Abstract
When two-dimensional van der Waals materials are stacked to build heterostructures, moiré patterns emerge from twisted interfaces or from a mismatch in the lattice constant of individual layers. Relaxation of the atomic positions is a direct, generic consequence of the moiré pattern, with many implications for the physical properties. Moiré-driven atomic relaxation may be naively thought to be restricted to the interfacial layers and thus irrelevant for multilayered heterostructures. However, we provide experimental evidence for the importance of the three-dimensional nature of the relaxation in two types of van der Waals heterostructures: First, in multilayer graphene twisted on graphite at small twist angles (θ≈0.14°), we observe propagation of relaxation domains even beyond 18 graphene layers. Second, we show how for multilayer PdTe2 on Bi2Se3 the moiré lattice constant depends on the number of PdTe2 layers. Motivated by the experimental findings, we develop a continuum approach to model multilayered relaxation processes based on the generalized stacking fault energy functional given by ab initio simulations. Leveraging the continuum property of the approach enables us to access large-scale regimes and achieve agreement with our experimental data for both systems. Furthermore, it is well known that the electronic structure of graphene sensitively depends on local lattice deformations. Therefore, we study the impact of multilayered relaxation on the local density of states of the twisted graphitic system. We identify measurable implications for the system, experimentally accessible by scanning tunneling microscopy. Our multilayered relaxation approach is not restricted to the discussed systems and can be used to uncover the impact of an interfacial defect on various layered systems of interest.
| Original language | English |
|---|---|
| Article number | 011026 |
| Journal | Physical Review X |
| Volume | 13 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 2023 |
| Externally published | Yes |
Funding
Nanoimaging research at Columbia is supported by DOE-BES Grant No. DE-SC0018426. Research at Columbia on moiré superlattices is entirely supported as part of Programmable Quantum Materials, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award No. DE-SC0019443. Research on atomic relaxation is supported by Grant No. W911NF2120147. We acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under RTG 1995 and RTG 2247, within the Priority Program SPP 2244 “2DMP,” under Germany’s Excellence Strategy—Cluster of Excellence Matter and Light for Quantum Computing Grant No. EXC 2004/1–390534769 and—Cluster of Excellence and Advanced Imaging of Matter Grant No. EXC 2056–390715994. We acknowledge computational resources provided by the Max Planck Computing and Data Facility and RWTH Aachen University under Project No. rwth0716. This work was supported by the Max Planck–New York City Center for Nonequilibrium Quantum Phenomena. D. N. B. is a Moore Investigator in Quantum Materials EPIQS GBMF9455. D. H. was supported by a grant from the Simons Foundation (Grant No. 579913). We thank Oxford Instruments Asylum Research for performing the large-scale tapping mode scan presented in Appendix (Fig. ).