Two-dimensional quantum materials host complex, interacting topological phases. Local information is often pivotal in understanding the nature of these states. By utilizing a scanning nano-superconducting quantum interference device (SQUID) on a tip, we directly image the local current distribution in quantum Hall edge states in graphene [1]. We discover that, in addition to carrying the well-understood “skipping orbit” chiral drift currents, the edge states also carry counter-propagating currents of a fundamentally different nature. Leveraging these currents in magic angle twisted bilayer graphene, we are able to image the local twist angle with high precision (< 0.002°) and spatial resolution (∼50 nm) [2]. This reveals a complex landscape of a spatially varying twist angle, introducing a new type of disorder with significant implications. For example, we identify flavor-symmetry-broken phases that depend sensitively on the local landscape. Time permitting, I will discuss how edge currents in Chern insulators parallel those in quantum Hall edges and elaborate on our imaging of space-dependent topology in a moiré material [3].


[1]  A. Uri et al., “Nanoscale imaging of equilibrium quantum hall edge currents and of the magnetic monopole response in graphene,” Nature Physics 16, 164–170 (2020).
[2]  A. Uri, S. Grover, Y. Cao et al., “Mapping the twist-angle disorder and landau levels in magic-angle graphene,” Nature 581, 47–52 (2020).

[3]  S. Grover, M. Bocarsly, A. Uri et al., “Chern mosaic and berry-curvature magnetism in magic-angle graphene,” Nature Physics 18, 885–892 (2022).