XY* transition and extraordinary boundary criticality from fractional exciton condensation in quantum Hall bilayer

TL;DR

This paper proposes studying XY* quantum criticality in quantum Hall bilayers at specific fillings, demonstrating a continuous transition driven by fractional exciton condensation, with unique boundary criticality and measurable experimental signatures.

Contribution

It introduces a new experimental platform using quantum Hall bilayers to observe XY* criticality and boundary phenomena, supported by exact diagonalization results.

Findings

Continuous transition driven by fractional exciton condensation.

Unusual properties include large anomalous exponent and fractional universal conductivity.

Edge states likely exhibit extraordinary boundary criticality.

Abstract

XY* transitions represent one of the simplest examples of unconventional quantum criticality, in which fractionally charged excitations condense into a superfluid, and display novel features that combine quantum criticality and fractionalization. Nevertheless their experimental realization is challenging. Here we propose to study the XY* transition in quantum Hall bilayers at filling $(\nu_1,\nu_2)=(\frac{1}{3},\frac{2}{3})$ where the exciton condensate (EC) phase plays the role of the superfluid. Supported by exact diagonalization calculation, we argue that there is a continuous transition between an EC phase at small bilayer separation to a pair of decoupled fractional quantum Hall states, at large separation. The transition is driven by condensation of a fractional exciton, a bound state of Laughlin quasiparticle and quasihole, and is in the XY* universality class. The fractionalization is manifested by unusual properties including a large anomalous exponent and fractional universal conductivity, which can be conveniently measured through inter-layer tunneling and counter-flow transport, respectively. We also show that the edge is likely to realize the newly predicted extra-ordinary boundary criticality. Our work highlights the promise of quantum Hall bilayers as an ideal platform for exploring exotic bulk and boundary critical behaviors, that are amenable to immediate experimental exploration in dual-gated bilayer systems.