Quantitative determination of twist angle and strain in Van der Waals moiré superlattices

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Abstract
Scanning probe techniques are popular, nondestructive ways to visualize the real space structure of Van der Waals moirés. The high lateral spatial resolution provided by these techniques enables extracting the moiré lattice vectors from a scanning probe image. We have found that the extracted values, while precise, are not necessarily accurate. Scan-to-scan variations in the behavior of the piezos that drive the scanning probe and thermally driven slow relative drift between probe and sample produce systematic errors in the extraction of lattice vectors. In this Letter, we identify the errors and provide a protocol to correct for them. Applying this protocol to an ensemble of ten successive scans of near-magic-angle twisted bilayer graphene, we are able to reduce our errors in extracting lattice vectors to less than 1%. This translates to extracting twist angles with a statistical uncertainty less than 0.001° and uniaxial heterostrain with uncertainty on the order of 0.002%.
Funding Information
  • U.S. Department of Energy (DE-AC02-76SF00515)
  • National Science Foundation (ECCS-2026822)
  • Gordon and Betty Moore Foundation (GBMF9460)
  • Japan Society for the Promotion of Science (21H05233)
  • Japan Society for the Promotion of Science (23H02052)
  • SLAC National Accelerator Laboratory (Q-BALMS LDRD)

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