Measuring local moiré lattice heterogeneity of twisted bilayer graphene

Abstract

We introduce a new method to continuously map inhomogeneities of a moiré lattice and apply it to open-device twisted bilayer graphene (TBG). We show that the variation in the twist angle, which is frequently conjectured to be the reason for differences between devices with a supposed similar twist angle, is about 0.04° over areas of several hundred nm, comparable to devices encapsulated between hBN slabs. We distinguish between an effective twist angle and local anisotropy and relate the latter to heterostrain. Our results suggest that the lack of evidence for superconductivity in open devices is not a consequence of higher heterogeneity in the twist angle, but possibly due to the absence of interaction with a top hBN layer. Furthermore, our results imply that for our devices, twist angle heterogeneity has a roughly equal effect to the electronic structure as local strain. The method introduced here is applicable to results from different imaging techniques, and on different moiré materials.

Imaging moiré deformation and dynamics in twisted bilayer graphene

“…The twist angle variation within each domain is much smaller than the variation in twist angle between the separate, fold-bounded areas. Within domains, standard deviations range from 0.005° to 0.015°, i.e., significantly smaller (by a factor 3–10) than previously reported 13 , 15 , 33 . The strain observed is around a few tenths of a percent, which is considerable.…”

“…Our data suggest that domain boundary displacement follows a random pattern of forward and backward steps. This indicates a possible source for the twist angle disorder observed in low(er) temperature experiments 10 , 13 , 15 , 33 : frozen-in thermal fluctuations of the moiré lattice. The thermal fluctuations found, corresponding to ±0.005° for twist angle and ±0.02% for strain, are smaller than the extracted static deformations, though not negligible.…”

“…2 e). 33 , 36 The distortions of the moiré pattern correspond directly to distortions of the atomic lattices, magnified by a factor 1/ θ and rotated by 90° + θ /2 33 , 37 .

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Imaging orbital ferromagnetism in a moiré Chern insulator

“…Although crystalline defects on the atomic scale are unlikely in tBLG thanks to the high quality of the constituent graphene and hBN layers, the thermodynamic instability of magic angle twisted bilayer graphene makes it highly susceptible to inhomogeneity at scales larger than the moiré period, as shown in prior spatially resolved studies (31,32). For example, the twist angle between the layers as well as their registry to the underlying hBN substrate may all vary spatially, providing potential pinning sites (33).…”

Degradation of phonons in disordered moiré superlattices

“…Thus, L c , which depends on the elastic constants of graphene and on the strength of the disorder potentials, is the length scale associated with twist-angle inhomogeneity. Experimentally, inhomogeneous twist angles have been widely observed in TBG devices [78][79][80], and shown to strongly affect the electronic properties (see also [81,82]). Within a region of size L c , the distribution of twist angles θ has a variance:…”