Anisotropic strain effects in small-twist-angle graphene on graphite
M Szendro and A Palinkas and P Sule and Z Osvath, PHYSICAL REVIEW B, 100, 125404 (2019).
The direct experimental probing of locally varying lattice parameters and anisotropic lattice deformations in atomic multilayers is extremely challenging. Here, we develop a combined numerical and graphical method for the analysis of irregular moire superstructures measured by scanning tunneling microscopy (STM) on a small-twist-angle (similar to 0.6 degrees) graphene on highly oriented pyrolytic graphite (gr/HOPG). We observe distorted moire patterns with a spatially varying period in annealed gr/HOPG. The nanoscale modulation of the moire period observed by STM reflects a locally strained (and sheared) graphene with anisotropic variation of the lattice parameters. We use a specific algorithm based on a rigid lattice Fourier method, which is able to reconstruct the irregular and distorted moire patterns emerging from strain-induced lattice deformations. Our model is universal and can be used to study different moire patterns occurring in two-dimensional van der Waals heterostructures. Additionally, room-temperature scanning tunneling spectroscopy measurements show electronic states at the Dirac point, localized on moire hills, which increase significantly the apparent corrugation of the moire pattern. The measured topography is compared to classical molecular dynamics simulations. Density functional theory calculations confirm that an AAB-stacked trilayer region itself can contribute electronic states near the Fermi level, in agreement with the measured peak in the local density of states. Furthermore, classical molecular dynamics calculations reveal direction-dependent bond alternations (similar to 0.5%) around the stacking regions, induced by shear strain, which could influence electronic properties.
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