Fractional quantum Hall states and oscillatory Landau charge squeezing in Bernal tetralayer graphene

The precise layer-number control in graphene provides valuable opportunities to explore the physics from the two-dimensional limit to the bulk crystalline regime. As the thickness increases, a fundamental question is how this increased dimensionality influences the integer and fractional quantum Hall states. Here, we perform magnetotransport measurements on high-quality Bernal tetralayer graphene and uncover a variety of fractional quantum Hall states at filling factors with both odd-denominator and even ones (ν − 1/2 = 3, 5, 7, 8, 10), which may be non-Abelian states. Moreover, the fractional quantum Hall states exhibit a sawtooth pattern when an out-of-plane displacement field D is tuned. Theoretical calculations reveal that these patterns arise from oscillatory Landau charge squeezing effect caused by subtle competitions between Landau levels with vastly disparate spatial distributions. Our results establish Bernal tetralayer graphene as a promising platform, where the layer degree of freedom provides distinctive tunability to explore rich correlated phenomena. Fractional quantum Hall states have been observed in monolayer, bilayer and trilayer graphene. Here, the authors observe in Bernal tetralayer graphene fractional quantum Hall states at filling factors with both even- and odd-denominators as well as an oscillatory Landau charge squeezing effect.