Fractional Quantized Hall States with Even Denominator*

Even-denominator fractional quantized Hall states have been seen in a variety of systems. In addition to the well-known states at filling fractions ν = 5/2 and 7/2 observed in GaAs narrow wells, even-denominator quantized states have been seen in Bernal-stacked bilayer graphene, in ZnO, and in GaAs double layers and wide quantum wells at total filling ν_total = ½. The precise nature of the quantized Hall states is a matter of debate in all these cases, and I will discuss some of the alternative theories. There is another case, however, where the situation is clear. Recent experiments on a system of two graphene layers separated by a thin insulator find, among other states, a quantized Hall state with filling ν = ¼ in each layer. Measurements of a quantized Hall drag, as well as quantized Hall resistance, show that the system has the characteristics of the 331 Abelian state.¹ [1] Xiaomeng Liu, Zeyu Hao, K. Watanabe, T. Taniguchi, B. Halperin, and P. Kim, arXiv:1810.08681.