Nanoscale imaging of quantum Hall edge currents in single layer graphene and in
magic angle twisted bilayer graphene
Aviram Uri, Weizmann Institute of Science
The recently predicted topological magnetoelectric effect [1] is a fundamental attribute of topological
states of matter with broken time reversal symmetry, and is the underlying mechanism of the quantum
Hall effect. Using a scanning SQUID-on-tip [2], acting as an ultrasensitive nanoscale magnetometer, we
directly image the equilibrium persistent currents of individual quantum Hall edge states in single layer
graphene for the first time [3]. We reveal that the edge states, which are commonly assumed to carry
only a chiral downstream current, in fact carry a pair of counter-propagating currents [4], in which the
topological downstream current in the incompressible region is counterbalanced by a heretofore
unobserved non-topological upstream current flowing in the adjacent compressible region. We then
apply the same technique to the recently discovered magic angle twisted bilayer graphene (MATBG). We
attain tomographic imaging of the Landau levels [5], which provides a highly sensitive local probe of the
charge disorder, twist angle θ and band structure. We obtain a map of local θ variations 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 of ~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 the twist angle gradients generate large unscreened electric fields that drastically
change the quantum Hall state by forming edge states in the bulk of the sample. These gate-tunable
electric fields may also significantly affect the phase diagram of correlated and superconducting states.
Twist angle disorder is established as a new type of disorder, fundamentally different than charge
disorder.
1. X.-L. Qi, T. L. Hughes, and S.-C. Zhang, ''Topological field theory of time-reversal invariant
insulators'', Phys. Rev. B 78, 195424 (2008).
2. D. Vasyukov, Y. Anahory, L. Embon, D. Halbertal, J. Cuppens, L. Neeman, A. Finkler, Y. Segev, Y.
Myasoedov, M. L. Rappaport, M. E. Huber, and E. Zeldov, ''A scanning superconducting quantum
interference device with single electron spin sensitivity'', Nat. Nanotechnol. 8, 639–644 (2013).
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'',
arXiv:1908.02466 (2019), Nat. Phys in press.
4. M. R. Geller and G. Vignale, ''Currents in the compressible and incompressible regions of the two-
dimensional electron gas'', Phys. Rev. B 50, 11714–11722 (1994).
5. 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 (2019), under review
in Nature.