Origin of the turn-on temperature behavior in ${\mathrm{WTe}}_2$

A hallmark of materials with extremely large magnetoresistance (XMR) is the transformative turn-on temperature behavior: when the applied magnetic field $H$ is above certain value, the resistivity versus temperature $\rho \left(T\right)$ curve shows a minimum at a field dependent temperature $T^{*}$, which has been interpreted as a magnetic-field-driven metal-insulator transition or attributed to an electronic structure change. Here, we demonstrate that $\rho \left(T\right)$ curves with turn-on behavior in the newly discovered XMR material ${\mathrm{WTe}}_2$ can be scaled as $\text{MR}\sim {(H/{\rho }_0)}^m$ with $m\approx 2$ and ${\rho }_0$ being the resistivity at zero field. We obtained experimentally and also derived from the observed scaling the magnetic field dependence of the turn-on temperature $T^{*}\sim {(H-H_c)}^{\nu }$ with $\nu \approx 1/2$, which was earlier used as evidence for a predicted metal-insulator transition. The scaling also leads to a simple quantitative expression for the resistivity ${\rho }^{*}\approx 2{\rho }_0$ at the onset of the XMR behavior, which fits the data remarkably well. These results exclude the possible existence of a magnetic-field-driven metal-insulator transition or significant contribution of an electronic structure change to the low-temperature XMR in ${\mathrm{WTe}}_2$. This work resolves the origin of the turn-on behavior observed in several XMR materials and also provides a general route for a quantitative understanding of the temperature dependence of MR in both XMR and non-XMR materials.

Figure 1

Temperature dependence of the resistivity of sample I in various magnetic fields. Open symbols are experimental data in magnetic fields from 0 to $9\mathrm{T}$ at intervals of $0.5\mathrm{T}$. The red solid circles highlight the locations of the resistance minima. Dashed line represents the temperature dependence of the resistivity minima ${\rho }^{*}=[1+{(m-1)}^{-1}]{\rho }_0$ derived from Kohler's rule scaling $\text{MR}\sim {(H/{\rho }_0)}^m$ with ${\rho }_0$ being the experimental resistivity at zero field and $m=1.92$ (see text for more discussion). The inset shows the Fermi liquid (FL) behavior ${\rho }_0=A+B{T}^2$ for the resistivity at temperatures below $100\mathrm{K}$. Data were taken with magnetic fields applied along the $c$ axis of the crystal ($H\parallel c$) and current flowing along the $a$ axis.

Figure 2

Kohler's rule analysis of the temperature dependence of the resistivity. (a) Kohler's rule scaling of data in Fig. 1. The symbols are experimental data and solid line represents a fit to $\mathrm{MR}=25{(H/{\rho }_0)}^{1.92}$. (b) Temperature dependence of the resistivity at $0\mathrm{T}$ and $6\mathrm{T}$ and their differences. The solid lines are fits to Eq. (1) with $\alpha =25{[\mu \mathrm{\Omega }\mathrm{cm}/\mathrm{T}]}^{1.92}$ and $m=1.92$. We present data up to $200\mathrm{K}$ for clarity since the MR at $T>200\mathrm{K}$ is small $[\text{MR}\le 5\%$, the value at $200\mathrm{K}$ and $9\mathrm{T}$, see Fig. S2(a)].

Figure 3

Magnetic field dependence of $T^{*}$ for sample I. The red solid line is a fit to ${\rho }_0\left(T^{*}\right)=H{\left[\alpha (m-1)\right]}^{1/m}$ and the dashed blue line represents ${T^{*}}^2\sim H-0.5$.

Figure 4

Direct fits to the two-band model represented by Eq. (S1) for both the longitudinal (${\rho }_{xx}$) and Hall (${\rho }_{xy}$) resistivities of sample I. The green linear is a guide for the eyes. The upper and lower insets show the derived mobilities and densities of the electrons and holes.