Evidence for electron-hole crystals in a Mott insulator.

The coexistence of correlated electron and hole crystals enables the realization of quantum excitonic states, capable of hosting counterflow superfluidity and topological orders with long-range quantum entanglement. Here we report evidence for imbalanced electron-hole crystals in a doped Mott insulator, namely, α-RuCl3, through gate-tunable non-invasive van der Waals doping from graphene. Real-space imaging via scanning tunnelling microscopy reveals two distinct charge orderings at the lower and upper Hubbard band energies, whose origin is attributed to the correlation-driven honeycomb hole crystal composed of hole-rich Ru sites and rotational-symmetry-breaking paired electron crystal composed of electron-rich Ru-Ru bonds, respectively. Moreover, a gate-induced transition of electron-hole crystals is directly visualized, further corroborating their nature as correlation-driven charge crystals. The realization and atom-resolved visualization of imbalanced electron-hole crystals in a doped Mott insulator opens new doors in the search for correlated bosonic states within strongly correlated materials.

Exciton-Enhanced Spontaneous Parametric Down-Conversion in Two-Dimensional Crystals.

We show that excitonic resonances and interexciton transitions can enhance the probability of spontaneous parametric down-conversion, a second-order optical response that generates entangled photon pairs. We benchmark our ab initio many-body calculations using experimental polar plots of second harmonic generation in NbOI_{2}, clearly demonstrating the relevance of excitons in the nonlinear response. A strong double-exciton resonance in 2D NbOCl_{2} leads to giant enhancement in the second order susceptibility. Our work paves the way for the realization of efficient ultrathin quantum light sources.

Compact Super Electron-Donor to Monolayer MoS2.

The surface functionalization of two-dimensional (2D) materials with organic electron donors (OEDs) is a powerful tool to modulate the electronic properties of the material. Here we report a novel molecular dopant, Me-OED, that demonstrates record-breaking molecular doping to MoS2, achieving a carrier density of 1.10 ± 0.37 × 1014 cm-2 at optimal functionalization conditions; the achieved carrier density is much higher than those by other OEDs such as benzyl viologen and an OED based on 4,4'-bipyridine. This impressive doping power is attributed to the compact size of Me-OED, which leads to high surface coverage on MoS2. To confirm, we study tBu-OED, which has an identical reduction potential to Me-OED but is significantly larger. Using field-effect transistor measurements and spectroscopic characterization, we estimate the doping powers of Me- and tBu-OED are 0.22-0.44 and 0.11 electrons per molecule, respectively, in good agreement with calculations. Our results demonstrate that the small size of Me-OED is critical to maximizing the surface coverage and molecular interactions with MoS2, enabling us to achieve unprecedented doping of MoS2.

Strong Moiré Excitons in High-Angle Twisted Transition Metal Dichalcogenide Homobilayers with Robust Commensuration.

The burgeoning field of twistronics, which concerns how changing the relative twist angles between two materials creates new optoelectronic properties, offers a novel platform for studying twist-angle dependent excitonic physics. Herein, by surveying a range of hexagonal phase transition metal dichalcogenides (TMD) twisted homobilayers, we find that 21.8 ± 1.0°-twisted (7a×7a) and 27.8 ± 1.0°-twisted (13a×13a) bilayers account for nearly 20% of the total population of twisted bilayers in solution-phase restacked bilayers and can be found also in chemical vapor deposition (CVD) samples. Examining the optical properties associated with these twisted angles, we found that 21.8 ± 1.0° twisted MoS2 bilayers exhibit an intense moiré exciton peak in the photoluminescence (PL) spectra, originating from the refolded Brillouin zones. Our work suggests that commensurately twisted TMD homobilayers with short commensurate wavelengths can have interesting optoelectronic properties that are different from the small twist angle counterparts.

Giant g-factor in Self-Intercalated 2D TaS2.

Central to the application of spintronic devices is the ability to manipulate spins by electric and magnetic fields, which relies on a large Landé g-factor. The self-intercalation of layered transitional metal dichalcogenides with native metal atoms can serve as a new strategy to enhance the g-factor by inducing ferromagnetic instability in the system via interlayer charge transfer. Here, scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) are performed to extract the g-factor and characterize the electronic structure of the self-intercalated phase of 2H-TaS2 . In Ta7 S12 , a sharp density of states (DOS) peak due to the Ta intercalant appears at the Fermi level, which satisfies the Stoner criteria for spontaneous ferromagnetism, leading to spin split states. The DOS peak shows sensitivity to magnetic field up to 1.85 mV T-1 , equivalent to an effective g-factor of ≈77. This work establishes self-intercalation as an approach for tuning the g-factor.

Organic-2D Material Heterostructures: A Promising Platform for Exciton Condensation and Multiplication.

We predict that high temperature Bose-Einstein condensation of charge transfer excitons can be achieved in organic-two-dimensional (2D) material heterostructures, at ∼50-100 K. Unlike 2D bilayers that can be angle-misaligned, organic-2D systems generally have momentum-direct low-energy excitons, thus favoring condensation. Our predictions are obtained for ZnPc-MoS2 using state-of-the-art first-principles calculations with the GW-BSE approach. The exciton energies we predict are in excellent agreement with recent experiments. The lowest energy charge transfer excitons in ZnPc-MoS2 are strongly bound with a spatial extent of ∼1-2 nm and long lifetimes (τ0 ∼ 1 ns), making them ideal for exciton condensation. We also predict the emergence of inter-ZnPc excitons that are stabilized by the interaction of the molecules with the 2D substrate. This novel way of stabilizing intermolecular excitons by indirect substrate mediation suggests design strategies for singlet fission and exciton multiplication, which are important to overcome the Shockley-Queisser efficiency limit in solar cells.

Unveiling Atomic-Scale Moiré Features and Atomic Reconstructions in High-Angle Commensurately Twisted Transition Metal Dichalcogenide Homobilayers.

Twisting the angle between van der Waals stacked 2D layers has recently sparked great interest as a new strategy to tune the physical properties of the materials. The twist angle and associated strain profiles govern the electrical and optical properties of the twisted 2D materials, but their detailed atomic structures remain elusive. Herein, using combined atomic-resolution electron microscopy and density functional theory (DFT) calculations, we identified five unique types of moiré features in commensurately twisted 7a×7a transition metal dichalcogenide (TMD) bilayers. These stacking variants are distinguishable only when the moiré wavelength is short. Periodic lattice strain is observed in various commensurately twisted TMD bilayers. Assisted by Zernike polynomial as a hierarchical active-learning framework, a hexagon-shaped strain soliton network has been atomically unveiled in nearly commensurate twisted TMD bilayers. Unlike stacking-polytype-dependent properties in untwisted structures, the stacking variants have the same electronic structures that suggest twisted bilayer systems are invariant against interlayer gliding.

Impurity-Induced Emission in Re-Doped WS2 Monolayers.

Impurity doping is a viable route toward achieving desired subgap optical response in semiconductors. In strongly excitonic two-dimensional (2D) semiconductors such as transition metal dichalcogenides (TMDs), impurities are expected to result in bound-exciton emission. However, doped TMDs often exhibit a broad Stokes-shifted emission without characteristic features, hampering strategic materials engineering. Here we report observation of a well-defined impurity-induced emission in monolayer WS2 substitutionally doped with rhenium (Re), which is an electron donor. The emission exhibits characteristics of localized states and dominates the spectrum up to 200 K. Gate dependence reveals that neutral impurity centers are responsible for the observed emission. Using GW-Bethe-Salpeter equation (GW-BSE) calculations, we attribute the emission to transitions between spin-split upper Re band and valence band edge.

Rapid, Scalable Construction of Highly Crystalline Acylhydrazone Two-Dimensional Covalent Organic Frameworks via Dipole-Induced Antiparallel Stacking.

Covalent organic frameworks are an emerging class of porous crystalline organic materials that can be designed and synthesized from the bottom up. Despite progress made in synthesizing COFs of diverse topologies, the synthesis methods are often tedious and unscalable, hampering practical applications. Herein, we demonstrate a scalable, robust method of producing highly crystalline acylhydrazone two-dimensional (2D) COFs with diversified structures (six examples) under open and stirred conditions, with growth typically completed in only 30 min. Our strategy involves selecting molecular building blocks that have bond dipole moments with spatial orientations that favor antiparallel stacking and whose structure allows the restriction of intramolecular bond rotation (RIR) via intra- and interlayer hydrogen bonding. This method is widely applicable for hydrazide linkers containing various side-chain functionalities and topicities. By this strategy, the gram-scale synthesis of two highly crystalline COFs (up to 1.4 g yield) was obtained in a one-pot reaction within 30 min.

Linkage Engineering by Harnessing Supramolecular Interactions to Fabricate 2D Hydrazone-Linked Covalent Organic Framework Platforms toward Advanced Catalysis.

Covalent organic frameworks (COFs) are an emerging class of crystalline porous polymers with tailor-made structures and functionalities. To facilitate their utilization for advanced applications, it is crucial to develop a systematic approach to control the properties of COFs, including the crystallinity, stability, and functionalities. However, such an integrated design is challenging to achieve. Herein, we report supramolecular strategy-based linkage engineering to fabricate a versatile 2D hydrazone-linked COF platform for the coordination of different transition metal ions. Intra- and intermolecular hydrogen bonding as well as electrostatic interactions in the antiparallel stacking mode were first utilized to obtain two isoreticular COFs, namely COF-DB and COF-DT. On account of suitable nitrogen sites in COF-DB, the further metalation of COF-DB was accomplished upon the complexation with seven divalent transition metal ions M(II) (M = Mn, Co, Ni, Cu, Zn, Pd, and Cd) under mild conditions. The resultant M/COF-DB exhibited extended π-conjugation, improved crystallinity, enhanced stability, and additional functionalities as compared to the parent COF-DB. Furthermore, the dynamic nature of the coordination bonding in M/COF-DB allows for the easy replacement of metal ions through a postsynthetic exchange. In particular, the coordination mode in Pd/COF-DB endows it with excellent catalytic activity and cyclic stability as a heterogeneous catalyst for the Suzuki-Miyaura cross-coupling reaction, outperforming its amorphous counterparts and Pd/COF-DT. This strategy provides an opportunity for the construction of 2D COFs with designable functions and opens an avenue to create COFs as multifunctional systems.

The organic-2D transition metal dichalcogenide heterointerface.

Since the first isolation of graphene, new classes of two-dimensional (2D) materials have offered fascinating platforms for fundamental science and technology explorations at the nanometer scale. In particular, 2D transition metal dichalcogenides (TMD) such as MoS2 and WSe2 have been intensely investigated due to their unique electronic and optical properties, including tunable optical bandgaps, direct-indirect bandgap crossover, strong spin-orbit coupling, etc., for next-generation flexible nanoelectronics and nanophotonics applications. On the other hand, organics have always been excellent materials for flexible electronics. A plethora of organic molecules, including donors, acceptors, and photosensitive molecules, can be synthesized using low cost and scalable procedures. Marrying the fields of organics and 2D TMDs will bring benefits that are not present in either material alone, enabling even better, multifunctional flexible devices. Central to the realization of such devices is a fundamental understanding of the organic-2D TMD interface. Here, we review the organic-2D TMD interface from both chemical and physical perspectives. We discuss the current understanding of the interfacial interactions between the organic layers and the TMDs, as well as the energy level alignment at the interface, focusing in particular on surface charge transfer and electronic screening effects. Applications from the literature are discussed, especially in optoelectronics and p-n hetero- and homo-junctions. We conclude with an outlook on future scientific and device developments based on organic-2D TMD heterointerfaces.

van der Waals Bonded Co/h-BN Contacts to Ultrathin Black Phosphorus Devices.

Because of the chemical inertness of two dimensional (2D) hexagonal-boron nitride (h-BN), few atomic-layer h-BN is often used to encapsulate air-sensitive 2D crystals such as black phosphorus (BP). However, the effects of h-BN on Schottky barrier height, doping, and contact resistance are not well-known. Here, we investigate these effects by fabricating h-BN encapsulated BP transistors with cobalt (Co) contacts. In sharp contrast to directly Co contacted p-type BP devices, we observe strong n-type conduction upon insertion of the h-BN at the Co/BP interface. First-principles calculations show that this difference arises from the much larger interface dipole at the Co/h-BN interface compared to the Co/BP interface, which reduces the work function of the Co/h-BN contact. The Co/h-BN contacts exhibit low contact resistances (∼4.5 kΩ) and are Schottky barrier-free. This allows us to probe high electron mobilities (4,200 cm2/(V s)) and observe insulator-metal transitions even under two-terminal measurement geometry.

Fabrication and Properties of a Free-Standing Two-Dimensional Titania.

The synthesis of free-standing two-dimensional titania (2-D TiO2) with a reduced band gap presents complex challenges to synthetic chemists. Here, we report a free-standing 2-D TiO2 sheet synthesized via a one-step solvothermal methodology, with a measured optical onset at ∼1.84 eV. Using first-principles calculations in combination with experiment, we propose that the as-formed 2-D TiO2 sheets are layers of the lepidocrocite TiO2 structure, but with large nonuniform strains consistent with its crumpled morphology. These strains cause a significant change in the quasiparticle band structure and optical absorption spectra, resulting in large absorption in the visible-light region. This narrow band gap 2-D TiO2 can catalyze the formation of singlet oxygen and the degradation of dye pollutants with low-energy photons of solar light. Our work demonstrates that lattice strains intrinsic to 2-D materials, especially its crumpled, free-standing forms, can result in new and useful properties.

Gap States at Low-Angle Grain Boundaries in Monolayer Tungsten Diselenide.

Two-dimensional (2D) transition metal dichalcogenides (TMDs) have revealed many novel properties of interest to future device applications. In particular, the presence of grain boundaries (GBs) can significantly influence the material properties of 2D TMDs. However, direct characterization of the electronic properties of the GB defects at the atomic scale remains extremely challenging. In this study, we employ scanning tunneling microscopy and spectroscopy to investigate the atomic and electronic structure of low-angle GBs of monolayer tungsten diselenide (WSe2) with misorientation angles of 3-6°. Butterfly features are observed along the GBs, with the periodicity depending on the misorientation angle. Density functional theory calculations show that these butterfly features correspond to gap states that arise in tetragonal dislocation cores and extend to distorted six-membered rings around the dislocation core. Understanding the nature of GB defects and their influence on transport and other device properties highlights the importance of defect engineering in future 2D device fabrication.

Large Frequency Change with Thickness in Interlayer Breathing Mode--Significant Interlayer Interactions in Few Layer Black Phosphorus.

Bulk black phosphorus (BP) consists of puckered layers of phosphorus atoms. Few-layer BP, obtained from bulk BP by exfoliation, is an emerging candidate as a channel material in post-silicon electronics. A deep understanding of its physical properties and its full range of applications are still being uncovered. In this paper, we present a theoretical and experimental investigation of phonon properties in few-layer BP, focusing on the low-frequency regime corresponding to interlayer vibrational modes. We show that the interlayer breathing mode A(3)g shows a large redshift with increasing thickness; the experimental and theoretical results agree well. This thickness dependence is two times larger than that in the chalcogenide materials, such as few-layer MoS2 and WSe2, because of the significantly larger interlayer force constant and smaller atomic mass in BP. The derived interlayer out-of-plane force constant is about 50% larger than that of graphene and MoS2. We show that this large interlayer force constant arises from the sizable covalent interaction between phosphorus atoms in adjacent layers and that interlayer interactions are not merely of the weak van der Waals type. These significant interlayer interactions are consistent with the known surface reactivity of BP and have been shown to be important for electric-field induced formation of Dirac cones in thin film BP.

Predictive DFT-based approaches to charge and spin transport in single-molecule junctions and two-dimensional materials: successes and challenges.

CONSPECTUS: The emerging field of flexible electronics based on organics and two-dimensional (2D) materials relies on a fundamental understanding of charge and spin transport at the molecular and nanoscale. It is desirable to make predictions and shine light on unexplained experimental phenomena independently of experimentally derived parameters. Indeed, density functional theory (DFT), the workhorse of first-principles approaches, has been used extensively to model charge/spin transport at the nanoscale. However, DFT is essentially a ground state theory that simply guarantees correct total energies given the correct charge density, while charge/spin transport is a nonequilibrium phenomenon involving the scattering of quasiparticles. In this Account, we critically assess the validity and applicability of DFT to predict charge/spin transport at the nanoscale. We also describe a DFT-based approach, DFT+Σ, which incorporates corrections to Kohn-Sham energy levels based on many-electron calculations. We focus on single-molecule junctions and then discuss how the important considerations for DFT descriptions of transport can differ in 2D materials. We conclude that when used appropriately, DFT and DFT-based approaches can play an important role in making predictions and gaining insight into transport in these materials. Specifically, we shall focus on the low-bias quasi-equilibrium regime, which is also experimentally most relevant for single-molecule junctions. The next question is how well can the scattering of DFT Kohn-Sham particles approximate the scattering of true quasiparticles in the junction? Quasiparticles are electrons (holes) that are surrounded by a constantly changing cloud of holes (electrons), but Kohn-Sham particles have no physical significance. However, Kohn-Sham particles can often be used as a qualitative approximation to quasiparticles. The errors in standard DFT descriptions of transport arise primarily from errors in the Kohn-Sham energy levels (self-energy errors). These errors are small in the strong-coupling regime where the molecular levels are significantly broadened at the Fermi level but are large in the coherent off-resonant tunneling regime where DFT overestimates conductance by orders of magnitude. The DFT+Σ approach uses a physically motivated, parameter free estimate of the self-energy corrections to correct the energy levels in DFT, giving conductance in quantitative agreement with experiment for a large but nonexhaustive class of single-molecule junctions. In 2D materials, the self-energy error is relatively small, and critical issues stem instead from the large length scales in experiments, which make it necessary to consider band-bending within the 2D material, as well as scattering due to electron-phonon interactions, spin-flip interactions, defects, etc.

Length dependence of electron transport through molecular wires--a first principles perspective.

One-dimensional wires constitute a fundamental building block in nanoscale electronics. However, truly one-dimensional metallic wires do not exist due to Peierls distortion. Molecular wires come close to being stable one-dimensional wires, but are typically semiconductors, with charge transport occurring via tunneling or thermally-activated hopping. In this review, we discuss electron transport through molecular wires, from a theoretical, quantum mechanical perspective based on first principles. We focus specifically on the off-resonant tunneling regime, applicable to shorter molecular wires (<∼4-5 nm) where quantum mechanics dictates electron transport. Here, conductance decays exponentially with the wire length, with an exponential decay constant, beta, that is independent of temperature. Different levels of first principles theory are discussed, starting with the computational workhorse - density functional theory (DFT), and moving on to many-electron GW methods as well as GW-inspired DFT + Sigma calculations. These different levels of theory are applied in two major computational frameworks - complex band structure (CBS) calculations to estimate the tunneling decay constant, beta, and Landauer-Buttiker transport calculations that consider explicitly the effects of contact geometry, and compute the transmission spectra directly. In general, for the same level of theory, the Landauer-Buttiker calculations give more quantitative values of beta than the CBS calculations. However, the CBS calculations have a long history and are particularly useful for quick estimates of beta. Comparing different levels of theory, it is clear that GW and DFT + Sigma calculations give significantly improved agreement with experiment compared to DFT, especially for the conductance values. Quantitative agreement can also be obtained for the Seebeck coefficient - another independent probe of electron transport. This excellent agreement provides confirmative evidence of off-resonant tunneling in the systems under investigation. Calculations show that the tunneling decay constant beta is a robust quantity that does not depend on details of the contact geometry, provided that the same contact geometry is used for all molecular lengths considered. However, because conductance is sensitive to contact geometry, values of beta obtained by considering conductance values where the contact geometry is changing with the molecular junction length can be quite different. Experimentally measured values of beta in general compare well with beta obtained using DFT + Sigma and GW transport calculations, while discrepancies can be attributed to changes in the experimental contact geometries with molecular length. This review also summarizes experimental and theoretical efforts towards finding perfect molecular wires with high conductance and small beta values.

Determination of energy level alignment and coupling strength in 4,4'-bipyridine single-molecule junctions.

We measure conductance and thermopower of single Au-4,4'-bipyridine-Au junctions in distinct low and high conductance binding geometries accessed by modulating the electrode separation. We use these data to determine the electronic energy level alignment and coupling strength for these junctions, which are known to conduct through the lowest unoccupied molecular orbital (LUMO). Contrary to intuition, we find that, in the high-conductance junction, the LUMO resonance energy is further away from the Au Fermi energy than in the low-conductance junction. However, the LUMO of the high-conducting junction is better coupled to the electrode. These results are in good quantitative agreement with self-energy corrected zero-bias density functional theory calculations. Our calculations show further that measurements of conductance and thermopower in amine-terminated oligophenyl-Au junctions, where conduction occurs through the highest occupied molecular orbitals, cannot be used to extract electronic parameters as their transmission functions do not follow a simple Lorentzian form.

Trimethyltin-mediated covalent gold-carbon bond formation.

We study the formation of covalent gold-carbon bonds in benzyltrimethylstannane (C10H16Sn) deposited on Au in ultra-high-vacuum conditions. Through X-ray photoemission spectroscopy and X-ray absorption measurements, we find that the molecule fragments at the Sn-benzyl bond when exposed to Au surfaces at temperatures as low as -110 °C. The resulting benzyl species is stabilized by the presence of Au(111) but only forms covalent Au-C bonds on more reactive Au surfaces like Au(110). We also present spectroscopic proof for the existence of an electronic "gateway" state localized on the Au-C bond that is responsible for its unique electronic properties. Finally, we use DFT-based nudged elastic band calculations to elucidate the crucial role played by the under-coordinated Au surface in the formation of Au-C bonds.

Theoretical study of thermoelectric properties of few-layer MoS2 and WSe2.

Molybdenum disulfide (MoS2) and tungsten diselenide (WSe2) are prototypical layered two-dimensional transition metal dichalcogenide materials, with each layer consisting of three atomic planes. We refer to each layer as a trilayer (TL). We study the thermoelectric properties of 1-4TL MoS2 and WSe2 using a ballistic transport approach based on the electronic band structures and phonon dispersions obtained from first-principles calculations. Our results show that the thickness dependence of the thermoelectric properties is different under n-type and p-type doping conditions. Defining ZT1st peak as the first peak in the thermoelectric figure of merit ZT as doping levels increase from zero at 300 K, we found that ZT1st peak decreases as the number of layers increases for MoS2, with the exception of 2TL in n-type doping, which has a slightly higher value than 1TL. However, for WSe2, 2TL has the largest ZT1st peak in both n-type and p-type doping, with a ZT1st peak value larger than 1 for n-type WSe2. At high temperatures (T > 300 K), ZT1st peak dramatically increases when the temperature increases, especially for n-type doping. The ZT1st peak of n-type 1TL-MoS2 and 2TL-WSe2 can reach 1.6 and 2.1, respectively.