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.

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.

Efficient Fizeau drag from Dirac electrons in monolayer graphene.

Fizeau demonstrated in 1850 that the speed of light can be modified when it is propagating in moving media1. However, such control of the light speed has not been achieved efficiently with a fast-moving electron media by passing an electrical current. Because the strong electromagnetic coupling between the electron and light leads to the collective excitation of plasmon polaritons, it is hypothesized that Fizeau drag in electron flow systems manifests as a plasmonic Doppler effect. Experimental observation of the plasmonic Doppler effect in electronic systems has been challenge because the plasmon propagation speed is much faster than the electron drift velocity in conventional noble metals. Here we report direct observation of Fizeau drag of plasmon polaritons in strongly biased monolayer graphene by exploiting the high electron mobility and the slow plasmon propagation of massless Dirac electrons. The large bias current in graphene creates a fast-drifting Dirac electron medium hosting the plasmon polariton. This results in non-reciprocal plasmon propagation, where plasmons moving with the drifting electron media propagate at an enhanced speed. We measure the Doppler-shifted plasmon wavelength using cryogenic near-field infrared nanoscopy, which directly images the plasmon polariton mode in the biased graphene at low temperature. We observe a plasmon wavelength difference of up to 3.6 per cent between a plasmon moving with and a plasmon moving against the drifting electron media. Our findings on the plasmonic Doppler effect provide opportunities for electrical control of non-reciprocal surface plasmon polaritons in non-equilibrium systems.

Imaging two-dimensional generalized Wigner crystals.

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.

Ultralow contact resistance between semimetal and monolayer semiconductors.

Advanced beyond-silicon electronic technology requires both channel materials and also ultralow-resistance contacts to be discovered1,2. Atomically thin two-dimensional semiconductors have great potential for realizing high-performance electronic devices1,3. However, owing to metal-induced gap states (MIGS)4-7, energy barriers at the metal-semiconductor interface-which fundamentally lead to high contact resistance and poor current-delivery capability-have constrained the improvement of two-dimensional semiconductor transistors so far2,8,9. Here we report ohmic contact between semimetallic bismuth and semiconducting monolayer transition metal dichalcogenides (TMDs) where the MIGS are sufficiently suppressed and degenerate states in the TMD are spontaneously formed in contact with bismuth. Through this approach, we achieve zero Schottky barrier height, a contact resistance of 123 ohm micrometres and an on-state current density of 1,135 microamps per micrometre on monolayer MoS2; these two values are, to the best of our knowledge, the lowest and highest yet recorded, respectively. We also demonstrate that excellent ohmic contacts can be formed on various monolayer semiconductors, including MoS2, WS2 and WSe2. Our reported contact resistances are a substantial improvement for two-dimensional semiconductors, and approach the quantum limit. This technology unveils the potential of high-performance monolayer transistors that are on par with state-of-the-art three-dimensional semiconductors, enabling further device downscaling and extending Moore's law.

Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices.

Moiré superlattices can be used to engineer strongly correlated electronic states in two-dimensional van der Waals heterostructures, as recently demonstrated in the correlated insulating and superconducting states observed in magic-angle twisted-bilayer graphene and ABC trilayer graphene/boron nitride moiré superlattices1-4. Transition metal dichalcogenide moiré heterostructures provide another model system for the study of correlated quantum phenomena5 because of their strong light-matter interactions and large spin-orbit coupling. However, experimental observation of correlated insulating states in this system is challenging with traditional transport techniques. Here we report the optical detection of strongly correlated phases in semiconducting WSe2/WS2 moiré superlattices. We use a sensitive optical detection technique and reveal a Mott insulator state at one hole per superlattice site and surprising insulating phases at 1/3 and 2/3 filling of the superlattice, which we assign to generalized Wigner crystallization on the underlying lattice6-11. Furthermore, the spin-valley optical selection rules12-14 of transition metal dichalcogenide heterostructures allow us to optically create and investigate low-energy excited spin states in the Mott insulator. We measure a very long spin relaxation lifetime of many microseconds in the Mott insulating state, orders of magnitude longer than that of charge excitations. Our studies highlight the value of using moiré superlattices beyond graphene to explore correlated physics.

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.

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.

Observation of moiré excitons in WSe2/WS2 heterostructure superlattices.

Moiré superlattices enable the generation of new quantum phenomena in two-dimensional heterostructures, in which the interactions between the atomically thin layers qualitatively change the electronic band structure of the superlattice. For example, mini-Dirac points, tunable Mott insulator states and the Hofstadter butterfly pattern can emerge in different types of graphene/boron nitride moiré superlattices, whereas correlated insulating states and superconductivity have been reported in twisted bilayer graphene moiré superlattices1-12. In addition to their pronounced effects on single-particle states, moiré superlattices have recently been predicted to host excited states such as moiré exciton bands13-15. Here we report the observation of moiré superlattice exciton states in tungsten diselenide/tungsten disulfide (WSe2/WS2) heterostructures in which the layers are closely aligned. These moiré exciton states manifest as multiple emergent peaks around the original WSe2 A exciton resonance in the absorption spectra, and they exhibit gate dependences that are distinct from that of the A exciton in WSe2 monolayers and in WSe2/WS2 heterostructures with large twist angles. These phenomena can be described by a theoretical model in which the periodic moiré potential is much stronger than the exciton kinetic energy and generates multiple flat exciton minibands. The moiré exciton bands provide an attractive platform from which to explore and control excited states of matter, such as topological excitons and a correlated exciton Hubbard model, in transition-metal dichalcogenides.

Author Correction: Observation of moiré excitons in WSe2/WS2 heterostructure superlattices.

Change history: In this Letter, the following text has been added to the Acknowledgements section: "the scanning transmission electron microscopy measurements at the Molecular Foundry were supported by the Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under contract number DE-AC02-05CH11231". See accompanying Amendment.

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.

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.

Imaging gate-tunable Tomonaga-Luttinger liquids in 1H-MoSe2 mirror twin boundaries.

One-dimensional electron systems exhibit fundamentally different properties than higher-dimensional systems. For example, electron-electron interactions in one-dimensional electron systems have been predicted to induce Tomonaga-Luttinger liquid behaviour. Naturally occurring grain boundaries in single-layer transition metal dichalcogenides exhibit one-dimensional conducting channels that have been proposed to host Tomonaga-Luttinger liquids, but charge density wave physics has also been suggested to explain their behaviour. Clear identification of the electronic ground state of this system has been hampered by an inability to electrostatically gate such boundaries and tune their charge carrier concentration. Here we present a scanning tunnelling microscopy and spectroscopy study of gate-tunable mirror twin boundaries in single-layer 1H-MoSe2 devices. Gating enables scanning tunnelling microscopy and spectroscopy for different mirror twin boundary electron densities, thus allowing precise characterization of electron-electron interaction effects. Visualization of the resulting mirror twin boundary electronic structure allows unambiguous identification of collective density wave excitations having two velocities, in quantitative agreement with the spin-charge separation predicted by finite-length Tomonaga-Luttinger liquid theory.

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.

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.

Structural phase transition in monolayer MoTe2 driven by electrostatic doping.

Monolayers of transition-metal dichalcogenides (TMDs) exhibit numerous crystal phases with distinct structures, symmetries and physical properties. Exploring the physics of transitions between these different structural phases in two dimensions may provide a means of switching material properties, with implications for potential applications. Structural phase transitions in TMDs have so far been induced by thermal or chemical means; purely electrostatic control over crystal phases through electrostatic doping was recently proposed as a theoretical possibility, but has not yet been realized. Here we report the experimental demonstration of an electrostatic-doping-driven phase transition between the hexagonal and monoclinic phases of monolayer molybdenum ditelluride (MoTe2). We find that the phase transition shows a hysteretic loop in Raman spectra, and can be reversed by increasing or decreasing the gate voltage. We also combine second-harmonic generation spectroscopy with polarization-resolved Raman spectroscopy to show that the induced monoclinic phase preserves the crystal orientation of the original hexagonal phase. Moreover, this structural phase transition occurs simultaneously across the whole sample. This electrostatic-doping control of structural phase transition opens up new possibilities for developing phase-change devices based on atomically thin membranes.

Layer-dependent topological phase in a two-dimensional quasicrystal and approximant.

The electronic and topological properties of materials are derived from the interplay between crystalline symmetry and dimensionality. Simultaneously introducing "forbidden" symmetries via quasiperiodic ordering with low dimensionality into a material system promises the emergence of new physical phenomena. Here, we isolate a two-dimensional (2D) chalcogenide quasicrystal and approximant, and investigate their electronic and topological properties. The 2D layers of the materials with a composition close to Ta1.6Te, derived from a layered transition metal dichalcogenide, are isolated with standard exfoliation techniques, and investigated with electron diffraction and atomic resolution scanning transmission electron microscopy. Density functional theory calculations and symmetry analysis of the large unit cell crystalline approximant of the quasicrystal, Ta21Te13, reveal the presence of symmetry-protected nodal crossings in the quasicrystalline and approximant phases, whose presence is tunable by layer number. Our study provides a platform for the exploration of physics in quasicrystalline, low-dimensional materials and the interconnected nature of topology, dimensionality, and symmetry in electronic systems.

Targeting One- and Two-Dimensional Ta-Te Structures via Nanotube Encapsulation.

Fine control over material synthesis on the nanoscale can facilitate the stabilization of competing crystalline structures. Here, we demonstrate how carbon nanotube reaction vessels can be used to selectively create one-dimensional TaTe3 chains or two-dimensional TaTe2 nanoribbons with exquisite control of the chain number or nanoribbon thickness and width. Transmission electron microscopy and scanning transmission electron microscopy reveal the detailed atomic structure of the encapsulated materials. Complex superstructures such as multichain spiraling and apparent multilayer moirés are observed. The rare 2H phase of TaTe2 (1H in monolayer) is found to be abundant as an encapsulated nanoribbon inside carbon nanotubes. The experimental results are complemented by density functional theory calculations for the atomic and electronic structure, which uncovers the prevalence of 2H-TaTe2 due to nanotube-to-nanoribbon charge transfer and size confinement. Calculations also reveal new 1T' type charge density wave phases in TaTe2 that could be observed in experimental studies.

Kirigami Engineering of Suspended Graphene Transducers.

The low mass density and high mechanical strength of graphene make it an attractive candidate for suspended-membrane energy transducers. Typically, the membrane size dictates the operational frequency and bandwidth. However, in many cases it would be desirable to both lower the resonance frequency and increase the bandwidth, while maintaining overall membrane size. We employ focused ion beam milling or laser ablation to create kirigami-like modification of suspended pure-graphene membranes ranging in size from microns to millimeters. Kirigami engineering successfully reduces the resonant frequency, increases the displacement amplitude, and broadens the effective bandwidth of the transducer. Our results present a promising route to miniaturized wide-band energy transducers with enhanced operational parameter range and efficiency.

Structured-Liquid Batteries.

Chemical systems may be maintained far from equilibrium by sequestering otherwise reactive species into different microenvironments. It remains a significant challenge to control the amount of chemical energy stored in such systems and to utilize it on demand to perform useful work. Here, we show that redox-active molecules compartmentalized in multiphasic structured-liquid devices can be charged and discharged to power a load on an external circuit. The two liquid phases of these devices feature charge-complementary polyelectrolytes that serve a dual purpose: they generate an ionically conductive coacervate membrane at the liquid-liquid interface, providing structural support; they also mitigate active-material crossover between phases via ion pairing with the oppositely charged anolyte and catholyte active materials. Structured-liquid batteries enabled by this design were rechargeable over hundreds of hours. We envision that these devices may be integrated with soft electronics to enable functional circuits for smart textiles, medical implants, and wearables.