Session G45: Pairing in Fractional Quantum Hall Effect

Pairing in bilayer quantum Hall systems

Among the peculiar quantum Hall states that have been observed in Coulomb-coupled bilayer quantum Hall systems, there are a number whose origin depends on some type of pairing between constituent fermions.  For example, a fractional quantized state observed in a double layer of graphene separated by insulating hBN, at Landau-level filling 3/7 in each layer, requires pairing between electron-like composite fermions in one layer and hole-like composite fermions in the other. The interlayer coherent quantum Hall state observed in GaAs double quantum wells and in graphene double layers, at total Landau-level filling 1, may be variously understood as arising from pairing between electrons in one layer and holes in the other, as p-wave pairing of composite fermions in opposite layers, or as s-wave pairing between electron composite fermions in one layer and hole composite fermions in the other. I will discuss these concepts in the context of recent experimental observations and  theoretical developments concerning these systems.[1-4]   

Odd- and even-denominator fractional quantum Hall states in monolayer WSe2

Monolayer semiconducting transition-metal dichalcogenides (TMDs) represent a unique class of two-dimensional electron systems. Their atomically thin structure facilitates gate tunability just like graphene does, but unlike graphene, TMDs have the advantage of a sizable band gap and strong spin-orbit coupling. Here, through bulk electronic compressibility measurements, we investigate the LL structure of monolayer WSe₂ in the extreme quantum limit and observe fractional quantum Hall states in the lowest three LLs. The odd-denominator fractional quantum Hall sequences demonstrate a systematic evolution with the LL orbital index, consistent with generic theoretical expectations. In addition, we observe an even-denominator state in the second LL that is expected to host non-Abelian statistics. Our results suggest that the 2D semiconductors can provide an experimental platform that closely resembles idealized theoretical models in the quantum Hall regime.   

Graviton Chirality and Topological Order in the Half-filled Landau Level

Recent work[1] has established that fractional quantum Hall liquids support graviton-like excitations that carries definitive chirality. We apply this insight to the fractional quantum Hall state at Landau level (LL) filling factor ν = 5/2, which is extremely interesting because it is likely the first non-Abelian state, but its precise nature remains unclear after decades of study. We demonstrate this can be resolved by studying the chirality of its graviton excitations, using circularly polarized Raman scattering [2]. We also discuss the advantage of this bulk probe over the existing edge probes.   

Parton description of non-Abelian paired states

The fractional quantum Hall effect (FQHE) forms a paradigm in our understanding of strongly correlated systems. FQHE in the lowest Landau level (LLL) predominantly occurs at odd-denominator fillings and can be understood in terms of weakly interacting composite fermions, which are bound states of electrons and vortices. In the second LL (SLL), FQHE has been observed at even-denominator fillings such as 5/2 and 2+3/8 and a description of these states lies beyond the purview of non-interacting composite fermions. In this talk, I will demonstrate that these states can be understood using the "parton" theory which generalizes the idea of composite fermion. In particular, I will elucidate our recent work on the parton construction of wave functions to describe non-Abelian paired states that potentially capture the underlying physical mechanism for the FQHE observed in the SLL [1,2], at 1/4 in wide quantum wells of GaAs [3] and at 1/2 in the third LL of monolayer graphene [4]. More generally, our work suggests that the parton theory provides a unified description of the quantum Hall effects [5].   

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.