Session N37: Unconventional fractional quantum Hall States

Even-denominator fractional quantum Hall effect in the lowest Landau level

I will present our observation of numerous, even-denominator fractional quantum Hall states in the lowest Landau level in world-record, ultra-high-mobility, 2D hole systems confined to GaAs quantum wells.   

Updates on the fractional quantum Hall effect in bilayer graphene

In a magnetic field, strong electron-electron interaction leads to the celebrated fractional quantum Hall (FQH) effect, in particular even-denominator FQH states, which are predicted to host non-Abelian excitations essential for topological quantum computing. Bernal-stacked bilayer graphene (BLG) introduces new twists to this well-studied phenomenon owing to orbital and valley pseudospins. In this talk, I’ll discuss our recent results in understanding the FQH effect in BLG and the realization of a Fabry-Pérot edge state interferometer. By finely tuning the electrical valley isospin Zeeman splitting in high-quality, dual-gated devices, we observe a new even-denominator state in BLG at filling factor ν = 5/2, which is spontaneously polarized in the limit of vanishing valley Zeeman splitting. Higher order FQH states with the denominators of 13 and 17, as described in Levin and Halperin, PRB 79, 205301 (2009), are observed in the vicinity of the even-denominator states at filling factors -1/2, 3/2, 5/2, and 7/2. Their appearance points to particle-hole asymmetric wave functions, i.e. Pfaffian or anti-Pfaffian, at the even-denominator FQH states[1].

I will also discuss the fabrication and operation of a Fabry-Pérot interferometer. We observe Aharonov-Bohm oscillations at integer quantum Hall states and discuss relevant parameters [2]. This new device architecture will enable future studies of fractional and non-Abelian braiding statistics in bilayer graphene. 

In collaboration with Ke Huang, Hailong Fu, Morteza Kayyalha, Danielle Hickey, Nasim Alem, Xi Lin, Kenji Watanabe, and Takashi Taniguchi

 

[1] Huang et al., “Valley Isospin Controlled Fractional Quantum Hall States in Bilayer Graphene”, Phys. Rev. X. 12, 031019 (2022).

[2] Fu et al., “Aharonov–Bohm Oscillations in Bilayer Graphene Quantum Hall Edge State Fabry–Pérot Interferometers”, https://doi.org/10.1021/acs.nanolett.2c05004

    

Author not Attending

The quantization of the electrical Hall conductance in quantum Hall (QH) states was established long back. Although electrical Hall conductance has been widely used to understand the topological order of a QH state, it turns out to be insufficient in the hierarchical fractional quantum Hall (FQH) states, where the edge structure is complicated, and transport may occur via both the downstream (dictated by the external magnetic field) and upstream modes. The electrical Hall conductance only reveals about the downstream charged chiral edge modes and remains insensitive to the total number of the edge modes, their chirality, and character. By contrast, the quantized thermal Hall conductance is not only sensitive to the downstream charged modes, but it can also detect the other upstream modes, including the charge-less neutral modes and the celebrated Majorana modes.  Here, we utilize the sensitive Jhonson-Nyquist noise thermometry to measure the quantized thermal conductance to probe the topological edge structure of the various QH states in single-layer and bilayer graphene. We establish the universality of thermal conductance in graphene by measuring its quantized values for integer and “particle-like” FQH states. Further, we show that the thermal conductance for “hole-like” FQH states having counter-propagating downstream (N_d) and upstream (N_u) modes depends on the extent of equilibration between the modes. By tuning the equilibration, we could achieve the crossover between the two asymptotic limits of the quantized values; (N_d + N_u)k_oT and (N_d - N_u)k_oT for ‘NO’ and ‘FULL’ equilibration, respectively. These experimental findings pave the way to resolve the dichotomy between different models of edge structure or, in general, to determine the topological edge quantum numbers of FQH states in graphene.   

Emergent phases in nearly degenerate Landau levels of the state-of-the-art GaAs quantum wells

Semiconductor GaAs/AlGaAs-based 2D systems, famous for first observations of fractional quantum Hall (FQH) effects, stripe and bubble phases, microwave–induced resistance oscillations/zero-resistance states, and excitonic Bose condensates, continue to attract interest and bring more surprises. In our recent studies we have employed an in-plane magnetic field to bring Landau levels close to degeneracy in the state-of-the-art GaAs quantum wells [1] and observed several emergent phases. First, the talk will report observation of a highly anisotropic phase which emerges in the vicinity of filling factor 7/3. While reminiscent of quantum Hall stripe phases in high half-filled Landau levels (commonly found at filling factors 9/2, 11/2, 13/2, …), this phase emerges only in a narrow range of in-plane magnetic fields. Second, the talk will discuss uncorrelated two-component FQH states, some of which have been previously observed in wide quantum wells, in which the second electrical subband was occupied in a purely perpendicular magnetic field. However, many more higher-order fractions (such as 109/99 and 106/117) have emerged in our experiments using “normal”, single-subband quantum wells. Finally, the talk will presenty evidence for unconventional FQH states at filling factors, such as 19/13, which were predicted to occur due to correlations between nearly degenerate Landau levels more than two decades ago [2].

[1] Y Yoon Jang Chung, K. A. Villegas Rosale, K. W. Baldwin, P. T. Madathil, K. W. West, M. Shayegan, L. N. Pfeiffer, Nat. Mater. 20, 632–637 (2021).

[2] V. W. Scarola and J. K. Jain, Phys. Rev. B 64, 085313 (2001).   

Exploring the quantum Hall landscape with duality

It is an important open problem to understand the landscape of exotic fractional quantum Hall (FQH) phases accessible to physically motivated theories of composite particles. Of particular interest are (i) non-Abelian FQH phases and (ii) strongly coupled quantum critical states of particles strongly interacting with emergent gauge fields. I will show that progress can be made using the recently proposed family of boson-fermion dualities in two spatial dimensions. In the quantum Hall context, these dualities connect the dynamics of the ordinary, Abelian composite particles to dual degrees of freedom coupled to (Abelian or non-Abelian) gauge fields. In the dual variables, exotic states may be more transparently accessible, for example through pairing, filling of Landau levels, or behavior in periodic electric or magnetic fields. In this talk, I will consider the particular example of the Fibonacci FQH state of bosons at filling ν = 2, which is salient as the simplest platform for a universal topological quantum computer. Starting with a parent trilayer of Abelian FQH states, I will present a construction of the Fibonacci state using duality with a theory of bosonic "composite vortices" coupled to an emergent U(2) gauge field, which cluster between the layers to form the Fibonacci state. Beyond non-Abelian phases, I will also discuss a proposal using duality for how strongly interacting quantum critical states of Dirac fermions coupled to gauge fields can emerge in Dirac materials with spatially periodic magnetic fields.