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Mapping the twist angle disorder and unconventional Landau levels in magic angle graphene


  Aviram Uri  ,  Sameer Grover  ,  Yuan Cao  ,  J. Alex Cross  ,  Kousik Bagani  ,  Daniel Rodan-Legrain  ,  Yuri Meyasoedov  ,  Kenji Watanabe  ,  Takashi Taniguchi  ,  Pilkyung Moon  ,  Mikito Koshino  ,  Pablo Jarillo-Herrero  ,  Eli Zeldov  
 Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
New York University Shanghai and NYU-ECNU Institute of Physics at NYU Shanghai, Shanghai, China
National Institute for Material Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
Department of Physics, New York University, New York 10003, USA
State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
Department of Physics, Osaka University, Toyonaka, 560–0043, Japan

The emergence of flat electronic bands and strongly correlated and superconducting phases in twisted bilayer graphene [1,2] crucially depends on the interlayer twist angle upon approaching the magic angle θ ≈ 1.1°. Utilizing a scanning nanoSQUID-on-tip [3], we attain tomographic imaging of the Landau levels in the quantum Hall state in magic angle twisted bilayer graphene (MATBG) [4], which provides a highly sensitive local probe of the charge disorder, twist angle θ and the band structure. We obtain a map of the local θ variations in hBN encapsulated devices with relative precision better than 0.002° and spatial resolution of a few moiré periods. We find that devices exhibiting high-quality global MATBG features including superconductivity, display significant variations in the local θ with a span close to 0.1°. Devices may even have substantial areas where no local MATBG behavior is detected, yet still display global MATBG characteristics in transport, highlighting the importance of percolation physics. The derived θ maps reveal substantial gradients and a network of jumps. We show that θ gradients generate large gate-tunable in-plane electric fields, unscreened even in the metallic regions. These field drastically change the quantum Hall state by forming edge states in the bulk of the sample. We propose that such gradients may also significantly affect the phase diagram of correlated and superconducting states. We establish θ disorder as a new kind of disorder, fundamentally different from charge disorder.

1. Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, ''Unconventional superconductivity in magic-angle graphene superlattices'', Nature 556, 43 (2018).
2. Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R. C. Ashoori, and P. Jarillo-Herrero, ''Correlated insulator behaviour at half-filling in magic-angle graphene superlattices'', Nature 556, 80 (2018).
3. A. Uri, Y. Kim, K. Bagani, C. K. Lewandowski, S. Grover, N. Auerbach, E. O. Lachman, Y. Myasoedov, T. Taniguchi, K. Watanabe, J. Smet, and E. Zeldov, ''Nanoscale imaging of equilibrium quantum Hall edge currents and of the magnetic monopole response in graphene'', Nat. Phys. (2019).
4. A. Uri, S. Grover, Y. Cao, J. A. Crosse, K. Bagani, D. Rodan-Legrain, Y. Myasoedov, K. Watanabe, T. Taniguchi, P. Moon, M. Koshino, P. Jarillo-Herrero, and E. Zeldov, ''Mapping the twist angle and unconventional Landau levels in magic angle graphene'', arxiv:1908.04595 (accepted for publication in Nature).