A novel method distinguishing between topological orders*

Non-abelian anyons are prospective candidates for fault-tolerant topological quantum computation due to their long-range entanglement. The =5/2 quantum Hall state has been long proposed to host non-abelian quasiparticles. The gapless edge modes can mirror the topological order of the state, resting on ‘bulk-edge’ correspondence. Supporting an odd number of Majorana (neutral) modes guarantees the non-abelian nature of the state. Recent measurements of the state’s thermal conductance,  with =p²k_B²/3h, provided solid evidence for the non-abelian Particle-Hole Pfaffian (PH-Pf) topological order. Numerical calculations, however, favor the Pfaffian (Pf) and anti-Pfaffian (A-Pf) orders. Since the =5/2 state hosts integer, fractional, and neutral modes, it was suggested that lack of thermal equilibration among the different edge modes of the A-Pf order could account for the apparent PH-Pf order.

Isolating the non-abelian fractional channel (1/2+neutrals), may allow measuring its equilibrated thermal conductance and the chirality of the neutral mode(s) with fewer uncertainties. We exploited a novel approach to gap out the integer modes of the =5/2 state by interfacing it with =2 & =3. The electrical conductance of the interface channel was 0.5e²/h, as expected. More importantly, we find a thermal conductance with a single counter-propagating Majorana mode. This confirms the non-abelian PH-Pf topological order of the =1/2 channel. Our results open new avenues to manipulate and test other exotic QHE states and raise a question about the validity of the present numerical methods.