Supermoiré Formation and Robust Topological Edge State in Helical Trilayer Graphene

Abstract

When two materials with nearly matched lattice constants meet, they form commensurate domains separated by incommensurate domain walls that absorb the mismatch. Recently, this picture has been extended to moiré lattices: when two moiré superlattices have nearly equal periodicities, they can form a "supermoiré" consisting of commensurate moiré domains separated by domain walls. Helical trilayer graphene (HTG) is a particularly interesting example: theory predicts that its commensurate domains are distinct topological insulators, separated by a network of conducting domain walls. Here, we use scanning tunneling microscopy and spectroscopy to visualize supermoiré domains and their electronic properties in HTG at a twist angle of $\sim1.7^\circ$. We find atomic-scale evidence of relaxation into supermoiré domains, each hosting flat bands separated from remote bands by large gaps of $\sim40$ meV. Domain walls exhibit spectrally uniform edge states along their length, in excellent agreement with calculations for valley-protected topological edge modes. The topological character of the flat bands is intimately tied to wavefunction localization on a graphene sublattice, and we reveal the topological change across a domain boundary by imaging the reversal of sublattice polarization.