Identification of an Isolated Non-Abelian Channel

Possiblities of long range entaglement in non-abelian anyons make them one of the most sought after in the field of condensed matter physics. This particular quality also brought them in the front line as prospective candidates for fault-tolerant topological quantum computation. Interestingly, what makes these quasiparticles elusive to most conventional measurement techniques is their charge-neutral characteristics. A proposed host of such quasiparticles is the ν=5/2 quantum Hall effect state. Their gapless edge modes are ideal candidates for braiding experiments, which can reveal state’s topological order and its robustness to decoherence. Since the ν=5/2 state hosts a variety of edge modes (integer, fractional, neutral), a robust technique is needed to isolate the non-abelian modes while assuring that their original character remain intact. Recent thermal conductance measurements of the ν=5/2 state already showed a fractional character [1], compared to an integer of abelian states. However, the nature of the isolated ν=1/2 mode must be demonstrated. In this work we exploit a novel technique to gap-out the integer modes of the ν=5/2 state by interfacing it with integer states ν=2 & ν=3 [2]. We observed a thermal conductance of 0.5κ₀T(with κ₀=π²k_B²/3h a universal constant), assuring the non-abelian nature of the ν=1/2 channel and its Particle-Hole Pffafian topological order [3]. Our result opens new avenue to manipulate and test other QHE states, as well as braid, via interference of the isolated exotic modes.

References:

[1] Banerjee, M. et al. Nature 559, 205-210, doi:10.1038/s41586-018-0184-1 (2018).

[2] Dutta, B. et al. arXiv preprint arXiv:2101.01419 (2021).

[3] B. Dutta. et al. arXiv preprint arXiv:2109.11205 (2021).