Observation of an interlayer-correlated fractional quantum Hall state in a trilayer electron system

In multilayer quantum Hall systems, when the interlayer separation is sufficiently small, the interplay between intralayer and interlayer Coulomb interactions can lead to exotic, multi-component, many-body states. A particular example is the even-denominator fractional quantum Hall state (FQHS) at total filling factor v = 1/2 in bilayer systems with negligible interlayer tunneling, understood as a generalized Laughlin state described by the Halperin-Laughlin Ψ₃₃₁ wavefunction. While such states have been extensively explored in bilayers, little is known about their counterparts in systems with more than two layers. Here, we investigate a trilayer two-dimensional electron system confined to ultrahigh-quality GaAs triple quantum wells with interlayer separation d/l_B ~ 2.8, where d is the center-to-center distance between neighboring wells and l_B is the magnetic length. We observe an exotic FQHS at total filling factor v = 5/7, evinced by a deep longitudinal resistance minimum and a quantized Hall plateau. This state is consistent with the long-predicted trilayer, generalized Laughlin state (ψ₃₃₃₁₁), characterized by v = 1/3-like intralayer correlation within each layer and v = 1-like interlayer correlation between neighboring layers [1]. Intriguingly, the v = 5/7 FQHS we observe is flanked by insulating phases, suggesting the emergence of correlated trilayer Wigner crystal phases.

[1] A. H. MacDonald, The fractional quantum Hall effect in multi-component systems, Surf. Sci. 229, 1-6 (1990).