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Shubnikov-de Haas oscillations of high mobility holes in monolayer and bilayer WSe$_2$: Landau level degeneracy, effective mass, and negative compressibility

We study the magnetotransport properties of high mobility holes in monolayer and bilayer WSe$_2$, which display well defined Shubnikov-de Haas (SdH) oscillations, and quantum Hall states (QHSs) in high magnetic fields. In both mono and bilayer WSe$_2$, the SdH oscillations and the QHSs occur predominantly at even filling factors, evincing a two-fold Landau level degeneracy. The Fourier transform analysis of the SdH oscillations in bilayer WSe$_2$ reveal the presence of two subbands localized in the top or the bottom layer, as well as negative compressibility. From the temperature dependence of the SdH oscillations we determine a hole effective mass of $0.45m_{0}$ for both mono and bilayer WSe$_2$.