Nonsaturating large magnetoresistance in semimetals

Abstract

The rapidly expanding class of quantum materials known as topological semimetals (TSMs) displays unique transport properties, including a striking dependence of resistivity on applied magnetic field, that are of great interest for both scientific and technological reasons. So far, many possible sources of extraordinarily large nonsaturating magnetoresistance have been proposed. However, experimental signatures that can identify or discern the dominant mechanism and connect to available theories are scarce. Here we present the magnetic susceptibility (χ), the tangent of the Hall angle ([Formula: see text]), along with magnetoresistance in four different nonmagnetic semimetals with high mobilities, NbP, TaP, NbSb₂, and TaSb₂, all of which exhibit nonsaturating large magnetoresistance (MR). We find that the distinctly different temperature dependences, [Formula: see text], and the values of [Formula: see text] in phosphides and antimonates serve as empirical criteria to sort the MR from different origins: NbP and TaP are uncompensated semimetals with linear dispersion, in which the nonsaturating magnetoresistance arises due to guiding center motion, while NbSb₂ and TaSb₂ are compensated semimetals, with a magnetoresistance emerging from nearly perfect charge compensation of two quadratic bands. Our results illustrate how a combination of magnetotransport and susceptibility measurements may be used to categorize the increasingly ubiquitous nonsaturating large magnetoresistance in TSMs.

Keywords: Weyl semimetals; magnetic susceptibility; nonsaturating magnetoresistance; topological semimetals.

Fig. 1.

Schematically depicted nonsaturating MR phenomena and representative energy dispersions for phosphides (TaP) (Left) and antimonates (TaSb₂) (Right). The phosphides’ MR is characterized by quasi-linear to linear transition as $H$ increases, while the antimonates’ MR is characterized by persistent quadratic $H$ dependence, arising from semiclassical charge compensation. Each bar indicates $\mathrm{\Delta }\rho /{\rho }_0=5\times 10^5\%$. Magnetic field was applied up to ${\mu }_{0}H=31$ T at $T=0.3$ K.

Fig. 2.

(A and B) The Hall angle ${\tan \theta }_H$ (A) for NbP (red) and NbSb₂ (green) as a function of $H$ and (B) for TaP (magenta) and TaSb₂ (black), measured at $T=0.3$ K. Strong quantum oscillations in phosphides result in spike-like features. (C) ${\tan }^2{\theta }_H$ measured at ${\mu }_{0}H=7$ T as a function of $T$. (Inset) ${\tan }^2{\theta }_H$ vs. $T$ plotted in log – scale in the y axis scale, where NbSb₂ and TaSb₂ data are clearly resolved.

Fig. 3.

${\rho }_{xx}\left(T\right)$ at different $H$s is shown for (A) NbP, (B) TaP, (C) NbSb₂, and (D) TaSb₂. ${\rho }_{xx}^{\prime }\left(T\right)$ at ${\mu }_{0}H=7$ T, defined in Eq. 1, is plotted in A–D, Insets.

Fig. 4.

(A–D) Kohler’s plots of phosphides in (A) NbP and (B) TaP and of antimonates in (C) NbSb₂ and (D) TaSb₂. Arrows in A and B indicate the locations of $H_S$, where ${\tan \theta }_H$ saturates and the MR switches to $H$ linear.

Fig. 5.

${\rho }_{xy}\left(H\right)$ as a function of $H$ in (A) NbP and (B) NbSb₂, measured at $T=0.3$ K. Note the difference of the magnitude of ${\rho }_{xy}$. Dashed line in A shows a fit to Eq. 3 and dashed line in B shows a fit to a two-band model (SI Appendix, section 1). ${\rho }_{xy}\left(H\right)$’s up to 31 T are shown in A and B, Insets, where the small boxes correspond to the main panels.

Fig. 6.

(A and B) $\chi$ vs. $T$ in the phosphides (red) and antimonates (blue), measured at ${\mu }_{0}H=1$ T. Solid line is fit to Eq. 2, which gives $\mu =-40$ meV for one linear node for NbP (A) and ${\mu }_1=51$ meV and ${\mu }_2=-11$ meV for two linear nodes for TaP (B). Arrows indicate the locations of $T_{min}$ (main text).