  Orthorhombic tungsten ditelluride (WTe2), with a distorted 1T structure,
exhibits a large magnetoresistance that depends on the orientation, and its
electrical characteristics changes rom semimetallic to insulating as the
thickness decreases. Through polarized Raman spectroscopy in combination with
transmission electron diffraction, we establish a reliable method to determine
the thickness and crystallographic orientation of few-layer WTe2. The Raman
spectrum shows a pronounced dependence on the polarization of the excitation
laser. We found that the separation between two Raman peaks at ~90 cm-1 and at
80-86 cm-1, depending on thickness, is a reliable fingerprint for determination
of the thickness. For determination of the crystallographic orientation, the
polarization dependence of the A1 modes, measured with the 632.8-nm excitation,
turns out to be the most reliable. We also discovered that the polarization
behaviors of some of the Raman peaks depend on the excitation wavelength as
well as thickness, indicating a close interplay between the band structure and
anisotropic Raman scattering cross section.
