Temperature dependent three-dimensional anisotropy of the magnetoresistance in WTe$_2$

Extremely large magnetoresistance (XMR) was recently discovered in WTe$_2$, triggering extensive research on this material regarding the XMR origin. Since WTe$_2$ is a layered compound with metal layers sandwiched between adjacent insulating chalcogenide layers, this material has been considered to be electronically two-dimensional (2D). Here we report two new findings on WTe$_2$: (1) WTe$_2$ is electronically 3D with a mass anisotropy as low as $2$, as revealed by the 3D scaling behavior of the resistance $R(H,\theta)=R(\varepsilon_\theta H)$ with $\varepsilon_\theta =(\cos^2 \theta + \gamma^{-2}\sin^2 \theta)^{1/2}$, $\theta$ being the magnetic field angle with respect to c-axis of the crystal and $\gamma$ being the mass anisotropy; (2) the mass anisotropy $\gamma$ varies with temperature and follows the magnetoresistance behavior of the Fermi liquid state. Our results not only provide a general scaling approach for the anisotropic magnetoresistance but also are crucial for correctly understanding the electronic properties of WTe$_2$, including the origin of the remarkable 'turn-on' behavior in the resistance versus temperature curve, which has been widely observed in many materials and assumed to be a metal-insulator transition.