Periodic Strain-Induced Moire Patterns in Graphene.

Lattice mismatch between graphene and a substrate produces local variations in the density of states (LDOS) as observed in STM images. These are known as moire patterns, in analogy with classical interference produced by two overlapping periodic arrays. These have been observed in twisted bilayer graphene[1], a system that can be thought of as monolayer graphene deposited on a substrate with misaligned crystalline orientations. In this regime, the resulting charge density distribution is related to superconductor and Mott insulator phases observed in experiments. It is natural to wonder if similar features could be obtained by depositing graphene on engineered substrates inducing modulated strain fields. Starting from the simplest case of two overlapping deformations, we obtain the LDOS profile for a one-dimensional array, and show the emergence of a different periodicity, a feature associated with moire patterns. We identify conditions for discrete and continuous charged regions, and extend our results to a 2D close-packed structure, demonstrating that periodic deformations can be used to generate moire patterns.
[1] Cao et al, Nature 556, 43 (2018).