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