Anyon superfluid in trilayer quantum Hall systems

TL;DR

This paper demonstrates that a trilayer quantum Hall system can host an exotic phase where neutral anyon-excitons condense, coexisting with topological order and gapless modes, bridging known quantum Hall states.

Contribution

It introduces the concept of an anyon-exciton condensate in trilayer quantum Hall systems, combining topological order with gapless collective excitations, supported by DMRG and field theory analysis.

Findings

Identification of an intermediate anyon-exciton condensate phase

Coexistence of Goldstone mode with fractionalized anyons

Experimental signatures include vanishing double-counter-flow resistance

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 $\nu_{1}=\nu_{2}=\nu_{3}= \frac13$, 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 $\nu_{\mathrm{tot}}=1$ exciton condensate ($d \to 0$) from three decoupled Laughlin liquids ($d \to \infty$). In this phase, neutral bi-excitons condense while a $\nu=\frac23$ 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.