ESPCI web site
Thursday September 29 at 2:00 pm (Paris time)
Room Charpak, entrance building
Identifying the topological order of exotic quantum Hall states and isolating ballistic non-abelian channels
Mitali Banerjee
Laboratory of Quantum Physics, Topology and Correlations, Institute of Physics,
Ecole Polytechnique Federal de Lausanne, 1015 Switzerland
Quantum Hall states – the progenitors of the growing family of topological insulators – are also a source of
exotic quantum states. These states can be abelian (e.g., integers & fractions) or non-abelian (e.g., special
fractions)., and thus may host electrons, fractionally charged quasiparticles, and neutral bosonic or
Majorana (in general, para-fermionic) quasiparticles. Since the bulk is insulating (with the quasiparticles
localized), counter-propagating gapless edge modes mirror the bulk’s topological order (due to ‘bulk-edge’
correspondence).
The most theoretically studied non-abelian state has a filling 𝜈=5/2. The state supports charge-
neutral quasiparticles accompanied by e/4 charges. This filling, however, permits different topological
orders, which can be abelian or non-abelian. While numerical calculations favor the non-abelian Anti-
Pfaffian (A-Pf) order, our recent thermal conductance measurements found the unexpected order, Particle-
Hole Pfaffian (PH-Pf). Employing a novel interface method, where the bulk of the 𝜈=5/2 filling was
interfaced with a bulk of integer filling 𝜈=2 or 𝜈=3, an isolated interface channel of 𝜈=1/2 emerged.
Studying the latter via measuring heat flow, we re-verified the PH-Pf order of the 𝜈=5/2 state (and its non-
abelian nature).
Identifying the correct topological order is crucial in testing the numerical predictions. While such
experiments are more complicated than the ubiquitous conductance measurements, their ‘power’ is already
evident. Moreover, isolating the fractional channel can be most helpful in complex interference (braiding)
experiments.
Banerjee et al, Nature. 545, 7652, 75-79 (2017)
Banerjee et al, Nature. 559, 7713, 205-210 (2018)
Dutta et al., Science. 375, 6577, 193-197 (2021)
Dutta et al., arXiv : 2109.11205, Science (submitted)
