Isolated Ballistic Non-Abelian Interface Channel

TL;DR

This paper demonstrates a method to isolate and confirm the non-abelian nature of fractional edge channels in the $ u$=5/2 quantum Hall state by interfacing it with integer states, enabling new quantum manipulation techniques.

Contribution

The authors introduce a novel approach to gap out integer modes in the $ u$=5/2 state, isolating the non-abelian fractional channel and confirming its topological order through conductance measurements.

Findings

Electrical conductance of 0.5e$^2$/h observed

Thermal conductance of 0.5$ imes\kappa_0$T confirmed non-abelian order

Method enables manipulation and testing of exotic quantum Hall states

Abstract

Non-abelian anyons are prospective candidates for fault-tolerant topological quantum computation due to their long-range entanglement. Curiously these quasiparticles are charge-neutral, hence elusive to most conventional measurement techniques. A proposed host of such quasiparticles is the $\nu$=5/2 quantum Hall state. The gapless edge modes can provide the topological order of the state, which in turn identifies the chirality of the non-abelian mode. Since the $\nu$=5/2 state hosts a variety of edge modes (integer, fractional, neutral), a robust technique is needed to isolate the fractional channel while retaining its original non-abelian character. Moreover, a single non-abelian channel can be easily manipulated to interfere, thus revealing the state's immunity to decoherence. In this work, we exploit a novel approach to gap-out the integer modes of the $\nu$=5/2 state by interfacing the state with integer states, $\nu$=2 & $\nu$=3 (1). The electrical conductance of the isolated interface channel was 0.5e$^2$/h, as expected. More importantly, we find a thermal conductance of 0.5$\kappa_0$T (with $\kappa_0$=$\pi^2k_B^2$/3h), confirming unambiguously the non-abelian nature of the $\nu$=1/2 interface channel and its Particle-Hole Pfaffian topological order. Our result opens new avenues to manipulate and test other exotic QHE states and braid, via interference, the isolated fractional channels.