Cryogenic nano-imaging of second-order moir\'e superlattices

Second-order superlattices form when moir\'e superlattices of similar periodicities interfere with each other, leading to even larger superlattice periodicities. These crystalline structures have been engineered utilizing two-dimensional (2D) materials such as graphene and hexagonal boron nitride (hBN) under specific alignment conditions. Such specific alignment has shown to play a crucial role in facilitating correlation-driven topological phases featuring the quantized anomalous Hall effect. While signatures of second-order superlattices have been identified in magnetotransport experiments, any real-space visualization is lacking to date. In this work, we present \NT{electronic transport measurements and cryogenic nanoscale photovoltage (PV) measurements} that reveal a second-order superlattice in magic-angle twisted bilayer graphene closely aligned to hBN. This is evidenced by long-range periodic photovoltage modulations across the entire sample backed by the corresponding electronic transport features. Supported by theoretical calculations, our experimental data show that even minuscule strain and twist-angle variations on the order of 0.01$^\circ$ can lead to a drastic change of the second-order superlattice structure between local one-dimensional, square or triangular types. Our real-space observations therefore serve as a strong `magnifying glass' for strain and twist angle and can shed new light on the mechanisms responsible for the breaking of spatial symmetries in twisted bilayer graphene, and pave an avenue to engineer long-range superlattice structures in 2D materials using strain fields.
Comment: 10 pages, 5 figures