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1. Rotational and dilational reconstruction in transition metal dichalcogenide moiré bilayers

   https://doi.org/10.1038/s41467-023-38504-7  

   Van Winkle, Madeline; Craig, Isaac M.; Carr, Stephen; Dandu, Medha; Bustillo, Karen C.; Ciston, Jim; Ophus, Colin; Taniguchi, Takashi; Watanabe, Kenji; Raja, Archana; et al (May 2023, Nature Communications)

   Abstract Lattice reconstruction and corresponding strain accumulation plays a key role in defining the electronic structure of two-dimensional moiré superlattices, including those of transition metal dichalcogenides (TMDs). Imaging of TMD moirés has so far provided a qualitative understanding of this relaxation process in terms of interlayer stacking energy, while models of the underlying deformation mechanisms have relied on simulations. Here, we use interferometric four-dimensional scanning transmission electron microscopy to quantitatively map the mechanical deformations through which reconstruction occurs in small-angle twisted bilayer MoS₂and WSe₂/MoS₂heterobilayers. We provide direct evidence that local rotations govern relaxation for twisted homobilayers, while local dilations are prominent in heterobilayers possessing a sufficiently large lattice mismatch. Encapsulation of the moiré layers in hBN further localizes and enhances these in-plane reconstruction pathways by suppressing out-of-plane corrugation. We also find that extrinsic uniaxial heterostrain, which introduces a lattice constant difference in twisted homobilayers, leads to accumulation and redistribution of reconstruction strain, demonstrating another route to modify the moiré potential. 

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2. Moiré metrology of energy landscapes in van der Waals heterostructures

   https://doi.org/10.1038/s41467-020-20428-1  

   Halbertal, Dorri; Finney, Nathan R.; Sunku, Sai S.; Kerelsky, Alexander; Rubio-Verdú, Carmen; Shabani, Sara; Xian, Lede; Carr, Stephen; Chen, Shaowen; Zhang, Charles; et al (December 2021, Nature Communications)

   null (Ed.)

   Abstract The emerging field of twistronics, which harnesses the twist angle between two-dimensional materials, represents a promising route for the design of quantum materials, as the twist-angle-induced superlattices offer means to control topology and strong correlations. At the small twist limit, and particularly under strain, as atomic relaxation prevails, the emergent moiré superlattice encodes elusive insights into the local interlayer interaction. Here we introduce moiré metrology as a combined experiment-theory framework to probe the stacking energy landscape of bilayer structures at the 0.1 meV/atom scale, outperforming the gold-standard of quantum chemistry. Through studying the shapes of moiré domains with numerous nano-imaging techniques, and correlating with multi-scale modelling, we assess and refine first-principle models for the interlayer interaction. We document the prowess of moiré metrology for three representative twisted systems: bilayer graphene, double bilayer graphene and H-stacked MoSe 2 /WSe 2 . Moiré metrology establishes sought after experimental benchmarks for interlayer interaction, thus enabling accurate modelling of twisted multilayers. 

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3. Local atomic stacking and symmetry in twisted graphene trilayers

   https://doi.org/10.1038/s41563-023-01783-y  

   Craig, Isaac M.; Van Winkle, Madeline; Groschner, Catherine; Zhang, Kaidi; Dowlatshahi, Nikita; Zhu, Ziyan; Taniguchi, Takashi; Watanabe, Kenji; Griffin, Sinéad M.; Bediako, D. Kwabena (January 2024, Nature Materials)

   Moiré superlattices formed by twisting trilayers of graphene are a useful model for studying correlated electron behaviour and offer several advantages over their formative bilayer analogues, including a more diverse collection of correlated phases and more robust superconductivity. Spontaneous structural relaxation alters the behaviour of moiré superlattices considerably and has been suggested to play an important role in the relative stability of superconductivity in trilayers. Here we use an interferometric four-dimensional scanning transmission electron microscopy approach to directly probe the local graphene layer alignment over a wide range of trilayer graphene structures. Our results inform a thorough understanding of how reconstruction modulates the local lattice symmetries crucial for establishing correlated phases in twisted graphene trilayers, evincing a relaxed structure that is markedly different from that proposed previously. 

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4. Spectroscopy of a tunable moiré system with a correlated and topological flat band

   https://doi.org/10.1038/s41467-021-23031-0  

   Liu, Xiaomeng; Chiu, Cheng-Li; Lee, Jong Yeon; Farahi, Gelareh; Watanabe, Kenji; Taniguchi, Takashi; Vishwanath, Ashvin; Yazdani, Ali (May 2021, Nature Communications)

   Abstract Moiré superlattices created by the twisted stacking of two-dimensional crystals can host electronic bands with flat energy dispersion in which enhanced interactions promote correlated electron states. The twisted double bilayer graphene (TDBG), where two Bernal bilayer graphene are stacked with a twist angle, is such a moiré system with tunable flat bands. Here, we use gate-tuned scanning tunneling spectroscopy to directly demonstrate the tunability of the band structure of TDBG with an electric field and to show spectroscopic signatures of electronic correlations and topology for its flat band. Our spectroscopic experiments are in agreement with a continuum model of TDBG band structure and reveal signatures of a correlated insulator gap at partial filling of its isolated flat band. The topological properties of this flat band are probed with the application of a magnetic field, which leads to valley polarization and the splitting of Chern bands with a large effective g-factor. 

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5. Tunable strain soliton networks confine electrons in van der Waals materials

   https://doi.org/10.1038/s41567-020-0953-2  

   Edelberg, Drew; Kumar, Hemant; Shenoy, Vivek; Ochoa, Héctor; Pasupathy, Abhay N. (July 2020, Nature Physics)

   Twisting or sliding two-dimensional crystals with respect to each other gives rise to moiré patterns determined by the difference in their periodicities. Such lattice mismatches can exist for several reasons: differences between the intrinsic lattice constants of the two layers, as is the case for graphene on BN; rotations between the two lattices, as is the case for twisted bilayer graphene; and strains between two identical layers in a bilayer. Moiré patterns are responsible for a number of new electronic phenomena observed in recent years in van der Waals heterostructures, including the observation of superlattice Dirac points for graphene on BN, collective electronic phases in twisted bilayers and twisted double bilayers, and trapping of excitons in the moiré potential. An open question is whether we can use moiré potentials to achieve strong trapping potentials for electrons. Here, we report a technique to achieve deep, deterministic trapping potentials via strain-based moiré engineering in van der Waals materials. We use strain engineering to create on-demand soliton networks in transition metal dichalcogenides. Intersecting solitons form a honeycomb-like network resulting from the three-fold symmetry of the adhesion potential between layers. The vertices of this network occur in bound pairs with different interlayer stacking arrangements. One vertex of the pair is found to be an efficient trap for electrons, displaying two states that are deeply confined within the semiconductor gap and have a spatial extent of 2 nm. Soliton networks thus provide a path to engineer deeply confined states with a strain-dependent tunable spatial separation, without the necessity of introducing chemical defects into the host materials. 

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