Wigner molecular crystals from multielectron moiré artificial atoms.

Semiconductor moiré superlattices provide a versatile platform to engineer quantum solids composed of artificial atoms on moiré sites. Previous studies have mostly focused on the simplest correlated quantum solid-the Fermi-Hubbard model-in which intra-atom interactions are simplified to a single onsite repulsion energy U. Here we report the experimental observation of Wigner molecular crystals emerging from multielectron artificial atoms in twisted bilayer tungsten disulfide moiré superlattices. Using scanning tunneling microscopy, we demonstrate that Wigner molecules appear in multielectron artificial atoms when Coulomb interactions dominate. The array of Wigner molecules observed in a moiré superlattice comprises a crystalline phase of electrons: the Wigner molecular crystal, which is shown to be highly tunable through mechanical strain, moiré period, and carrier charge type.

Imaging tunable Luttinger liquid systems in van der Waals heterostructures.

One-dimensional (1D) interacting electrons are often described as a Luttinger liquid1-4 having properties that are intrinsically different from those of Fermi liquids in higher dimensions5,6. In materials systems, 1D electrons exhibit exotic quantum phenomena that can be tuned by both intra- and inter-1D-chain electronic interactions, but their experimental characterization can be challenging. Here we demonstrate that layer-stacking domain walls (DWs) in van der Waals heterostructures form a broadly tunable Luttinger liquid system, including both isolated and coupled arrays. We have imaged the evolution of DW Luttinger liquids under different interaction regimes tuned by electron density using scanning tunnelling microscopy. Single DWs at low carrier density are highly susceptible to Wigner crystallization consistent with a spin-incoherent Luttinger liquid, whereas at intermediate densities dimerized Wigner crystals form because of an enhanced magneto-elastic coupling. Periodic arrays of DWs exhibit an interplay between intra- and inter-chain interactions that gives rise to new quantum phases. At low electron densities, inter-chain interactions are dominant and induce a 2D electron crystal composed of phased-locked 1D Wigner crystal in a staggered configuration. Increased electron density causes intra-chain fluctuation potentials to dominate, leading to an electronic smectic liquid crystal phase in which electrons are ordered with algebraical correlation decay along the chain direction but disordered between chains. Our work shows that layer-stacking DWs in 2D heterostructures provides opportunities to explore Luttinger liquid physics.

SiX2 (X = S, Se) Single Chains and (Si-Ge)X2 Quaternary Alloys.

Layered or chain materials have received significant research attention owing to their interesting physical properties, which can dramatically change when the material is thinned from bulk (three-dimensional) to thin two-dimensional sheet or one-dimensional (1D) chain form. Materials with the stoichiometry AX2 with A = Si or Ge and X = S or Se form an especially intriguing semiconducting class. For example, bulk silicon dichalcogenides (SiX2) consist of 1D chains held together by van der Waals forces. Although this structural configuration has the potential to reveal interesting physical phenomena within the 1D limit, obtaining SiX2 single chains has been challenging. We here examine experimentally and theoretically SiX2 materials in the low chain number limit. Carbon nanotubes serve as growth templates and stabilize and protect the structures, and atomic-resolution scanning transmission electron microscopy directly identifies the atomic structure. Two distinct chain structures are observed for SiX2. SixGe1-xS2(1-y)Se2y quaternary alloy chains are also synthesized and characterized, demonstrating tunable semiconducting properties at the atomic-chain level. Density functional theory calculations reveal that the band gap of these alloy chains can be widely tuned through composition engineering. This work offers the possibilities for synthesizing and controlling semiconductor compositions at the single-chain limit to tailor material properties.

Low Resistance Contact to P-Type Monolayer WSe2.

Advanced microelectronics in the future may require semiconducting channel materials beyond silicon. Two-dimensional (2D) semiconductors, with their atomically thin thickness, hold great promise for future electronic devices. One challenge to achieving high-performance 2D semiconductor field effect transistors (FET) is the high contact resistance at the metal-semiconductor interface. In this study, we develop a charge-transfer doping strategy with WSe2/α-RuCl3 heterostructures to achieve low-resistance ohmic contact for p-type monolayer WSe2 transistors. We show that hole doping as high as 3 × 1013 cm-2 can be achieved in the WSe2/α-RuCl3 heterostructure due to its type-III band alignment, resulting in an ohmic contact with resistance of 4 kΩ µm. Based on that, we demonstrate p-type WSe2 transistors with an on-current of 35 µA·µm-1 and an ION/IOFF ratio exceeding 109 at room temperature.

Imaging moiré excited states with photocurrent tunnelling microscopy.

Moiré superlattices provide a highly tuneable and versatile platform to explore novel quantum phases and exotic excited states ranging from correlated insulators to moiré excitons. Scanning tunnelling microscopy has played a key role in probing microscopic behaviours of the moiré correlated ground states at the atomic scale. However, imaging of quantum excited states in moiré heterostructures remains an outstanding challenge. Here we develop a photocurrent tunnelling microscopy technique that combines laser excitation and scanning tunnelling spectroscopy to directly visualize the electron and hole distribution within the photoexcited moiré exciton in twisted bilayer WS2. The tunnelling photocurrent alternates between positive and negative polarities at different locations within a single moiré unit cell. This alternating photocurrent originates from the in-plane charge transfer moiré exciton in twisted bilayer WS2, predicted by our GW-Bethe-Salpeter equation calculations, that emerges from the competition between the electron-hole Coulomb interaction and the moiré potential landscape. Our technique enables the exploration of photoexcited non-equilibrium moiré phenomena at the atomic scale.

Mapping charge excitations in generalized Wigner crystals.

Transition metal dichalcogenide-based moiré superlattices exhibit strong electron-electron correlations, thus giving rise to strongly correlated quantum phenomena such as generalized Wigner crystal states. Evidence of Wigner crystals in transition metal dichalcogenide moire superlattices has been widely reported from various optical spectroscopy and electrical conductivity measurements, while their microscopic nature has been limited to the basic lattice structure. Theoretical studies predict that unusual quasiparticle excitations across the correlated gap between upper and lower Hubbard bands can arise due to long-range Coulomb interactions in generalized Wigner crystal states. However, the microscopic proof of such quasiparticle excitations is challenging because of the low excitation energy of the Wigner crystal. Here we describe a scanning single-electron charging spectroscopy technique with nanometre spatial resolution and single-electron charge resolution that enables us to directly image electron and hole wavefunctions and to determine the thermodynamic gap of generalized Wigner crystal states in twisted WS2 moiré heterostructures. High-resolution scanning single-electron charging spectroscopy combines scanning tunnelling microscopy with a monolayer graphene sensing layer, thus enabling the generation of individual electron and hole quasiparticles in generalized Wigner crystals. We show that electron and hole quasiparticles have complementary wavefunction distributions and that thermodynamic gaps of ∼50 meV exist for the 1/3 and 2/3 generalized Wigner crystal states in twisted WS2.

Engineering correlated insulators in bilayer graphene with a remote Coulomb superlattice.

Electron superlattices allow the engineering of correlated and topological quantum phenomena. The recent emergence of moiré superlattices in two-dimensional heterostructures has led to exciting discoveries related to quantum phenomena. However, the requirement for the moiré pattern poses stringent limitations, and its potential cannot be switched on and off. Here, we demonstrate remote engineering and on/off switching of correlated states in bilayer graphene. Employing a remote Coulomb superlattice realized by localized electrons in twisted bilayer WS2, we impose a Coulomb superlattice in the bilayer graphene with period and strength determined by the twisted bilayer WS2. When the remote superlattice is turned off, the two-dimensional electron gas in the bilayer graphene is described by a Fermi liquid. When it is turned on, correlated insulating states at both integer and fractional filling factors emerge. This approach enables in situ control of correlated quantum phenomena in two-dimensional materials hosting a two-dimensional electron gas.

Solving complex nanostructures with ptychographic atomic electron tomography.

Transmission electron microscopy (TEM) is essential for determining atomic scale structures in structural biology and materials science. In structural biology, three-dimensional structures of proteins are routinely determined from thousands of identical particles using phase-contrast TEM. In materials science, three-dimensional atomic structures of complex nanomaterials have been determined using atomic electron tomography (AET). However, neither of these methods can determine the three-dimensional atomic structure of heterogeneous nanomaterials containing light elements. Here, we perform ptychographic electron tomography from 34.5 million diffraction patterns to reconstruct an atomic resolution tilt series of a double wall-carbon nanotube (DW-CNT) encapsulating a complex ZrTe sandwich structure. Class averaging the resulting tilt series images and subpixel localization of the atomic peaks reveals a Zr11Te50 structure containing a previously unobserved ZrTe2 phase in the core. The experimental realization of atomic resolution ptychographic electron tomography will allow for the structural determination of a wide range of beam-sensitive nanomaterials containing light elements.

1D Magnetic MX3 Single-Chains (M = Cr, V and X = Cl, Br, I).

Magnetic materials in reduced dimensions are not only excellent platforms for fundamental studies of magnetism, but they play crucial roles in technological advances. The discovery of intrinsic magnetism in monolayer 2D van der Waals systems has sparked enormous interest, but the single-chain limit of 1D magnetic van der Waals materials has been largely unexplored. This paper reports on a family of 1D magnetic van der Waals materials with composition MX3 (M = Cr, V, and X = Cl, Br, I), prepared in fully-isolated fashion within the protective cores of carbon nanotubes. Atomic-resolution scanning transmission electron microscopy identifies unique structures that differ from the well-known 2D honeycomb lattice MX3 structure. Density functional theory calculations reveal charge-driven reversible magnetic phase transitions.

Imaging the electron charge density in monolayer MoS2 at the Ångstrom scale.

Four-dimensional scanning transmission electron microscopy (4D-STEM) has recently gained widespread attention for its ability to image atomic electric fields with sub-Ångstrom spatial resolution. These electric field maps represent the integrated effect of the nucleus, core electrons and valence electrons, and separating their contributions is non-trivial. In this paper, we utilized simultaneously acquired 4D-STEM center of mass (CoM) images and annular dark field (ADF) images to determine the projected electron charge density in monolayer MoS2. We evaluate the contributions of both the core electrons and the valence electrons to the derived electron charge density; however, due to blurring by the probe shape, the valence electron contribution forms a nearly featureless background while most of the spatial modulation comes from the core electrons. Our findings highlight the importance of probe shape in interpreting charge densities derived from 4D-STEM and the need for smaller electron probes.

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

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.

Imaging Field-Driven Melting of a Molecular Solid at the Atomic Scale.

Solid-liquid phase transitions are basic physical processes, but atomically resolved microscopy has yet to capture their full dynamics. A new technique is developed for controlling the melting and freezing of self-assembled molecular structures on a graphene field-effect transistor (FET) that allows phase-transition behavior to be imaged using atomically resolved scanning tunneling microscopy. This is achieved by applying electric fields to 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane-decorated FETs to induce reversible transitions between molecular solid and liquid phases at the FET surface. Nonequilibrium melting dynamics are visualized by rapidly heating the graphene substrate with an electrical current and imaging the resulting evolution toward new 2D equilibrium states. An analytical model is developed that explains observed mixed-state phases based on spectroscopic measurement of solid and liquid molecular energy levels. The observed nonequilibrium melting dynamics are consistent with Monte Carlo simulations.

Evolution of nanopores in hexagonal boron nitride.

The engineering of atomically-precise nanopores in two-dimensional materials presents exciting opportunities for both fundamental science studies as well as applications in energy, DNA sequencing, and quantum information technologies. The exceptional chemical and thermal stability of hexagonal boron nitride (h-BN) suggest that exposed h-BN nanopores will retain their atomic structure even when subjected to extended periods of time in gas or liquid environments. Here we employ transmission electron microscopy to examine the time evolution of h-BN nanopores in vacuum and in air and find, even at room temperature, dramatic geometry changes due to atom motion and edge contamination adsorption, for timescales ranging from one hour to one week. The discovery of nanopore evolution contrasts with general expectations and has profound implications for nanopore applications of two-dimensional materials.

Tuning the Sharing Modes and Composition in a Tetrahedral GeX2 (X = S, Se) System via One-Dimensional Confinement.

The packing and connectivity of tetrahedral units are central themes in the structural and electronic properties of a host of solids. Here, we report one-dimensional (1D) chains of GeX2 (X = S or Se) with modification of the tetrahedral connectivity at the single-chain limit. Precise tuning of the edge- and corner-sharing modes between GeX2 blocks is achieved by diameter-dependent 1D confinement inside a carbon nanotube. Atomic-resolution scanning transmission electron microscopy directly confirms the existence of two distinct types of GeX2 chains. Density functional theory calculations corroborate the diameter-dependent stability of the system and reveal an intriguing electronic structure that sensitively depends on tetrahedral connectivity and composition. GeS2(1-x)Se2x compound chains are also realized, which demonstrate the tunability of the system's semiconducting properties through composition engineering.

High-Order Fractal Quantum Oscillations in Graphene/BN Superlattices in the Extreme Doping Limit.

Recent studies of van der Waals (vdW) heterostructures and superlattices have shown intriguing quantum phenomena, but these have been largely explored only in the moderate carrier density regime. Here, we report the probe of high-temperature fractal Brown-Zak (BZ) quantum oscillations through magnetotransport in the extreme doping regimes by applying a newly developed electron beam doping technique. This technique gives access to both ultrahigh electron and hole densities beyond the dielectric breakdown limit in graphene/BN superlattices, enabling the observation of nonmonotonic carrier-density dependence of fractal BZ states and up to fourth-order fractal BZ features despite strong electron-hole asymmetry. Theoretical tight-binding simulations qualitatively reproduce all observed fractal BZ features and attribute the nonmonotonic dependence to the weakening of superlattice effects at high carrier densities.

Observation of hydrodynamic plasmons and energy waves in graphene.

Thermally excited electrons and holes form a quantum-critical Dirac fluid in ultraclean graphene and their electrodynamic responses are described by a universal hydrodynamic theory. The hydrodynamic Dirac fluid can host intriguing collective excitations distinctively different from those in a Fermi liquid1-4. Here we report the observation of the hydrodynamic plasmon and energy wave in ultraclean graphene. We use the on-chip terahertz (THz) spectroscopy technique to measure the THz absorption spectra of a graphene microribbon as well as the propagation of the energy wave in graphene close to charge neutrality. We observe a prominent high-frequency hydrodynamic bipolar-plasmon resonance and a weaker low-frequency energy-wave resonance of the Dirac fluid in ultraclean graphene. The hydrodynamic bipolar plasmon is characterized by the antiphase oscillation of massless electrons and holes in graphene. The hydrodynamic energy wave is an electron-hole sound mode with both charge carriers oscillating in phase and moving together. The spatial-temporal imaging technique shows that the energy wave propagates at a characteristic speed of [Formula: see text] near the charge neutrality2-4. Our observations open new opportunities to explore collective hydrodynamic excitations in graphene systems.

Deep-Learning Electron Diffractive Imaging.

We report the development of deep-learning coherent electron diffractive imaging at subangstrom resolution using convolutional neural networks (CNNs) trained with only simulated data. We experimentally demonstrate this method by applying the trained CNNs to recover the phase images from electron diffraction patterns of twisted hexagonal boron nitride, monolayer graphene, and a gold nanoparticle with comparable quality to those reconstructed by a conventional ptychographic algorithm. Fourier ring correlation between the CNN and ptychographic images indicates the achievement of a resolution in the range of 0.70 and 0.55 Å. We further develop CNNs to recover the probe function from the experimental data. The ability to replace iterative algorithms with CNNs and perform real-time atomic imaging from coherent diffraction patterns is expected to find applications in the physical and biological sciences.

All-Liquid Reconfigurable Electronics Using Jammed MXene Interfaces.

Rigid, solid-state components represent the current paradigm for electronic systems, but they lack post-production reconfigurability and pose ever-increasing challenges to efficient end-of-life recycling. Liquid electronics may overcome these limitations by offering flexible in-the-field redesign and separation at end-of-life via simple liquid phase chemistries. Up to now, preliminary work on liquid electronics has focused on liquid metal components, but these devices still require an encapsulating polymer and typically use alloys of rare elements like indium. Here, using the self-assembly of jammed 2D titanium carbide (Ti3 C2 Tx ) MXene nanoparticles at liquid-liquid interfaces, "all-liquid" electrically conductive sheets, wires, and simple functional devices are described including electromechanical switches and photodetectors. These assemblies combine the high conductivity of MXene nanosheets with the controllable form and reconfigurability of structured liquids. Such configurations can have applications not only in electronics, but also in catalysis and microfluidics, especially in systems where the product and substrate have affinity for solvents of differing polarity.

Tuning colour centres at a twisted hexagonal boron nitride interface.

The colour centre platform holds promise for quantum technologies, and hexagonal boron nitride has attracted attention due to the high brightness and stability, optically addressable spin states and wide wavelength coverage discovered in its emitters. However, its application is hindered by the typically random defect distribution and complex mesoscopic environment. Here, employing cathodoluminescence, we demonstrate on-demand activation and control of colour centre emission at the twisted interface of two hexagonal boron nitride flakes. Further, we show that colour centre emission brightness can be enhanced by two orders of magnitude by tuning the twist angle. Additionally, by applying an external voltage, nearly 100% brightness modulation is achieved. Our ab initio GW and GW plus Bethe-Salpeter equation calculations suggest that the emission is correlated to nitrogen vacancies and that a twist-induced moiré potential facilitates electron-hole recombination. This mechanism is further exploited to draw nanoscale colour centre patterns using electron beams.

Beam-driven Dynamics of Aluminium Dopants in Graphene.

Substituting heteroatoms into graphene can tune its properties for applications ranging from catalysis to spintronics. The further recent discovery that covalent impurities in graphene can be manipulated at atomic precision using a focused electron beam may open avenues towards sub-nanometer device architectures. However, the preparation of clean samples with a high density of dopants is still very challenging. Here, we report vacancy-mediated substitution of aluminium into laser-cleaned graphene, and without removal from our ultra-high vacuum apparatus, study their dynamics under 60 keV electron irradiation using aberration-corrected scanning transmission electron microscopy and spectroscopy. Three- and four-coordinated Al sites are identified, showing excellent agreement with ab initio predictions including binding energies and electron energy-loss spectrum simulations. We show that the direct exchange of carbon and aluminium atoms predicted earlier occurs under electron irradiation, although unexpectedly it is less probable than the same process for silicon. We also observe a previously unknown nitrogen-aluminium exchange that occurs at Al─N double-dopant sites at graphene divacancies created by our plasma treatment.