Refining the Two-Band Model for Highly Compensated Semimetals Using Thermoelectric Coefficients

TL;DR

This paper refines the two-band model for highly compensated semimetals by analyzing thermoelectric coefficients in NbSb$_2$, revealing how magnetic field dependence can improve understanding of carrier compensation and thermoelectric performance.

Contribution

It introduces a method to refine the two-band model using thermoelectric coefficients' field dependence, providing more accurate carrier compensation estimates in semimetals.

Findings

Thermoelectric coefficients increase quadratically and linearly with magnetic field.

Refined compensation factor is two orders of magnitude smaller than previous estimates.

Thermoelectric Hall angle relates to carrier imbalance and magnetic field parameters.

Abstract

In studying compensated semimetals, the two-band model has proven extremely useful in capturing electrical conductivity under magnetic field, as a function of density and mobility of electron-like and hole-like carriers. However, it rarely offers practical insight into magneto-thermoelectric properties. Here, we report the field dependence of thermoelectric (TE) coefficients in a highly compensated semimetal NbSb$_2$, where we find the Seebeck and Nernst coefficients increase quadratically and linearly with applied magnetic field, respectively. Such field dependence was predicted in previous work that studied a system of two parabolic bands, within semiclassical Boltzmann transport theory when the following two conditions are simultaneously met:$\omega_c\tau \gg 1$ and $\tan\theta_H \ll 1$. Under these conditions, we find the field dependence of the TE coefficients directly provides a relation between the electron-like ($n_e$) and hole-like ($n_h$) carrier densities, which in turn can be used to refine two-band model fitting. With this, we find the compensation factor ($\frac{|\Delta n|}{n_e}$) of NbSb$_2$ is two orders of magnitude smaller than what was found in unrestricted fitting, resulting in a larger saturation field scale for magnetoresistance. Within the same framework of the semiclassical theory, we also deduce that the thermoelectric Hall angle $\tan\theta_{\gamma} = \frac{S_{xy}}{S_{xx}}$ can be expressed as $\big(\frac{|\Delta n|}{n_e} \times \omega_c\tau\big)^{-1}$, which serves as a parameter to predict the degree of compensation. Our findings offer crucial insights into identifying empirical conditions for field-induced enhancement of TE performance and into engineering efficient thermoelectric devices based on semimetallic materials.