Imaging Electron Beam-Sensitive Twisted Hybrid Perovskite Bilayers at One-Angstrom Resolution

Twisted halide perovskite bilayers, a type of moiré material, show square moiré patterns with exciting optical properties. Atomic-scale structure analysis and its correlation with properties are difficult to achieve due to the extreme sensitivity of organic-inorganic halide perovskites to the illuminated electron beam in conventional/scanning transmission electron microscopy. Here, we developed a low-dose exit wave reconstruction methodology with a real-space resolution of one angstrom at ∼50 e/Å2, which recovers the phase information on the moiré fringes in CH3NH3PbI3 (MAPbI3) twisted perovskite bilayers at atomic scale, enabling detailed structural analysis of defects and corresponding strain distribution in such moiré materials. This work provides an atomic-level understanding of electron beam-sensitive twisted bilayer materials.

Designing Moiré Patterns by Shearing

We analyze the elastic properties, structural effects, and low-energy physics of a sheared nanoribbon placed on top of graphene, which creates a gradually changing moiré pattern. By means of a classical elastic model we derive the strains in the ribbon and we obtain its electronic energy spectrum with a scaled tight-binding model. The size of the sheared region is determined by the balance between elastic and van der Waals energy, and different regimes are identified. Near the clamped edge, moderate strains and small twist angles lead to one-dimensional channels. Near the sheared edge, a long region behaves like magic angle twisted bilayer graphene (TBG), showing a sharp peak in the density of states, mostly isolated from the rest of the spectrum. We also calculate the band topology along the ribbon and we find that it is stable for large intervals of strains and twist angles. Together with the experimental observations, these results show that the sheared nanoribbon geometry is ideal for exploring superconductivity and correlated phases in TBG in the very sought-after regime of ultralow twist angle disorder.

Correlation-Induced Symmetry-Broken States in Large-Angle Twisted Bilayer Graphene on MoS2

Strongly correlated states commonly emerge in twisted bilayer graphene (TBG) with "magic-angle" (1.1°), where the electron-electron (e-e) interaction U becomes prominent relative to the small bandwidth W of the nearly flat band. However, the stringent requirement of this magic angle makes the sample preparation and the further application facing great challenges. Here, using scanning tunneling microscopy (STM) and spectroscopy (STS), we demonstrate that the correlation-induced symmetry-broken states can also be achieved in a 3.45° TBG, via engineering this nonmagic-angle TBG into regimes of U/W > 1. We enhance the e-e interaction through controlling the microscopic dielectric environment by using a MoS2 substrate. Simultaneously, the width of the low-energy van Hove singularity (VHS) peak is reduced by enhancing the interlayer coupling via STM tip modulation. When partially filled, the VHS peak exhibits a giant splitting into two states flanked by the Fermi level and shows a symmetry-broken LDOS distribution with a stripy charge order, which confirms the existence of strong correlation effect in our 3.45° TBG. Our result demonstrates the feasibility of the study and application of the correlation physics in TBGs with a wider range of twist angle.

Kagome Quantum Oscillations in Graphene Superlattices

Electronic spectra of solids subjected to a magnetic field are often discussed in terms of Landau levels and Hofstadter-butterfly-style Brown-Zak minibands manifested by magneto-oscillations in two-dimensional electron systems. Here, we present the semiclassical precursors of these quantum magneto-oscillations which appear in graphene superlattices at low magnetic field near the Lifshitz transitions and persist at elevated temperatures. These oscillations originate from Aharonov-Bohm interference of electron waves following open trajectories that belong to a kagome-shaped network of paths characteristic for Lifshitz transitions in the moire superlattice minibands of twistronic graphenes.

Role of Curvature in Stabilizing Boron-Doped Nanocorrugated Graphene

Boron-doped carbon nanostructures have attracted great interest recently because of their remarkable electrocatalytic performance comparable to or better than that of conventional metal catalysts. In a previous work (Carbon 123, 605 (2017)), we reported that along with significant performance improvement, B doping enhances the oxidation resistance of few-layer graphene (FLG) that provides increased structural stability for intermediate-temperature fuel-cell electrodes. In general, detailed characterization of the atomic and electronic structure transformations that occur in B-doped carbon nanostructures during fuel-cell operation is lacking. In this work, we use aberration-corrected scanning transmission electron microscopy, nanobeam electron diffraction, and electron energy-loss spectroscopy (EELS) to characterize the atomic and electronic structures of B-doped FLG before and after fuel-cell operation. These data point to the nanoscale corrugation of B-doped FLGs as the key factor responsible for increased stability and high corrosion resistance. The similarity of the 1s to π* and σ* transition features in the B K-edge EELS to those in B-doped carbon nanotubes provides an estimate for the curvature of nanocorrugation in B-FLG.

Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update

This is an update of a previous review (Naumiset al2017Rep. Prog. Phys.80096501). Experimental and theoretical advances for straining graphene and other metallic, insulating, ferroelectric, ferroelastic, ferromagnetic and multiferroic 2D materials were considered. We surveyed (i) methods to induce valley and sublattice polarisation (P) in graphene, (ii) time-dependent strain and its impact on graphene's electronic properties, (iii) the role of local and global strain on superconductivity and other highly correlated and/or topological phases of graphene, (iv) inducing polarisationPon hexagonal boron nitride monolayers via strain, (v) modifying the optoelectronic properties of transition metal dichalcogenide monolayers through strain, (vi) ferroic 2D materials with intrinsic elastic (σ), electric (P) and magnetic (M) polarisation under strain, as well as incipient 2D multiferroics and (vii) moiré bilayers exhibiting flat electronic bands and exotic quantum phase diagrams, and other bilayer or few-layer systems exhibiting ferroic orders tunable by rotations and shear strain. The update features the experimental realisations of a tunable two-dimensional Quantum Spin Hall effect in germanene, of elemental 2D ferroelectric bismuth, and 2D multiferroic NiI2. The document was structured for a discussion of effects taking place in monolayers first, followed by discussions concerning bilayers and few-layers, and it represents an up-to-date overview of exciting and newest developments on the fast-paced field of 2D materials.

One-Dimensional Moiré Physics and Chemistry in Heterostrained Bilayer Graphene

Twisted bilayer graphene (tBLG) has emerged as a promising platform for exploring exotic electronic phases. However, the formation of moiré patterns in tBLG has thus far been confined to the introduction of twist angles between the layers. Here, we propose heterostrained bilayer graphene (hBLG), as an alternative avenue for accessing twist angle-free moiré physics via lattice mismatch. Using atomistic and first-principles calculations, we demonstrate that the uniaxial heterostrain can promote isolated flat electronic bands around the Fermi level. Furthermore, the heterostrain-induced out-of-plane lattice relaxation may lead to a spatially modulated reactivity of the surface layer, paving the way for moiré-driven chemistry and magnetism. We anticipate that our findings can be readily generalized to other layered materials.

Programming twist angle and strain profiles in 2D materials

Moiré superlattices in twisted two-dimensional materials have generated tremendous excitement as a platform for achieving quantum properties on demand. However, the moiré pattern is highly sensitive to the interlayer atomic registry, and current assembly techniques suffer from imprecise control of the average twist angle, spatial inhomogeneity in the local twist angle, and distortions caused by random strain. We manipulated the moiré patterns in hetero- and homobilayers through in-plane bending of monolayer ribbons, using the tip of an atomic force microscope. This technique achieves continuous variation of twist angles with improved twist-angle homogeneity and reduced random strain, resulting in moiré patterns with tunable wavelength and ultralow disorder. Our results may enable detailed studies of ultralow-disorder moiré systems and the realization of precise strain-engineered devices.

Imaging moiré deformation and dynamics in twisted bilayer graphene

In 'magic angle' twisted bilayer graphene (TBG) a flat band forms, yielding correlated insulator behavior and superconductivity. In general, the moiré structure in TBG varies spatially, influencing the overall conductance properties of devices. Hence, to understand the wide variety of phase diagrams observed, a detailed understanding of local variations is needed. Here, we study spatial and temporal variations of the moiré pattern in TBG using aberration-corrected Low Energy Electron Microscopy (AC-LEEM). We find a smaller spatial variation than reported previously. Furthermore, we observe thermal fluctuations corresponding to collective atomic displacements over 70 pm on a timescale of seconds. Remarkably, no untwisting is found up to 600 ∘C. We conclude that thermal annealing can be used to decrease local disorder. Finally, we observe edge dislocations in the underlying atomic lattice, the moiré structure acting as a magnifying glass. These topological defects are anticipated to exhibit unique local electronic properties.

Heterostrain Determines Flat Bands in Magic-Angle Twisted Graphene Layers

The moiré of twisted graphene bilayers can generate flat bands in which charge carriers do not possess enough kinetic energy to escape Coulomb interactions with each other, leading to the formation of novel strongly correlated electronic states. This exceptionally rich physics relies on the precise arrangement between the layers. Here, we survey published scanning tunneling microscope measurements to prove that near the magic-angle, native heterostrain, the relative deformations between the layers, dominates twist in determining the flat bands as opposed to the common belief. This is demonstrated at full filling where electronic correlations have a weak effect and where we also show that tip-induced strain can have a strong influence. In the opposite situation of zero doping, we find that electronic correlation further renormalizes the flat bands in a way that strongly depends on experimental details.

Subatomic Distortion of Surface Monolayer Lattice Visualized by Moiré Pattern

Mapping of the local lattice distortion is required to understand the details of the chemical and physical properties of thin films. However, the resolution by the direct microscopic methods was insufficient to detect the local distortion. Here, we have demonstrated that the local distortion of a monatomic film on a substrate is estimated with high resolution using the moiré pattern of the topographic scanning tunneling microscopy image. The analysis focused on the apparently low centers of the moiré pattern of the hexagonal iron nitride monolayer on the Cu(111) substrate. The local distortion was visualized by estimating the displacement of the experimentally detected center position from the ideal position that is extracted from the adjacent center positions. The map of the local distortion revealed that the subsurface impurities are preferentially located on the largely distorted areas. This approach is widely applicable to other thin films on the substrates.

Charge-polarized interfacial superlattices in marginally twisted hexagonal boron nitride

When two-dimensional crystals are brought into close proximity, their interaction results in reconstruction of electronic spectrum and crystal structure. Such reconstruction strongly depends on the twist angle between the crystals, which has received growing attention due to interesting electronic and optical properties that arise in graphene and transitional metal dichalcogenides. Here we study two insulating crystals of hexagonal boron nitride stacked at small twist angle. Using electrostatic force microscopy, we observe ferroelectric-like domains arranged in triangular superlattices with a large surface potential. The observation is attributed to interfacial elastic deformations that result in out-of-plane dipoles formed by pairs of boron and nitrogen atoms belonging to opposite interfacial surfaces. This creates a bilayer-thick ferroelectric with oppositely polarized (BN and NB) dipoles in neighbouring domains, in agreement with our modeling. These findings open up possibilities for designing van der Waals heterostructures and offer an alternative probe to study moiré-superlattice electrostatic potentials.

Electronic Raman Scattering in Twistronic Few-Layer Graphene

We study electronic contribution to the Raman scattering signals of two-, three- and four-layer graphene with layers at one of the interfaces twisted by a small angle with respect to each other. We find that the Raman spectra of these systems feature two peaks produced by van Hove singularities in moiré minibands of twistronic graphene, one related to direct hybridization of the Dirac states, and the other resulting from band folding caused by moiré superlattice. The positions of both peaks strongly depend on the twist angle, so that their detection can be used for noninvasive characterization of the twist, even in hBN-encapsulated structures.

Electronic Spectrum of Twisted Graphene Layers under Heterostrain

We demonstrate that stacking layered materials allows a strain engineering where each layer is strained independently, which we call heterostrain. We combine detailed structural and spectroscopic measurements with tight-binding calculations to show that small uniaxial heterostrain suppresses Dirac cones and leads to the emergence of flat bands in twisted graphene layers (TGLs). Moreover, we demonstrate that heterostrain reconstructs, much more severely, the energy spectrum of TGLs than homostrain for which both layers are strained identically, a result which should apply to virtually all van der Waals structures opening exciting possibilities for straintronics with 2D materials.

Visualizing Strain-Induced Pseudomagnetic Fields in Graphene through an hBN Magnifying Glass

Graphene's remarkable properties are inherent to its two-dimensional honeycomb lattice structure. Its low dimensionality, which makes it possible to rearrange the atoms by applying an external force, offers the intriguing prospect of mechanically controlling the electronic properties. In the presence of strain, graphene develops a pseudomagnetic field (PMF) that reconstructs the band structure into pseudo Landau levels (PLLs). However, a feasible route to realizing, characterizing and controlling PMFs is still lacking. Here we report on a method to generate and characterize PMFs in a graphene membrane supported on nanopillars. A direct measure of the local strain is achieved by using the magnifying effect of the moiré pattern formed against a hexagonal boron nitride substrate under scanning tunneling microscopy. We quantify the strain-induced PMF through the PLLs spectra observed in scanning tunneling spectroscopy. This work provides a pathway to strain induced engineering and electro-mechanical graphene-based devices.

Tunable Lattice Constant and Band Gap of Single- and Few-Layer ZnO

Single and few-layer ZnO(0001) (ZnO(nL), n = 1-4) grown on Au(111) have been characterized via scanning tunneling microscopy (STM), scanning tunneling spectroscopy (STS), and density functional theory (DFT) calculations. We find that the in-plane lattice constants of the ZnO(nL, n ≤ 3) are expanded compared to that of the bulk wurtzite ZnO(0001). The lattice constant reaches a maximum expansion of 3% in the ZnO(2L) and decreases to the bulk wurtzite ZnO value in the ZnO(4L). The band gap decreases monotonically with increasing number of ZnO layers from 4.48 eV (ZnO(1L)) to 3.42 eV (ZnO(4L)). These results suggest that a transition from a planar to the bulk-like ZnO structure occurs around the thickness of ZnO(4L). The work also demonstrates that the lattice constant and the band gap in ultrathin ZnO can be tuned by controlling the number of layers, providing a basis for further investigation of this material.

Strain-Engineered Graphene Grown on Hexagonal Boron Nitride by Molecular Beam Epitaxy

Graphene grown by high temperature molecular beam epitaxy on hexagonal boron nitride (hBN) forms continuous domains with dimensions of order 20 μm, and exhibits moiré patterns with large periodicities, up to ~30 nm, indicating that the layers are highly strained. Topological defects in the moiré patterns are observed and attributed to the relaxation of graphene islands which nucleate at different sites and subsequently coalesce. In addition, cracks are formed leading to strain relaxation, highly anisotropic strain fields, and abrupt boundaries between regions with different moiré periods. These cracks can also be formed by modification of the layers with a local probe resulting in the contraction and physical displacement of graphene layers. The Raman spectra of regions with a large moiré period reveal split and shifted G and 2D peaks confirming the presence of strain. Our work demonstrates a new approach to the growth of epitaxial graphene and a means of generating and modifying strain in graphene.