Studying non-abelian anyons is exciting due to their unique braiding statistics. The 5/2 quantum Hall state has been long proposed to host such localized quasiparticles in the 2D bulk. Resting on ‘bulk-edge’ correspondence, their gapless edge modes are expected to mirror the topological order of the 5/2 quantum state. Supporting an odd number of Majorana (neutral) modes guarantees the non-abelian nature of the state.

Current measurements and its fluctuations provide the state's quantized conductance and the quasiparticles’ charge. However, these measurements are blind to charge-neutral, energy-carrying currents. However, measurements of heat flow are sensitive to all energy-carrying modes. The thermal conductance , with J_th - heat power, T - temperature, and k - thermal conductance coefficient. Interestingly, k=k₀ for a single abelian modes (fractional or integer, and bosonic neutral), while k=0.5k₀ for a Majorana mode (being ‘half a fermion’). [ =p²k_B²/3h; k_B-Boltzman, h-Planck]

Recent thermal conductance measurements of the 5/2 state found, ; thus proving its non-abelian nature, and, moreover, its Particle-Hole Pfaffian (PH-Pf) topological order (in a few samples with similar disorder). Numerical calculations, however, favored the anti-Pfaffian (A-Pf) topological order. It has been suggested that a possible lack of thermal equilibration among the different counter-propagating edge modes (charge and neutral) could account for the apparent PH-Pf topological order.

In order to simplify the inter-multiple-mode thermal equilibration, the fractional channel of the 5/2 state (‘1/2 charge’+neutral modes) was isolated by gapping out the integer modes. This was accomplished by interfacing the ‘5/2 bulk’ with a neighboring ‘integer bulk’ (fillings 2 & 3), leading, as expected, to an interface channel with conductance 0.5e²/h. Two experiments were performed on the isolated ‘1/2 channel’: i Testing the chirality of the neutral (Majorana) modes in the non-thermally equilibrated regime of the ‘1/2 channel’ (via noise measurements); ii. Measuring the thermal conductance of the ‘1/2 channel’ in the equilibrated regime. These measurements confirmed the non-abelian PH-Pf order of the 5/2 state. Work is now conducted on samples with different disorder, in order to verify the universality of the observed topological order.

Banerjee et al, Nature 545, 2017;  Banerjee et al, Nature 559, 2018;  Dutta et al., Science 375, 2022;  Dutta et al., Science 377, 2022.