Strain fields in twisted bilayer graphene

Complete strain tensor fields of twisted bilayer graphene are quantitatively mapped, revealing two-regime reconstruction mechanics depending on twist angle. Van der Waals heteroepitaxy allows deterministic control over lattice mismatch or azimuthal orientation between atomic layers to produce long-wavelength superlattices. The resulting electronic phases depend critically on the superlattice periodicity and localized structural deformations that introduce disorder and strain. In this study we used Bragg interferometry to capture atomic displacement fields in twisted bilayer graphene with twist angles <2 degrees. Nanoscale spatial fluctuations in twist angle and uniaxial heterostrain were statistically evaluated, revealing the prevalence of short-range disorder in moire heterostructures. By quantitatively mapping strain tensor fields, we uncovered two regimes of structural relaxation and disentangled the electronic contributions of constituent rotation modes. Further, we found that applied heterostrain accumulates anisotropically in saddle-point regions, generating distinctive striped strain phases. Our results establish the reconstruction mechanics underpinning the twist-angle-dependent electronic behaviour of twisted bilayer graphene and provide a framework for directly visualizing structural relaxation, disorder and strain in moire materials.

Automated summary

Twisted bilayer graphene exhibits two-regime reconstruction mechanics based on twist angle, with applied heterostrain accumulating anisotropically in saddle-point regions to generate distinctive striped strain phases. Nanoscale spatial fluctuations in twist angle and uniaxial heterostrain were statistically evaluated, revealing the prevalence of short-range disorder in moire heterostructures. This study provides insights into the twist-angle-dependent electronic behavior and structural relaxation, disorder, and strain in moire materials.