Tuning commensurability in twisted van der Waals bilayers.

Moiré superlattices based on van der Waals bilayers1-4 created at small twist angles lead to a long wavelength pattern with approximate translational symmetry. At large twist angles (θt), moiré patterns are, in general, incommensurate except for a few discrete angles. Here we show that large-angle twisted bilayers offer distinctly different platforms. More specifically, by using twisted tungsten diselenide bilayers, we create the incommensurate dodecagon quasicrystals at θt = 30° and the commensurate moiré crystals at θt = 21.8° and 38.2°. Valley-resolved scanning tunnelling spectroscopy shows disparate behaviours between moiré crystals (with translational symmetry) and quasicrystals (with broken translational symmetry). In particular, the K valley shows rich electronic structures exemplified by the formation of mini-gaps near the valence band maximum. These discoveries demonstrate that bilayers with large twist angles offer a design platform to explore moiré physics beyond those formed with small twist angles.

Electrostatic moiré potential from twisted hexagonal boron nitride layers.

Moiré superlattices host a rich variety of correlated electronic phases. However, the moiré potential is fixed by interlayer coupling, and it is dependent on the nature of carriers and valleys. In contrast, it has been predicted that twisted hexagonal boron nitride (hBN) layers can impose a periodic electrostatic potential capable of engineering the properties of adjacent functional layers. Here, we show that this potential is described by a theory of electric polarization originating from the interfacial charge redistribution, validated by its dependence on supercell sizes and distance from the twisted interfaces. This enables controllability of the potential depth and profile by controlling the twist angles between the two interfaces. Employing this approach, we further demonstrate how the electrostatic potential from a twisted hBN substrate impedes exciton diffusion in semiconductor monolayers, suggesting opportunities for engineering the properties of adjacent functional layers using the surface potential of a twisted hBN substrate.

Single-Atomic-Layer Stanene on Ferromagnetic Co Nanoislands with Topological Band Structures.

Introducing magnetism to two-dimensional topological insulators is a central issue in the pursuit of magnetic topological materials in low dimensionality. By means of low-temperature growth at 80 K, we succeeded in fabricating a monolayer stanene on Co/Cu(111) and resolving ferromagnetic spin contrast by field-dependent spin-polarized scanning tunneling microscopy (SP-STM). Increases of both remanence to saturation magnetization ratio (Mr/Ms) and coercive field (Hc) due to an enhanced perpendicular magnetic anisotropy (PMA) are further identified by out-of-plane magneto-optical Kerr effect (MOKE). In addition to ultraflat stanene fully relaxed on bilayer Co/Cu(111) from density functional theory (DFT), characteristic topological properties including an in-plane s-p band inversion and a spin-orbit coupling (SOC) induced gap about 0.25 eV at the Γ̅ point have also been verified in the Sn-projected band structure. Interfacial coupling of single-atomic-layer stanene with ferromagnetic Co biatomic layers allows topological band features to coexist with ferromagnetism, facilitating a conceptual design of atomically thin magnetic topological heterostructures.

Creating a Nanoscale Lateral Junction in a Semiconductor Monolayer with a Large Built-in Potential.

The ability to engineer atomically thin nanoscale lateral junctions is critical to lay the foundation for future two-dimensional (2D) device technology. However, the traditional approach to creating a heterojunction by direct growth of a heterostructure of two different materials constrains the available band offsets, and it is still unclear if large built-in potentials are attainable for 2D materials. The electronic properties of atomically thin semiconducting transition metal dichalcogenides (TMDs) are not static, and their exciton binding energy and quasiparticle band gap depend strongly on the proximal environment. Recent studies have shown that this effect can be harnessed to engineer the lateral band profile of a monolayer TMD to create a lateral electronic junction. Here we demonstrate the synthesis of a nanoscale lateral junction in monolayer MoSe2 by intercalating Se at the interface of an hBN/Ru(0001) substrate. The Se intercalation creates a spatially abrupt modulation of the local hBN/Ru work function, which is imprinted directly onto an overlying MoSe2 monolayer to create a lateral junction with a large built-in potential of 0.83 ± 0.06 eV. We spatially resolve the MoSe2 band profile and work function using scanning tunneling spectroscopy to map out the nanoscale depletion region. The Se intercalation also modifies the dielectric environment, influencing the local band gap renormalization and increasing the MoSe2 band gap by ∼0.26 ± 0.1 eV. This work illustrates that environmental proximity engineering provides a robust method to indirectly manipulate the band profile of 2D materials outside the limits of their intrinsic properties.

Remarkably Deep Moiré Potential for Intralayer Excitons in MoSe2/MoS2 Twisted Heterobilayers.

A moiré superlattice formed in twisted van der Waals bilayers has emerged as a new tuning knob for creating new electronic states in two-dimensional materials. Excitonic properties can also be altered drastically due to the presence of moiré potential. However, quantifying the moiré potential for excitons is nontrivial. By creating a large ensemble of MoSe2/MoS2 heterobilayers with a systematic variation of twist angles, we map out the minibands of interlayer and intralayer excitons as a function of twist angles, from which we determine the moiré potential for excitons. Surprisingly, the moiré potential depth for intralayer excitons is up to ∼130 meV, comparable to that for interlayer excitons. This result is markedly different from theoretical calculations based on density functional theory, which show an order of magnitude smaller moiré potential for intralayer excitons. The remarkably deep intralayer moiré potential is understood within the framework of structural reconstruction within the moiré unit cell.

Visualizing the interplay of Dirac mass gap and magnetism at nanoscale in intrinsic magnetic topological insulators.

In intrinsic magnetic topological insulators, Dirac surface-state gaps are prerequisites for quantum anomalous Hall and axion insulating states. Unambiguous experimental identification of these gaps has proved to be a challenge, however. Here, we use molecular beam epitaxy to grow intrinsic MnBi2Te4 thin films. Using scanning tunneling microscopy/spectroscopy, we directly visualize the Dirac mass gap and its disappearance below and above the magnetic order temperature. We further reveal the interplay of Dirac mass gaps and local magnetic defects. We find that, in high defect regions, the Dirac mass gap collapses. Ab initio and coupled Dirac cone model calculations provide insight into the microscopic origin of the correlation between defect density and spatial gap variations. This work provides unambiguous identification of the Dirac mass gap in MnBi2Te4 and, by revealing the microscopic origin of its gap variation, establishes a material design principle for realizing exotic states in intrinsic magnetic topological insulators.

Confined Monolayer Ag As a Large Gap 2D Semiconductor and Its Momentum Resolved Excited States.

2D materials have intriguing quantum phenomena that are distinctively different from their bulk counterparts. Recently, epitaxially synthesized wafer-scale 2D metals, composed of elemental atoms, are attracting attention not only for their potential applications but also for exotic quantum effects such as superconductivity. By mapping momentum-resolved electronic states using time-resolved and angle-resolved photoemission spectroscopy (ARPES), we reveal that monolayer Ag confined between bilayer graphene and SiC is a large gap (>1 eV) 2D semiconductor, consistent with ab initio GW calculations. The measured valence band dispersion matches the GW quasiparticle band structure. However, the conduction band dispersion shows an anomalously large effective mass of 2.4 m0. Possible mechanisms for this large enhancement in the "apparent mass" are discussed.

Excitons in semiconductor moiré superlattices.

Semiconductor moiré superlattices represent a rapidly developing area of engineered photonic materials and a new platform to explore correlated electron states and quantum simulation. In this Review, we briefly introduce early experiments that identified new exciton resonances in transition metal dichalcogenide heterobilayers and discuss several topics including two types of transition metal dichalcogenide moiré superlattice, new optical selection rules, early evidence of moiré excitons, and how the resonant energy, dynamics and diffusion properties of moiré excitons can be controlled via the twist angle. To interpret optical spectra, it is important to measure the energy modulation within a moiré supercell. In this context, we describe a few scanning tunnelling microscopy experiments that measure the moiré potential landscape directly. Finally, we review a few recent experiments that applied excitonic optical spectroscopy to probe correlated electron phenomena in transition metal dichalcogenide moiré superlattices.

Monolayer 1T-NbSe2 as a 2D-correlated magnetic insulator.

Monolayer group V transition metal dichalcogenides in their 1T phase have recently emerged as a platform to investigate rich phases of matter, such as spin liquid and ferromagnetism, resulting from strong electron correlations. Newly emerging 1T-NbSe2 has inspired theoretical investigations predicting collective phenomena such as charge transfer gap and ferromagnetism in two dimensions; however, the experimental evidence is still lacking. Here, by controlling the molecular beam epitaxy growth parameters, we demonstrate the successful growth of high-quality single-phase 1T-NbSe2. By combining scanning tunneling microscopy/spectroscopy and ab initio calculations, we show that this system is a charge transfer insulator with the upper Hubbard band located above the valence band maximum. To demonstrate the electron correlation resulted magnetic property, we create a vertical 1T/2H NbSe2 heterostructure, and we find unambiguous evidence of exchange interactions between the localized magnetic moments in 1T phase and the metallic/superconducting phase exemplified by Kondo resonances and Yu-Shiba-Rusinov­like bound states.

PTCDA Molecular Monolayer on Pb Thin Films: An Unusual π-Electron Kondo System and Its Interplay with a Quantum-Confined Superconductor.

The hybridization of magnetism and superconductivity has been an intriguing playground for correlated electron systems, hosting various novel physical phenomena. Usually, localized d or f electrons are central to magnetism. In this study, by placing a PTCDA (3,4,9,10-perylene tetracarboxylic dianhydride) molecular monolayer on ultrathin Pb films, we built a hybrid magnetism/superconductivity (M/SC) system consisting of only sp electronic levels. The magnetic moments reside in the unpaired molecular orbital originating from interfacial charge transfers. We reported distinctive tunneling spectroscopic features of such a Kondo screened π electron impurity lattice on a superconductor in the regime of T_{K}≫Δ, suggesting the formation of a two-dimensional bound states band. Moreover, moiré superlattices with tunable twist angle and the quantum confinement in the ultrathin Pb films provide easy and flexible implementations to tune the interplay between the Kondo physics and the superconductivity, which are rarely present in M/SC hybrid systems.

Influence of Nanosize Hole Defects and their Geometric Arrangements on the Superfluid Density in Atomically Thin Single Crystals of Indium Superconductor.

Using Indium sqrt[7]×sqrt[3] on Si(111) as an atomically thin superconductor platform, and by systematically controlling the density of nanohole defects (nanometer size voids), we reveal the impacts of defect density and defect geometric arrangements on superconductivity at macroscopic and microscopic length scales. When nanohole defects are uniformly dispersed in the atomic layer, the superfluid density monotonically decreases as a function of defect density (from 0.7% to 5% of the surface area) with minor change in the transition temperature T_{C}, measured both microscopically and macroscopically. With a slight increase in the defect density from 5% to 6%, these point defects are organized into defect chains that enclose individual two-dimensional patches. This new geometric arrangement of defects dramatically impacts the superconductivity, leading to the total disappearance of macroscopic superfluid density and the collapse of the microscopic superconducting gap. This study sheds new light on the understanding of how local defects and their geometric arrangements impact superconductivity in the two-dimensional limit.

Time-resolved ARPES Determination of a Quasi-Particle Band Gap and Hot Electron Dynamics in Monolayer MoS2.

The electronic structure and dynamics of 2D transition metal dichalcogenide (TMD) monolayers provide important underpinnings both for understanding the many-body physics of electronic quasi-particles and for applications in advanced optoelectronic devices. However, extensive experimental investigations of semiconducting monolayer TMDs have yielded inconsistent results for a key parameter, the quasi-particle band gap (QBG), even for measurements carried out on the same layer and substrate combination. Here, we employ sensitive time- and angle-resolved photoelectron spectroscopy (trARPES) for a high-quality large-area MoS2 monolayer to capture its momentum-resolved equilibrium and excited-state electronic structure in the weak-excitation limit. For monolayer MoS2 on graphite, we obtain QBG values of ≈2.10 eV at 80 K and of ≈2.03 eV at 300 K, results well-corroborated by the scanning tunneling spectroscopy (STS) measurements on the same material.

Phonon renormalization in reconstructed MoS2 moiré superlattices.

In moiré crystals formed by stacking van der Waals materials, surprisingly diverse correlated electronic phases and optical properties can be realized by a subtle change in the twist angle. Here, we discover that phonon spectra are also renormalized in MoS2 twisted bilayers, adding an insight to moiré physics. Over a range of small twist angles, the phonon spectra evolve rapidly owing to ultra-strong coupling between different phonon modes and atomic reconstructions of the moiré pattern. We develop a low-energy continuum model for phonons that overcomes the outstanding challenge of calculating the properties of large moiré supercells and successfully captures the essential experimental observations. Remarkably, simple optical spectroscopy experiments can provide information on strain and lattice distortions in moiré crystals with nanometre-size supercells. The model promotes a comprehensive and unified understanding of the structural, optical and electronic properties of moiré superlattices.

Tuning of Two-Dimensional Plasmon-Exciton Coupling in Full Parameter Space: A Polaritonic Non-Hermitian System.

Non-Hermitian photonic systems with gains and/or losses have recently emerged as a powerful approach for topology-protected optical transport and novel device applications. To date, most of these systems employ coupled optical systems of diffraction-limited dielectric waveguides or microcavities, which exchange energy spatially or temporally. Here, we introduce a diffraction-unlimited approach using a plasmon-exciton coupling (polariton) system with tunable plasmonic resonance (energy and line width) and coupling strength. By designing a chirped silver nanogroove cavity array and coupling a single tungsten disulfide monolayer with a large contrast in resonance line width, we show the tuning capability through energy level anticrossing and plasmon-exciton hybridization (line width crossover), as well as spontaneous symmetry breaking across the exceptional point at zero detuning. This two-dimensional hybrid material system can be applied as a scalable and integratable platform for non-Hermitian photonics, featuring seamless integration of two-dimensional materials, broadband tuning, and operation at room temperature.

Epitaxial Growth of Two-Dimensional Insulator Monolayer Honeycomb BeO.

The emergence of two-dimensional (2D) materials launched a fascinating frontier of flatland electronics. Most crystalline atomic layer materials are based on layered van der Waals materials with weak interlayer bonding, which naturally leads to thermodynamically stable monolayers. We report the synthesis of a 2D insulator composed of a single atomic sheet of honeycomb structure BeO (h-BeO), although its bulk counterpart has a wurtzite structure. The h-BeO is grown by molecular beam epitaxy (MBE) on Ag(111) thin films that are also epitaxially grown on Si(111) wafers. Using scanning tunneling microscopy and spectroscopy (STM/S), the honeycomb BeO lattice constant is determined to be 2.65 Å with an insulating band gap of 6 eV. Our low-energy electron diffraction measurements indicate that the h-BeO forms a continuous layer with good crystallinity at the millimeter scale. Moiré pattern analysis shows the BeO honeycomb structure maintains long-range phase coherence in atomic registry even across Ag steps. We find that the interaction between the h-BeO layer and the Ag(111) substrate is weak by using STS and complementary density functional theory calculations. We not only demonstrate the feasibility of growing h-BeO monolayers by MBE, but also illustrate that the large-scale growth, weak substrate interactions, and long-range crystallinity make h-BeO an attractive candidate for future technological applications. More significantly, the ability to create a stable single-crystalline atomic sheet without a bulk layered counterpart is an intriguing approach to tailoring 2D electronic materials.

Engineering Giant Rabi Splitting via Strong Coupling between Localized and Propagating Plasmon Modes on Metal Surface Lattices: Observation of √N Scaling Rule.

We present a strong coupling system realized by coupling the localized surface plasmon mode in individual silver nanogrooves and propagating surface plasmon modes launched by periodic nanogroove arrays with varied periodicities on a continuous silver medium. When the propagating modes are in resonance with the localized mode, we observe a √N scaling of Rabi splitting energy, where N is the number of propagating modes coupled to the localized mode. Here, we confirm a giant Rabi splitting on the order of 450-660 meV (N = 2) in the visible spectral range, and the corresponding coupling strength is 160-235 meV. In some of the strong coupling cases studied by us, the coupling strength is about 10% of the mode energy, reaching the ultrastrong coupling regime.

Moiré potential impedes interlayer exciton diffusion in van der Waals heterostructures.

The properties of van der Waals heterostructures are drastically altered by a tunable moiré superlattice arising from periodically varying atomic alignment between the layers. Exciton diffusion represents an important channel of energy transport in transition metal dichalcogenides (TMDs). While early studies performed on TMD heterobilayers suggested that carriers and excitons exhibit long diffusion, a rich variety of scenarios can exist. In a moiré crystal with a large supercell and deep potential, interlayer excitons may be completely localized. As the moiré period reduces at a larger twist angle, excitons can tunnel between supercells and diffuse over a longer lifetime. The diffusion should be the longest in commensurate heterostructures where the moiré superlattice is completely absent. Here, we experimentally demonstrate the rich phenomena of interlayer exciton diffusion in WSe2/MoSe2 heterostructures by comparing several samples prepared with chemical vapor deposition and mechanical stacking with accurately controlled twist angles.

Unveiling defect-mediated carrier dynamics in monolayer semiconductors by spatiotemporal microwave imaging.

The optoelectronic properties of atomically thin transition-metal dichalcogenides are strongly correlated with the presence of defects in the materials, which are not necessarily detrimental for certain applications. For instance, defects can lead to an enhanced photoconduction, a complicated process involving charge generation and recombination in the time domain and carrier transport in the spatial domain. Here, we report the simultaneous spatial and temporal photoconductivity imaging in two types of WS2 monolayers by laser-illuminated microwave impedance microscopy. The diffusion length and carrier lifetime were directly extracted from the spatial profile and temporal relaxation of microwave signals, respectively. Time-resolved experiments indicate that the critical process for photoexcited carriers is the escape of holes from trap states, which prolongs the apparent lifetime of mobile electrons in the conduction band. As a result, counterintuitively, the long-lived photoconductivity signal is higher in chemical-vapor deposited (CVD) samples than exfoliated monolayers due to the presence of traps that inhibits recombination. Our work reveals the intrinsic time and length scales of electrical response to photoexcitation in van der Waals materials, which is essential for their applications in optoelectronic devices.

Engineering Point-Defect States in Monolayer WSe2.

Defect engineering is a key approach for tailoring the properties of the emerging two-dimensional semiconductors. Here, we report an atomic engineering of the W vacancy in monolayer WSe2 by single potassium atom decoration. The K decoration alters the energy states and reshapes the wave function such that previously hidden midgap states become visible with well-resolved multiplets in scanning tunneling spectroscopy. Their energy levels are in good agreement with first-principle calculations. More interestingly, the calculations show that an unpaired electron donated by the K atom can lead to a local magnetic moment, exhibiting an on-off switching by the odd-even number of electron filling. Experimentally the Fermi level is pinned above all defect states due to the graphite substrate, corresponding to an off state. The close agreement between theory and experiment in the off state, on the other hand, suggests the possibility of gate-programmable magnetic moments at the defects.