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We report a study of the quantum Hall states (QHSs) sequence of holes inmono- and bilayer WSe$_2$. The QHSs sequence transitions between predominantlyeven and predominantly odd filling factors as the hole density is tuned in therange $1.6 - 12\times10^{12}$ cm$^{-2}$. The QHSs sequence is insensitive tothe transverse electric field, and tilted magnetic field measurements reveal aninsensitivity of the QHSs sequence to the in-plane magnetic field, evincingthat the hole spin is locked perpendicular to the WSe$_2$ plane. Theseobservations imply that the QHSs sequence is controlled by theZeeman-to-cyclotron energy ratio, which remains constant as a function ofperpendicular magnetic field at a fixed carrier density, but changes as afunction of density due to strong electron-electron interaction.

Density-Dependent Quantum Hall States and Zeeman Splitting in Monolayer and Bilayer WSe$_2$