Anyon superfluid in trilayer quantum Hall systems

Abstract

Intertwining intrinsic topological order with gapless collective modes remains a central challenge in many-body physics. We show that a quantum-Hall trilayer at $\hat{I}{½}_1=\hat{I}{½}_2=\hat{I}{½}_3=\frac{1}{3}$, tuned solely by the inter-layer spacing $d$, realizes this goal. Large-scale density-matrix renormalization group (DMRG) calculations and a Chern-Simons field theory analysis reveal an intermediate ``anyon-exciton condensate'' separating the familiar $\hat{I}{½}_{\mathrm{tot}}=1$ exciton condensate ($d\to 0$) from three decoupled Laughlin liquids ($d\to \infty$). In this phase, neutral bi-excitons condense while a $\hat{I}½=\frac{2}{3}$ Laughlin topological order survives, yielding a Goldstone mode coexisting with fractionalized anyons. A Ginzburg-Landau analysis maps out the finite-temperature phase diagram. The anyon-exciton condensate can be experimentally verified through a vanishing double-counter-flow resistance and a fractional layer-resolved Hall resistivity $R_{xy}=\frac{5}{2}h/e^2$, both within reach of existing high-mobility trilayer devices.

7 pages, 1 figure