be useful as a spectroscopic probe of different electronic energy scales involved in such quantities in gapped materials.