Superconductivity of neutral modes in quantum Hall edges

The edges of quantum Hall phases give rise to a multitude of exotic modes supporting quasiparticles of different values of charge and quantum statistics. Among these are neutralons (chargeless anyons with semion statistics), which were found to be ubiquitous in fractional quantum Hall matter. Studying and manipulating the neutral sector is an intriguing and interesting challenge, all the more so since these particles are accessible experimentally. Here, we address the limit of strongly interacting neutralons giving rise to neutralon superconductivity, where pairing is replaced by a quarteting mechanism. We discuss several manifestations of this effect, realizable in existing experimental platforms. Furthermore, this superconducting gapping mechanism may be exploited to facilitate the observation of interference of the accompanying charged anyons.

Figure 1

(a) Bilayer FQH structure where neutralons can be gapped. We consider an interface where both the bottom and top layers of the structure have an interface described by the KFP theory for the $\nu =2/3$ FQH state. The filling fractions are chosen in a way that produces opposite spin polarizations for the top and bottom layers. (b) Edge spectrum of the clean limit. Correlated intralayer backscattering process (green curved arrows) that contributes to pairing of neutralons at low energies. (c) The characteristic temperature scales and the two-step RG flow towards low temperature (large white arrows). The bare edge modes at high temperatures on the left, with a Coulomb interaction (yellow wiggly line), random backscattering (solid line with a cross), and correlated intralayer backscattering (curved arrows connected by a dashed line). As temperature is lowered below $D_{\text{KFP}}$, the edge is described by the KFP low-energy theory (middle panel) of $2e/3$ charge modes and disordered neutral modes with a pairing interaction (green wiggly double line line). At temperatures below ${\mathrm{\Delta }}_n$, quartets of neutralons become gapped (blue ellipse) and only the charge modes remain (right panel). Their opposite spin polarization prevents backscattering.

Figure 2

Two quantum point contact (QPC) designs showing the composite edge of Fig. 1 from the top. For the sake of clarity, we have shifted the top and bottom layers laterally. Both sides of the QPC are at the fixed point where neutral modes are localized. Each side therefore hosts a helical pair of $2e/3$ charge modes with a spin up (down) mode living on the bottom (top) layer of the double quantum well. Tunneling across the QPC is assumed to conserve the spin eigenvalue. The figures show two different setups: In (a) the top layer quasiparticles tunnel through a $\nu =2/3$ bulk rather than a trivial vacuum (in the bottom layer tunneling is through a $\nu =1$ trivial vacuum). In (b), in both layers quasiparticles tunnel through a fractional $\nu =2/3$ vacuum. These two setups have different zero-bias anomalies in the tunneling current and different shot noise Fano factors. Inset: A Mach-Zehnder interferometer is not susceptible to dephasing from neutral modes provided its linear size $L$ exceeds the neutral mode decay length, $L\gg v_0/{\mathrm{\Delta }}_n$, and the bias voltage is low, $eV\ll {\mathrm{\Delta }}_n$.