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.

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.

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.

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.

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.

Imaging moiré flat bands in three-dimensional reconstructed WSe2/WS2 superlattices.

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.

Imaging Quantum Interference in Stadium-Shaped Monolayer and Bilayer Graphene Quantum Dots.

Experimental realizations of graphene-based stadium-shaped quantum dots (QDs) have been few and have been incompatible with scanned probe microscopy. Yet, the direct visualization of electronic states within these QDs is crucial for determining the existence of quantum chaos in these systems. We report the fabrication and characterization of electrostatically defined stadium-shaped QDs in heterostructure devices composed of monolayer graphene (MLG) and bilayer graphene (BLG). To realize a stadium-shaped QD, we utilized the tip of a scanning tunneling microscope to charge defects in a supporting hexagonal boron nitride flake. The stadium states visualized are consistent with tight-binding-based simulations but lack clear quantum chaos signatures. The absence of quantum chaos features in MLG-based stadium QDs is attributed to the leaky nature of the confinement potential due to Klein tunneling. In contrast, for BLG-based stadium QDs (which have stronger confinement) quantum chaos is precluded by the smooth confinement potential which reduces interference and mixing between states.

Tunneling Spectroscopy in Carbon Nanotube-Hexagonal Boron Nitride-Carbon Nanotube Heterojunctions.

Electron tunneling spectroscopy is a powerful technique to probe the unique physical properties of one-dimensional (1D) single-walled carbon nanotubes (SWNTs), such as the van Hove singularities in the density of states or the power-law tunneling probability of a Luttinger liquid. However, little is known about the tunneling behavior between two 1D SWNTs over a large energy spectrum. Here, we investigate the electron tunneling behavior between two crossed SWNTs across a wide spectral window up to 2 eV in the unique carbon nanotube-hexagonal boron nitride-carbon nanotube heterojunctions. We observe many sharp resonances in the differential tunneling conductance at different bias voltages applied between the SWNTs. These resonances can be attributed to elastic tunneling into the van Hove singularities of different 1D subbands in both SWNTs, and they allow us to determine the quasi-particle bandgaps and higher-lying 1D subbands in SWNTs on the insulating substrate.

Layer-Dependent Electronic Structure of Atomically Resolved Two-Dimensional Gallium Selenide Telluride.

Alloying two-dimensional (2D) semiconductors provides a powerful method to tune their physical properties, especially those relevant to optoelectronic applications. However, as the crystal structure becomes more complex, it becomes increasingly difficult to accurately correlate response characteristics to detailed atomic structure. We investigate, via annular dark-field scanning transmission electron microscopy, electron energy loss spectroscopy, and second harmonic generation, the layered III-VI alloy GaSe0.5Te0.5 as a function of layer number. The local atomic structure and stacking sequence for different layers is explicitly determined. We complement the measurements with first-principles calculations of the total energy and electronic band structure of GaSe0.5Te0.5 for different crystal structures and layer number. The electronic band gap as well as the π and π + σ plasmons are found to be sensitive to layer number.

Visualization and Control of Single-Electron Charging in Bilayer Graphene Quantum Dots.

Graphene p-n junctions provide an ideal platform for investigating novel behavior at the boundary between electronics and optics that arise from massless Dirac Fermions, such as whispering gallery modes and Veselago lensing. Bilayer graphene also hosts Dirac Fermions, but they differ from single-layer graphene charge carriers because they are massive, can be gapped by an applied perpendicular electric field, and have very different pseudospin selection rules across a p-n junction. Novel phenomena predicted for these massive Dirac Fermions at p-n junctions include anti-Klein tunneling, oscillatory Zener tunneling, and electron cloaked states. Despite these predictions there has been little experimental focus on the microscopic spatial behavior of massive Dirac Fermions in the presence of p-n junctions. Here we report the experimental manipulation and characterization of massive Dirac Fermions within bilayer graphene quantum dots defined by circular p-n junctions through the use of scanning tunneling microscopy-based (STM) methods. Our p-n junctions are created via a flexible technique that enables realization of exposed quantum dots in bilayer graphene/hBN heterostructures. These quantum dots exhibit sharp spectroscopic resonances that disperse in energy as a function of applied gate voltage. Spatial maps of these features show prominent concentric rings with diameters that can be tuned by an electrostatic gate. This behavior is explained by single-electron charging of localized states that arise from the quantum confinement of massive Dirac Fermions within our exposed bilayer graphene quantum dots.

Persistent Charge-Density-Wave Order in Single-Layer TaSe2.

We present the electronic characterization of single-layer 1H-TaSe2 grown by molecular beam epitaxy using a combined angle-resolved photoemission spectroscopy, scanning tunneling microscopy/spectroscopy, and density functional theory calculations. We demonstrate that 3 × 3 charge-density-wave (CDW) order persists despite distinct changes in the low energy electronic structure highlighted by the reduction in the number of bands crossing the Fermi energy and the corresponding modification of Fermi surface topology. Enhanced spin-orbit coupling and lattice distortion in the single-layer play a crucial role in the formation of CDW order. Our findings provide a deeper understanding of the nature of CDW order in the two-dimensional limit.

Coupled One-Dimensional Plasmons and Two-Dimensional Phonon Polaritons in Hybrid Silver Nanowire/Silicon Carbide Structures.

Surface plasmons (SPs) and phonon polaritons (PhPs) are two distinctive quasiparticles resulting from the strong coupling of photons with electrons and optical phonons, respectively. In this Letter, we investigate the interactions between one-dimensional (1D) plasmons in silver nanowires with two-dimensional (2D) surface phonon polaritons of the silicon carbide (SiC) substrate. Using near-field infrared spectroscopy of the silver nanowire-SiC heterostructure at wavelengths close to the phonon resonance of SiC, we observe that the 1D plasmon dispersion is strongly modified by the 2D phonon polaritons in SiC. In particular, we observe for the first time well-defined 1D plasmon oscillations with the plasmon wavelengths longer than the free-space photon wavelengths due to the 1D plasmon-2D phonon polariton coupling. Our work demonstrates that unusual polariton behavior can emerge from interactions between polariton excitons of different dimensionality, which can enable new ways to engineer plasmons in hybrid structures.

Optically Discriminating Carrier-Induced Quasiparticle Band Gap and Exciton Energy Renormalization in Monolayer MoS_{2}.

Optoelectronic excitations in monolayer MoS_{2} manifest from a hierarchy of electrically tunable, Coulombic free-carrier and excitonic many-body phenomena. Investigating the fundamental interactions underpinning these phenomena-critical to both many-body physics exploration and device applications-presents challenges, however, due to a complex balance of competing optoelectronic effects and interdependent properties. Here, optical detection of bound- and free-carrier photoexcitations is used to directly quantify carrier-induced changes of the quasiparticle band gap and exciton binding energies. The results explicitly disentangle the competing effects and highlight longstanding theoretical predictions of large carrier-induced band gap and exciton renormalization in two-dimensional semiconductors.

Nanoscale Control of Rewriteable Doping Patterns in Pristine Graphene/Boron Nitride Heterostructures.

Nanoscale control of charge doping in two-dimensional (2D) materials permits the realization of electronic analogs of optical phenomena, relativistic physics at low energies, and technologically promising nanoelectronics. Electrostatic gating and chemical doping are the two most common methods to achieve local control of such doping. However, these approaches suffer from complicated fabrication processes that introduce contamination, change material properties irreversibly, and lack flexible pattern control. Here we demonstrate a clean, simple, and reversible technique that permits writing, reading, and erasing of doping patterns for 2D materials at the nanometer scale. We accomplish this by employing a graphene/boron nitride heterostructure that is equipped with a bottom gate electrode. By using electron transport and scanning tunneling microscopy (STM), we demonstrate that spatial control of charge doping can be realized with the application of either light or STM tip voltage excitations in conjunction with a gate electric field. Our straightforward and novel technique provides a new path toward on-demand graphene p-n junctions and ultrathin memory devices.

Direct Growth of Single- and Few-Layer MoS2 on h-BN with Preferred Relative Rotation Angles.

Monolayer molybdenum disulfide (MoS2) is a promising two-dimensional direct-bandgap semiconductor with potential applications in atomically thin and flexible electronics. An attractive insulating substrate or mate for MoS2 (and related materials such as graphene) is hexagonal boron nitride (h-BN). Stacked heterostructures of MoS2 and h-BN have been produced by manual transfer methods, but a more efficient and scalable assembly method is needed. Here we demonstrate the direct growth of single- and few-layer MoS2 on h-BN by chemical vapor deposition (CVD) method, which is scalable with suitably structured substrates. The growth mechanisms for single-layer and few-layer samples are found to be distinct, and for single-layer samples low relative rotation angles (<5°) between the MoS2 and h-BN lattices prevail. Moreover, MoS2 directly grown on h-BN maintains its intrinsic 1.89 eV bandgap. Our CVD synthesis method presents an important advancement toward controllable and scalable MoS2-based electronic devices.

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.

Visualizing delocalized correlated electronic states in twisted double bilayer graphene.

The discovery of interaction-driven insulating and superconducting phases in moiré van der Waals heterostructures has sparked considerable interest in understanding the novel correlated physics of these systems. While a significant number of studies have focused on twisted bilayer graphene, correlated insulating states and a superconductivity-like transition up to 12 K have been reported in recent transport measurements of twisted double bilayer graphene. Here we present a scanning tunneling microscopy and spectroscopy study of gate-tunable twisted double bilayer graphene devices. We observe splitting of the van Hove singularity peak by ~20 meV at half-filling of the conduction flat band, with a corresponding reduction of the local density of states at the Fermi level. By mapping the tunneling differential conductance we show that this correlated system exhibits energetically split states that are spatially delocalized throughout the different regions in the moiré unit cell, inconsistent with order originating solely from onsite Coulomb repulsion within strongly-localized orbitals. We have performed self-consistent Hartree-Fock calculations that suggest exchange-driven spontaneous symmetry breaking in the degenerate conduction flat band is the origin of the observed correlated state. Our results provide new insight into the nature of electron-electron interactions in twisted double bilayer graphene and related moiré systems.