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

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.