Few-layer tungsten diselenide (WSe2) is investigated using circularly polarized Raman spectroscopy with up to eight excitation energies. The main E2g1 and A1g modes near 250 cm-1 appear as a single peak in the Raman spectrum taken without consideration of polarization but are resolved by using circularly polarized Raman scattering. The resonance behaviors of the E2g1 and A1g modes are examined. Firstly, both the E2g1 and A1g modes are enhanced near resonances with the exciton states. The A1g mode exhibits Davydov splitting for trilayers or thicker near some of the exciton resonances. The low-frequency Raman spectra show shear and breathing modes involving rigid vibrations of the layers and also exhibit strong dependence on the excitation energy. An unidentified peak at ~19 cm-1 that does not depend on the number of layers appears near resonance with the B exciton state at 1.96 eV (632.8 nm). The strengths of the intra- and inter-layer interactions are estimated by comparing the mode frequencies and Davydov splitting with the linear chain model, and the contribution of the next-nearest-neighbor interaction to the inter-layer interaction turns out to be about 34% of the nearest-neighbor interaction. Fano resonance is observed for 1.58-eV excitation, and its origin is found to be the interplay between two-phonon scattering and indirect band transition.
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