Electron Wigner solids (WSs)1-12 provide an ideal system for understanding the competing effects of electron-electron and electron-disorder interactions, a central unsolved problem in condensed matter physics. Progress in this topic has been limited by a lack of single-defect-resolved experimental measurements as well as accurate theoretical tools to enable realistic experiment/theory comparison. Here we overcome these limitations by combining atomically resolved scanning tunnelling microscopy (STM) with neural-quantum-state quantum Monte Carlo (NQS-QMC) simulation of disordered 2D electron WSs to discover new disorder-induced physical regimes of correlated electron behaviour. STM was used to image the electron density (ne)-dependent evolution of electron WSs in gate-tunable bilayer MoSe2 (BL-MoSe2) devices with varying long-range (nLR) and short-range (nSR) disorder densities. These images were compared with NQS-QMC simulations using realistic disorder maps extracted from experiment, thus allowing the roles of different disorder types to be disentangled. We identify two distinct physical regimes for disordered electron WSs that depend on nSR. For nSR ≲ ne, the WS behaviour is dominated by long-range disorder and features extensive mixed solid-liquid phases, a new type of local re-entrant melting/crystallization and prominent Friedel oscillations. By contrast, when nSR ≫ ne, these features are suppressed and a more robust amorphous WS phase emerges that persists to higher ne, highlighting the importance of short-range disorder in this regime. Our work establishes a powerful framework for studying disordered quantum solids through a combined experimental-theoretical approach.

Two-dimensional moiré materials provide a versatile platform to explore phase transitions in strongly correlated systems. Using scanning tunneling microscopy (STM) we have imaged the density-driven melting of generalized Wigner crystals (GWCs) and Mott insulators (MIs) in electron-doped, near-60° twisted MoSe2 bilayers featuring a triangular moiré superlattice. We observe striking electron-hole asymmetry in GWC melting: hole-doped GWCs yield interaction-driven disordered states whereas electron-doped GWCs melt into delocalized liquid-like states. This asymmetry arises from the broken particle-hole symmetry of the moiré superlattice, which produces electron and hole Fermi pockets with different momentum geometries upon GWC condensation. MI states melt without such asymmetry, consistent with the absence of a symmetry-breaking density modulation. This work provides direct visualization of the novel emergent phases that appear as GWCs undergo quantum melting transitions.

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 WS 2 , we impose a Coulomb superlattice in the bilayer graphene with period and strength determined by the twisted bilayer WS 2 . 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.

We report on the three-dimensional (3D) structure determination of a twisted hexagonal boron nitride (h-BN) heterointerface from a single-view dataset using multislice ptychography. We identify the buried heterointerface between two twisted h-BN flakes with a lateral resolution of 0.57 & Aring; and a depth resolution of 2.5 nm. The latter represents a significant improvement (similar to 2.7 times) over the aperture-limited depth resolution of incoherent imaging modes, such as annular-dark-field scanning transmission electron microscopy. This improvement is attributed to the diffraction signal extending beyond the aperture edge, with the depth resolution set by the curvature of the Ewald sphere. Future advancements in this approach could enhance the depth resolution to the subnanometer level and enable the identification of individual dopants, defects, and color centers in twisted heterointerfaces and other materials.

Advanced microelectronics in the future may require semiconducting channel materials beyond silicon. Two-dimensional (2D) semiconductors, characterized by their atomically thin thickness, hold immense promise for high-performance electronic devices at the nanometer scale with lower heat dissipation. One challenge for achieving high-performance 2D semiconductor field effect transistors (FET), especially for p-type materials, is the high electrical contact resistance present at the metal-semiconductor interface. In conventional bulk semiconductors, low resistance ohmic contact is realized through heavy substitutional doping with acceptor or donor impurities at the contact region. The strategy of substitutional doping, however, does not work for p-type 2D semiconductors such as monolayer tungsten diselenide (WSe$_2$).In this study, we developed highly efficient charge-transfer doping with WSe$_2$/$\alpha$-RuCl$_3$ heterostructures to achieve low-resistance ohmic contact for p-type WSe$_2$ transistors. We show that a hole doping as high as 3$\times$10$^{13}$ cm$^{-2}$ can be achieved in the WSe$_2/\alpha$-RuCl$_3$ heterostructure due to its type-III band alignment. It results in an Ohmic contact with resistance lower than 4 k Ohm $\mu$m at the p-type monolayer WSe$_2$/metal junction. at room temperature. Using this low-resistance contact, we demonstrate high-performance p-type WSe$_2$ transistors with a saturation current of 35 $\mu$A$\cdot$ $\mu$m$^{-1}$ and an I$_{ON}$/I$_{OFF}$ ratio exceeding 10$^9$ It could enable future microelectronic devices based on 2D semiconductors and contribute to the extension of Moore's law.

Moiré systems made from stacked two-dimensional materials host correlated and topological states that can be electrically controlled with applied gate voltages. One prevalent form of topological state that can occur are Chern insulators that display a quantum anomalous Hall effect. Here we manipulate Chern domains in an interaction-driven quantum anomalous Hall insulator made from twisted monolayer–bilayer graphene and observe chiral interface states at the boundary between different domains. By tuning the carrier concentration, we stabilize neighbouring domains of opposite Chern number that then provide topological interfaces devoid of any structural boundaries. This allows the wavefunction of chiral interface states to be directly imaged using a scanning tunnelling microscope. Our theoretical analysis confirms the chiral nature of observed interface states and allows us to determine the characteristic length scale of valley polarization reversal across neighbouring Chern domains.

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.

The accumulation of carbon dioxide (CO2) within enclosed spaces, along with volatile organic compounds, under certain humidity, temperature, and ventilation conditions is associated with detrimental human health symp-toms such as fatigue. Color-based chemical sensing is a promising approach to detect CO2 levels relevant to indoor air quality through producing fast, quantifiable output visible to the naked eye. In a prior work, a colorimetric gas sensor was fabricated through synthesizing the metal-organic framework, ZIF-8, as the adsor-bent, followed by post-synthetic mixing with a dye, phenol red (PSP), and primary amine, ethylenediamine (ED). While this sensor (termed PSP-ED/ZIF-8) maintained its structural integrity in atmospheric conditions and exhibited an increasing fuchsia-to-yellow color change with increasing CO2 levels in dry environment, the colorimetric response greatly suffered in the presence of humid CO2. In this work, a significantly improved colorimetric CO2 sensor (referred to as ED/PSP:ZIF-8) is accomplished through directly incorporating phenol red in the ZIF-8 metal and linker precursor solutions and then blending with ethylenediamine. MATLAB-generated color distributions and in-situ ultraviolet-visible (UV-Vis) spectroscopic studies quantitatively demonstrate an enhanced colorimetric gas response of ED/PSP:ZIF-8 compared to that of PSP-ED/ZIF-8 across an important range of CO2 for indoor air quality monitoring (500 - 3500 ppm) and across a range of humidity. The new sensor also exhibits high selectivity to CO2 compared to select volatile organic compounds, such as acetone and ethanol, which contribute to human health symptoms experienced indoors. The enhanced performance is attributed to the proposed incorporation of phenol red within ZIF-8, while maintaining the chemical stability of the MOF.

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

We demonstrate the application of multislice ptychography to a twisted hexagonal boron nitride (h-BN) heterointerface from a single-view data set. The propagation from the top flake, through the interface, to the bottom flake is visualized from separate slices of the reconstruction. The depth resolution of the reconstruction is determined to be 2.74 nm, which is a significant improvement over the aperture-limited depth resolution of 6.74 nm. This is attributed to the diffraction signal extending beyond the aperture edge with the depth resolution set by the curvature of the Ewald sphere. Future advances to this approach could improve the depth resolution to the sub-nanometer level and enable the identification of individual dopants, defects and color centers in twisted heterointerfaces and other materials.

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.

We report three-dimensional (3D) structure determination of a twisted hexagonal boron nitride (h-BN) heterointerface from a single-view data set using multislice ptychography. We identify the buried heterointerface between two twisted h-BN flakes with a lateral resolution of 0.57 Å and a depth resolution of 2.5 nm. The latter is a significant improvement ( 2.7 times) over the aperture-limited depth resolution of incoherent imaging modes such as annular-dark-field scanning transmission electron microscopy. This is attributed to the diffraction signal extending beyond the aperture edge with the depth resolution set by the curvature of the Ewald sphere. Future advances to this approach could improve the depth resolution to the sub-nanometer level and enable the identification of individual dopants, defects and color centers in twisted heterointerfaces and other materials.

Moir\'e systems made from stacked two-dimensional materials host novel correlated and topological states that can be electrically controlled via applied gate voltages. We have used this technique to manipulate Chern domains in an interaction-driven quantum anomalous Hall insulator made from twisted monolayer-bilayer graphene (tMBLG). This has allowed the wavefunction of chiral interface states to be directly imaged using a scanning tunneling microscope (STM). To accomplish this tMBLG carrier concentration was tuned to stabilize neighboring domains of opposite Chern number, thus providing topological interfaces completely devoid of any structural boundaries. STM tip pulse-induced quantum dots were utilized to induce new Chern domains and thereby create new chiral interface states with tunable chirality at predetermined locations. Theoretical analysis confirms the chiral nature of observed interface states and enables the determination of the characteristic length scale of valley polarization reversal across neighboring tMBLG Chern domains. tMBLG is shown to be a useful platform for imaging the exotic topological properties of correlated moir\'e systems.

The interplay between electron-electron interactions and structural ordering can yield exceptionally rich correlated electronic phases. We have used scanning tunneling microscopy to investigate bulk 1T-TaSe2 and have uncovered surprisingly diverse correlated surface states thereof. These surface states exhibit the same in-plane charge density wave ordering but dramatically different electronic ground states ranging from insulating to metallic. The insulating variety of surface state shows signatures of a decoupled surface Mott layer. The metallic surface states, on the other hand, exhibit zero-bias peaks of varying strength that suggest Kondo phases arising from coupling between the Mott surface layer and the metallic bulk of 1T-TaSe2. The surface of bulk 1T-TaSe2 thus constitutes a rare realization of the periodic Anderson model covering a wide parameter regime, thereby providing a model system for accessing different correlated phenomena in the same crystal. Our results highlight the central role played by strong correlations in this material family.

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.

The Wigner crystal1 has fascinated condensed matter physicists for nearly 90 years2–14. Signatures of two-dimensional (2D) Wigner crystals were first observed in 2D electron gases under high magnetic field2–4, and recently reported in transition metal dichalcogenide moiré superlattices6–9. Direct observation of the 2D Wigner crystal lattice in real space, however, has remained an outstanding challenge. Conventional scanning tunnelling microscopy (STM) has sufficient spatial resolution but induces perturbations that can potentially alter this fragile state. Here we demonstrate real-space imaging of 2D Wigner crystals in WSe2/WS2 moiré heterostructures using a specially designed non-invasive STM spectroscopy technique. This employs a graphene sensing layer held close to the WSe2/WS2 moiré superlattice. Local STM tunnel current into the graphene layer is modulated by the underlying Wigner crystal electron lattice in the WSe2/WS2 heterostructure. Different Wigner crystal lattice configurations at fractional electron fillings of n = 1/3, 1/2 and 2/3, where n is the electron number per site, are directly visualized. The n = 1/3 and n = 2/3 Wigner crystals exhibit triangular and honeycomb lattices, respectively, to minimize nearest-neighbour occupations. The n = 1/2 state spontaneously breaks the original C3 symmetry and forms a stripe phase. Our study lays a solid foundation for understanding Wigner crystal states in WSe2/WS2 moiré heterostructures and provides an approach that is generally applicable for imaging novel correlated electron lattices in other systems. So far, only indirect evidence of Wigner crystals has been reported, but a specially designed scanning tunnelling microscope is used here to directly image them in a moiré heterostructure.

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 interactions1-9. 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 tunnelling spectroscopy (STS) of high-quality exfoliated TMD heterostructure devices with ab initio simulations of TMD moiré superlattices. A strong 3D buckling reconstruction accompanied by large in-plane strain redistribution is identified in our WSe2/WS2 moiré heterostructures. STS imaging demonstrates that this results in a remarkably narrow and highly localized K-point moiré flat band at the valence band edge of the heterostructure. A series of moiré flat bands are observed at different energies that exhibit varying degrees of localization. Our observations contradict previous simplified theoretical models but agree quantitatively with ab initio simulations that fully capture the 3D structural reconstruction. Our results reveal that the strain redistribution and 3D buckling in TMD heterostructures dominate the effective moiré potential and the corresponding moiré flat bands at the Brillouin zone K points.

Two-dimensional triangular-lattice antiferromagnets are predicted under some conditions to exhibit a quantum spin liquid ground state with no energy barrier to create emergent, fractionalized spinon excitations that carry spin but no charge. Materials that realize this kind of spin liquid are expected to have a low-energy behaviour described by a spinon Fermi surface. Directly imaging the resulting spinons, however, is difficult due to their chargeless nature. Here we use scanning tunnelling spectroscopy to image density waves consistent with the predictions of spinon density modulation arising from a spinon Fermi surface instability in single-layer 1T-TaSe 2 . We confirm the existence of a triangular lattice of localized spins in this material by contacting it with a metallic 1H-TaSe 2 substrate and measuring the Kondo effect. Spectroscopic imaging of isolated single-layer 1T-TaSe 2 reveals long-wavelength super-modulations at Hubbard band energies, consistent with the predicted behaviour of itinerant spinons. These super-modulations allow the direct experimental measurement of the spinon Fermi wavevector, in good agreement with theoretical predictions for a two-dimensional quantum spin liquid.

The Wigner crystal state, first predicted by Eugene Wigner in 1934, has fascinated condensed matter physicists for nearly 90 years2-14. Studies of two-dimensional (2D) electron gases first revealed signatures of the Wigner crystal in electrical transport measurements at high magnetic fields2-4. More recently optical spectroscopy has provided evidence of generalized Wigner crystal states in transition metal dichalcogenide (TMDC) moiré superlattices. Direct observation of the 2D Wigner crystal lattice in real space, however, has remained an outstanding challenge. Scanning tunneling microscopy (STM) in principle has sufficient spatial resolution to image a Wigner crystal, but conventional STM measurements can potentially alter fragile Wigner crystal states in the process of measurement. Here we demonstrate real-space imaging of 2D Wigner crystals in WSe2/WS2 moiré heterostructures using a novel non-invasive STM spectroscopy technique. We employ a graphene sensing layer in close proximity to the WSe2/WS2 moiré superlattice for Wigner crystal imaging, where local STM tunneling current into the graphene sensing layer is modulated by the underlying electron lattice of the Wigner crystal in the WSe2/WS2 heterostructure. Our measurement directly visualizes different lattice configurations associated with Wigner crystal states at fractional electron fillings of n = 1/3, 1/2, and 2/3, where n is the electron number per site. The n=1/3 and n=2/3 Wigner crystals are observed to exhibit a triangle and a honeycomb lattice, respectively, in order to minimize nearest-neighbor occupations. The n = 1/2 state, on the other hand, spontaneously breaks the original C3 symmetry and forms a stripe structure in real space. Our study lays a solid foundation toward the fundamental understanding of rich Wigner crystal states in WSe2/WS2 moiré heterostructures.