Density-Dependent Quantum Hall States and Zeeman Splitting in Monolayer and Bilayer WSe_{2}.

We report a study of the quantum Hall states (QHS) of holes in mono- and bilayer WSe_{2}. The QHS sequence transitions between predominantly even and predominantly odd filling factors as the hole density is tuned in the range 1.6-12×10^{12}  cm^{-2}. Measurements in tilted magnetic fields reveal an insensitivity of the QHS to the in-plane magnetic field, evincing that the hole spin is locked perpendicular to the WSe_{2} plane. Furthermore, the QHS sequence is insensitive to an applied electric field. These observations imply that the QHS sequence is controlled by the Zeeman-to-cyclotron energy ratio, which remains constant as a function of perpendicular magnetic field at a fixed carrier density, but changes as a function of density due to strong electron-electron interaction.