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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 $R(H,θ)=R(\varepsilon_θH)$ with $\varepsilon_θ=(\cos^2 θ+ γ^{-2}\sin^2 θ)^{1/2}$, $θ$ being the magnetic field angle with respect to c-axis of the crystal and $γ$ being the mass anisotropy; (2) the mass anisotropy $γ$ 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.