Entropy-Seebeck ratio as a tool for elementary charge determination

TL;DR

This paper explores the entropy-Seebeck ratio in silicene nanoribbons as a thermodynamic tool for determining the elementary charge and characterizing electronic properties in two-dimensional systems.

Contribution

It introduces the entropy-Seebeck ratio as a novel thermodynamic method for elementary charge estimation and electronic characterization in 2D materials.

Findings

The ratio s/S converges to the elementary charge e within the band gap region.

s/S is undefined for gapless ribbons in the first transmission channel.

The ratio serves as a reliable probe for electronic band gap quality.

Abstract

In this work, we investigate the relationship between the Seebeck coefficient $(S)$, and the differential entropy per particle (DEP, $s$), as a tool for characterizing charge carriers in two-dimensional systems. Using armchair silicene nanoribbons as a model platform, we analyze how both quantities and their ratio depend on chemical potential at room temperature. While the Seebeck coefficient captures transport properties through the energy dependence of the electronic transmission, the DEP is directly connected to the system's electronic entropy, offering a direct thermodynamic alternative for estimating $S$. We evaluate these transport-thermodynamic properties considering diverse ribbon widths, defining metallic and semiconducting regimes. We find both quantities $S$ and $s$, are highly interconnected within the ribbon's band gap energy region, and their ratio $s/S$ converges to the elementary charge $e$ across that energy window, fulfilling the Kelvin formula $S=s/e$. On the contrary, $s/S$ is undefined for gapless ribbons in the energy window of the first transmission channel. These results establish the ratio between the DEP and the Seebeck coefficient as a reliable and complementary probe for the determination of the elementary charge, and to identify the cleanness of electronic band gaps as $s/S$ matches with $e$.