Quantitative determination of twist angle and strain in Van der Waals moir\'e superlattices

TL;DR

This paper develops a protocol to correct systematic errors in scanning probe measurements of Van der Waals moiré superlattices, enabling highly precise determination of twist angles and strain with uncertainties below 0.001 degrees.

Contribution

It introduces a correction protocol for systematic errors in scanning probe techniques, significantly improving the accuracy of lattice vector, twist angle, and strain measurements.

Findings

Reduced errors in lattice vector extraction to less than 1%

Achieved twist angle uncertainty below 0.001 degrees

Uniaxial heterostrain uncertainty around 0.002%

Abstract

Scanning probe techniques are popular, non-destructive ways to visualize the real space structure of Van der Waals moir\'es. The high lateral spatial resolution provided by these techniques enables extracting the moir\'e 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 which 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{\deg} and uniaxial heterostrain with uncertainty on the order of 0.002%.