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1. 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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2. Manipulating Moirés by Controlling Heterostrain in van der Waals Devices

   https://doi.org/10.1021/acs.nanolett.4c04201  

   Sequeira, Ian; Barabas, Andrew Z; Barajas-Aguilar, Aaron H; Bacani, Michaela G; Nakatsuji, Naoto; Koshino, Mikito; Taniguichi, Takashi; Watanabe, Kenji; Sanchez-Yamagishi, Javier D (December 2024, Nano Letters)

   Van der Waals (vdW) moirés offer tunable superlattices that can strongly manipulate electronic properties. We demonstrate the in situ manipulation of moiré superlattices via heterostrain control in a vdW device. By straining a graphene layer relative to its hexagonal boron nitride substrate, we modify the shape and size of the moiré. Our sliding-based technique achieves uniaxial heterostrain values exceeding 1%, resulting in distorted moirés values that are larger than those achievable without strain. The stretched moiré is evident in transport measurements, resulting in shifted superlattice resistance peaks and Landau fans, consistent with an enlarged superlattice unit cell. Electronic structure calculations reveal how heterostrain shrinks and distorts the moiré Brillouin zone, resulting in a reduced electronic bandwidth as well as the appearance of highly anisotropic and quasi-one-dimensional Fermi surfaces. Our heterostrain control approach opens a wide parameter space of moiré lattices to explore beyond what is possible by twist angle control alone. 

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3. 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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4. Local spectroscopy of a gate-switchable moiré quantum anomalous Hall insulator

   https://doi.org/10.1038/s41467-023-39110-3  

   Zhang, Canxun; Zhu, Tiancong; Soejima, Tomohiro; Kahn, Salman; Watanabe, Kenji; Taniguchi, Takashi; Zettl, Alex; Wang, Feng; Zaletel, Michael P.; Crommie, Michael F. (June 2023, Nature Communications)

   Abstract In recent years, correlated insulating states, unconventional superconductivity, and topologically non-trivial phases have all been observed in several moiré heterostructures. However, understanding of the physical mechanisms behind these phenomena is hampered by the lack of local electronic structure data. Here, we use scanning tunnelling microscopy and spectroscopy to demonstrate how the interplay between correlation, topology, and local atomic structure determines the behaviour of electron-doped twisted monolayer–bilayer graphene. Through gate- and magnetic field-dependent measurements, we observe local spectroscopic signatures indicating a quantum anomalous Hall insulating state with a total Chern number of ±2 at a doping level of three electrons per moiré unit cell. We show that the sign of the Chern number and associated magnetism can be electrostatically switched only over a limited range of twist angle and sample hetero-strain values. This results from a competition between the orbital magnetization of filled bulk bands and chiral edge states, which is sensitive to strain-induced distortions in the moiré superlattice. 

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5. 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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