We demonstrate that one-dimensional moiré patterns, analogous to those found in twisted bilayer graphene, can arise in collapsed chiral carbon nanotubes. Resorting to a combination of approaches, namely, molecular dynamics to obtain the relaxed geometries and tight-binding calculations validated against ab initio modeling, we find that magic angle physics occur in collapsed carbon nanotubes. Velocity reduction, flat bands and localization in AA regions with diminishing moiré angle are revealed, showing a magic angle close to 1$^{\rm o}$. From the spatial extension of the AA regions and the width of the flat bands, we estimate that many-body interactions in these systems are stronger than in twisted bilayer graphene. Chiral collapsed carbon nanotubes stand out as promising candidates to explore many-body effects and superconductivity in low dimensions, emerging as the one-dimensional analogues of twisted bilayer graphene.
Recent experimental progresses have demonstrated the great potential of electronic and excitonic moiré superlattices in transition metal dichalcogenides (TMDs) for quantum many-body simulations and quantum optics applications. Here we reveal that the moiré potential landscapes in the TMDs heterostructures have an electrostatic origin from the spontaneous charge transfer across the heterointerfaces dependent on the atomic registry. This allows engineering tunable multi-chromatic superlattices through the interference of moiré potentials from independently configurable heterointerfaces in multil…
Moiré superlattices in transition metal dichalcogenide (TMD) heterostructures can host novel correlated quantum phenomena due to the interplay of narrow moiré flat bands and strong, long-range Coulomb interactions1-5. However, microscopic knowledge of the atomically-reconstructed moiré superlattice and resulting flat bands is still lacking, which is critical for fundamental understanding and control of the correlated moiré phenomena. Here we quantitatively study the moiré flat bands in three-dimensional (3D) reconstructed WSe2/WS2 moiré superlattices by comparing scanning tunneling spectroscop…
Moiré superlattices from stacks of van der Waals materials offer an exciting arena in the fields of condensed matter physics and materials science. Typically, these moiré superlattices consist of materials with identical or similar structures, and the long moiré period arises from a small twist angle or lattice mismatch. In this article, we discuss that long moiré period appears in a new moiré system by stacking two dissimilar van der Waals layers with large lattice mismatch, resulting in couplings between moiré bands from remote valleys in the momentum space. In this system, the first layer i…
We study a Dirac Harper model for moiré bilayer superlattices where layer antisymmetric strain periodically modulates the interlayer coupling between two honeycomb lattices in one spatial dimension. Discrete and continuum formulations of this model are analyzed. For sufficiently long moiré period the we find low energy spectra that host a manifold of weakly dispersive bands arising from a hierarchy of momentum and position dependent mass inversions. We analyze their charge distributions, mode count and valley-coherence using exact symmetries of the lattice model and approximate symmetries of a…
Ferroelectric hysteresis in singly aligned graphene-hBN moiré superlattices
CIC nanoGUNE（纳米科技联合研究中心）；University of the Basque Country (UPV/EHU)（巴斯克大学）；National Institute for Materials Science（物质材料研究机构）；Centro de Física de Materiales (CFM-MPC) Centro Mixto CSIC-UPV/EHU（物质物理中心（CFM-MPC）CSIC-巴斯克大学联合中心）
A double moiré superlattice can be realized by stacking three layers of atomically thin two-dimensional materials with designer interlayer twisting or lattice mismatches. In this novel structure, atomic reconstruction of constituent layers could introduce significant modifications to the lattice symmetry and electronic structure at small twist angles. Here, we employ conductive atomic force microscopy (cAFM) to investigate symmetry breaking and local electrical properties in twisted trilayer graphene. We observe clear double moiré superlattices with two distinct moire periods all over the samp…
Spontaneous Symmetry Breaking of Cavity Vacuum and Emergent Gyrotropic Effects in Embedded moiré Superlattices
New Cornerstone Science Lab, Department of Physics, The University of Hong Kong（香港大学新Cornerstone科学实验室物理系）；HK Institute of Quantum Science & Technology, University of Hong Kong（香港大学香港量子科学与技术研究所）；Institute of Applied Physics and Materials Engineering, University of Macau（澳门大学应用物理与材料工程研究所）
Most studies on moiré superlattices formed from a stack of h-BN and graphene have focused on single layer graphene; graphene with multiple layers is less understood. Here, we show that a moiré superlattice of multilayer graphene shows new features arising from the anisotropic Fermi surface affected by the superlattice structure. The moiré superlattice of a h-BN/AB-stacked tetralayer graphene heterostructure exhibited resistivity peaks showing a complicated dependence on the perpendicular electric field. The peaks were not due to secondary Dirac cones forming, but rather opening of the energy g…
In two-dimensional (2D) twisted bilayers, the van der Waals (vdW) interlayer interaction introduces atomic-scale reconstruction at interface by locally rotating lattice to form strain-field vortex networks in their moiré superlattice. However, direct imaging the tiny local lattice rotation of the strain-field vortex requires extremely high spatial resolution and is an outstanding challenge in experiment. Here, a topmost small-period graphene moiré pattern is introduced to magnify sub-Angstrom distortions of the lattice and tiny local lattice rotation in underlying twisted bilayer graphene (TBG…
Two-dimensional electronic flat bands and their induced correlated electronic interactions have been discovered, probed, and tuned in interlayer regions of hexagonally shaped van der Waals moire superlattices. Fabrication of anisotropic one-dimensional correlated bands by moire interference of 2D, however, remains a challenge. Here, we report an experimental discovery of 1D electronic flat bands near the Fermi level in an anisotropic rectangular moire superlattice composed of in situ grown, vdW stacked two-atomic-layer thick Bi(110) well-aligned on a SnSe(001) substrate. The epitaxial lattice …
The metal-insulator transition (MIT) driven by electronic correlations is a fundamental and challenging problem in condensed-matter physics. Particularly, whether such a transition can be continuous remains open. The emergence of semiconducting moiré materials with continuously tunable bandwidth provides an ideal platform to study interaction-driven MITs. Although a bandwidth-tuned MIT at fixed full electron filling of the moiré superlattice has been reported recently, that at fractional filling, which involves translational symmetry breaking of the underlying superlattice, remains elusive. He…
Introduction of a twist between layers of two-dimensional materials which leads to the formation of a moiré pattern is an emerging pathway to tune the electronic, vibrational and optical properties. The fascinating properties of these systems is often linked to large-scale structural reconstruction of the moiré pattern. Hence, an essential first step in the theoretical study of these systems is the construction and structural relaxation of the atoms in the moiré superlattice. We present the Twister package, a collection of tools that constructs commensurate superlattices for any combination of…
One-Dimensional Electronic States in a Moiré Superlattice of Twisted Bilayer WTe2
Osaka University（大阪大学）；Kyushu University（九州大学）；The University of Tokyo（东京大学）；Stony Brook University（石溪大学）；Japan Advanced Institute of Science and Technology（日本科学技术高级学院）
Two-dimensional moiré materials provide a highly tunable platform to investigate strongly correlated electronic states. Such emergent many-body phenomena can be optically probed in moiré systems created by stacking two layers of transition metal dichalcogenide semiconductors: optically injected excitons can interact with itinerant carriers occupying narrow moiré bands to form exciton-polarons sensitive to strong correlations. Here, we investigate the behaviour of excitons dressed by a Fermi sea localised by the moiré superlattice of a molybdenum diselenide (MoSe$_2$) / tungsten diselenide (WSe…
We discover chiral phonons at the lowest-energy bands in moiré superlattices. The moiré chiral phonons we uncover are the collective excitations of the stacking domains. Their origin is uniquely attributed to the stacking configurations whose interlayer binding energy breaks the $C_{2z}$ symmetry on the moiré length scale. Within elastic theory, we use a general symmetry analysis to provide a complete classification of van der Waals heterostructures in respect to hosting moiré chiral phonons and show the calculation for twisted MoS$_2$ as an example. We present a low-energy effective model to …
Moire superlattices are twisted bilayer materials, in which the tunable interlayer quantum confinement offers access to new physics and novel device functionalities. Previously, moire superlattices were built exclusively using materials with weak van der Waals interactions and synthesizing moire superlattices with strong interlayer chemical bonding was considered to be impractical. Here using lead sulfide (PbS) as an example, we report a strategy for synthesizing of moire superlattices coupled by strong chemical bonding. We use water-soluble ligands as a removable template to obtain free-stand…
We report the nanoscale conductivity imaging of correlated electronic states in angle-aligned WSe2/WS2 heterostructures using microwave impedance microscopy. The noncontact microwave probe allows us to observe the Mott insulating state with one hole per moiré unit cell that persists for temperatures up to 150 K, consistent with other characterization techniques. In addition, we identify for the first time a Mott insulating state at one electron per moiré unit cell. Appreciable inhomogeneity of the correlated states is directly visualized in the hetero-bilayer region, indicative of local disord…
Moiré superlattices comprised of stacked two-dimensional materials present a versatile platform for engineering and investigating new emergent quantum states of matter. At present, the vast majority of investigated systems have long moiré wavelengths, but investigating these effects at shorter, incommensurate wavelengths, and at higher energy scales, remains a challenge. Here, we employ angle-resolved photoemission spectroscopy (ARPES) with sub-micron spatial resolution to investigate a series of different moiré superlattices which span a wide range of wavelengths, from a short moiré wavelengt…
Transition metal dichalcogenide (TMD) moiré heterostructures provide an ideal platform to explore the extended Hubbard model1 where long-range Coulomb interactions play a critical role in determining strongly correlated electron states. This has led to experimental observations of Mott insulator states at half filling2-4 as well as a variety of extended Wigner crystal states at different fractional fillings5-9. Microscopic understanding of these emerging quantum phases, however, is still lacking. Here we describe a novel scanning tunneling microscopy (STM) technique for local sensing and manip…
Twisted bilayers of van der Waals materials have recently attracted great attention due to their tunable strongly correlated phenomena. Here, we investigate the chirality-specific physics in 3D moiré superlattices induced by Eshelby twist. Our direct DFT calculations reveal helical rotation leads to optical circular dichroism, and chirality-specific nonlinear Hall effect, even though there is no magnetization or magnetic field. Both these phenomena can be reversed by changing the structural chirality. This provides a way to constructing chirality-specific materials.
The flat bands resulting from moiré superlattices in magic-angle twisted bilayer graphene (MATBG) and ABC-trilayer graphene aligned with hexagonal boron nitride (ABC-TLG/hBN) have been shown to give rise to fascinating correlated electron phenomena such as correlated insulators and superconductivity. More recently, orbital magnetism associated with correlated Chern insulators was found in this class of layered structures centered at integer multiples of n0, the density corresponding to one electron per moiré superlattice unit cell. Here we report the experimental observation of ferromagnetism …
Twisted moiré superlattices (TMSs) are fascinating materials with exotic physical properties. Despite tremendous studies on electronic, photonic and phononic TMSs, it has never been witnessed that TMSs can exhibit higher-order band topology. Here, we report on the experimental observation of higher-order topological states in acoustic TMSs. By introducing moiré twisting in bilayer honeycomb lattices of coupled acoustic resonators, we find a regime with designed interlayer couplings where a sizable band gap with higher-order topology emerges. This higher-order topological phase host unique topo…
The atomic structure at the interface between two-dimensional (2D) and three-dimensional (3D) materials influences properties such as contact resistance, photo-response, and high-frequency electrical performance. Moiré engineering is yet to be utilized for tailoring this 2D/3D interface, despite its success in enabling correlated physics at 2D/2D interfaces. Using epitaxially aligned MoS2/Au{111} as a model system, we demonstrate the use of advanced scanning transmission electron microscopy (STEM) combined with a geometric convolution technique in imaging the crystallographic 32 A moiré patter…
Moiré superlattices in van der Waals heterostructures are gaining increasing attention because they offer new opportunities to tailor and explore unique electronic phenomena when stacking 2D materials with small twist angles. Here, we reveal local surface potentials associated with stacking domains in twisted double bilayer graphene (TDBG) moiré superlattices. Using a combination of both lateral Piezoresponse Force Microscopy (LPFM) and Scanning Kelvin Probe Microscopy (SKPM), we distinguish between Bernal (ABAB) and rhombohedral (ABCA) stacked graphene and directly correlate these stacking co…
We develop a continuum dislocation description of twist and stretch moire superlattices in 2D material bilayers. The continuum formulation is based on the topological constraints introduced by the periodic dislocation network associated with the moire structure. The approach is based on solving analytically for the structural distortion and displacement fields that satisfy the topological constraints, and which minimize the total energy. The total energy is described by both the strain energy of each individual distorted layer, and a Peierls-Nabarro like interfacial contribution arising from s…
