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

## TL;DR

This study investigates the quantum Hall states in monolayer and bilayer WSe$_2$, revealing how their sequence depends on hole density and is influenced by electron-electron interactions and Zeeman effects.

## Contribution

It demonstrates the density-dependent transition of quantum Hall state sequences and their insensitivity to electric and in-plane magnetic fields in WSe$_2$, highlighting the role of Zeeman-to-cyclotron energy ratio.

## Key findings

- QHSs sequence transitions between even and odd filling factors with density.
- QHSs sequence is unaffected by transverse electric field.
- Sequence remains insensitive to in-plane magnetic field.

## Abstract

We report a study of the quantum Hall states (QHSs) sequence of holes in mono- and bilayer WSe$_2$. The QHSs sequence transitions between predominantly even and predominantly odd filling factors as the hole density is tuned in the range $1.6 - 12\times10^{12}$ cm$^{-2}$. The QHSs sequence is insensitive to the transverse electric field, and tilted magnetic field measurements reveal an insensitivity of the QHSs sequence to the in-plane magnetic field, evincing that the hole spin is locked perpendicular to the WSe$_2$ plane. These observations imply that the QHSs 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.