Graphene and Beyond: Recent Advances in Two-Dimensional Materials Synthesis, Properties, and Devices.

Since the isolation of graphene in 2004, two-dimensional (2D) materials research has rapidly evolved into an entire subdiscipline in the physical sciences with a wide range of emergent applications. The unique 2D structure offers an open canvas to tailor and functionalize 2D materials through layer number, defects, morphology, moiré pattern, strain, and other control knobs. Through this review, we aim to highlight the most recent discoveries in the following topics: theory-guided synthesis for enhanced control of 2D morphologies, quality, yield, as well as insights toward novel 2D materials; defect engineering to control and understand the role of various defects, including in situ and ex situ methods; and properties and applications that are related to moiré engineering, strain engineering, and artificial intelligence. Finally, we also provide our perspective on the challenges and opportunities in this fascinating field.

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.

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.

Data-driven discovery of high performance layered van der Waals piezoelectric NbOI2.

Using high-throughput first-principles calculations to search for layered van der Waals materials with the largest piezoelectric stress coefficients, we discover NbOI2 to be the one among 2940 monolayers screened. The piezoelectric performance of NbOI2 is independent of thickness, and its electromechanical coupling factor of near unity is a hallmark of optimal interconversion between electrical and mechanical energy. Laser scanning vibrometer studies on bulk and few-layer NbOI2 crystals verify their huge piezoelectric responses, which exceed internal references such as In2Se3 and CuInP2S6. Furthermore, we provide insights into the atomic origins of anti-correlated piezoelectric and ferroelectric responses in NbOX2 (X = Cl, Br, I), based on bond covalency and structural distortions in these materials. Our discovery that NbOI2 has the largest piezoelectric stress coefficients among 2D materials calls for the development of NbOI2-based flexible nanoscale piezoelectric devices.

Shear Modes in a 2D Polar Metal.

Low-frequency shear and breathing modes are important Raman signatures of two-dimensional (2D) materials, providing information on the number of layers and insights into interlayer interactions. We elucidate the nature of low-frequency modes in a 2D polar metal-2D Ga covalently bonded to a SiC substrate, using a first-principles Green's function-based approach. The low-frequency Raman modes are dominated by surface resonance modes, consisting primarily of out-of-phase shear modes in Ga, coupled to SiC phonons. Breathing modes are strongly coupled to the substrate and do not give rise to peaks in the phonon spectra. The highest-frequency shear mode blue-shifts significantly with increasing thickness, reflecting both an increase in the number of Ga layers and an increase in the effective interlayer force constant. The surface resonance modes evolve into localized 2D Ga modes as the phonon momentum increases. The predicted low-frequency modes are consistent with Raman measurements on 2D polar Ga.

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.

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.

Atomic-Level Structure Determines Electron-Phonon Scattering Rates in 2-D Polar Metal Heterostructures.

The electron dynamics of atomically thin 2-D polar metal heterostructures, which consisted of a few crystalline metal atomic layers intercalated between hexagonal silicon carbide and graphene grown from the silicon carbide, were studied using nearly degenerate transient absorption spectroscopy. Optical pumping created charge carriers in both the 2-D metals and graphene components. Wavelength-dependent probing suggests that graphene-to-metal carrier transfer occurred on a sub-picosecond time scale. Following rapid (<300 fs) carrier-carrier scattering, charge carriers monitored through the metal interband transition relaxed through several consecutive cooling mechanisms that included sub-picosecond carrier-phonon scattering and dissipation to the silicon carbide substrate over tens of picoseconds. By studying 2-D In, 2-D Ga, and a Ga/In alloy, we resolved accelerated electron-phonon scattering rates upon alloy formation as well as structural influences on the excitation of in-plane phonon shear modes. More rapid cooling in alloys is attributed to increased lattice disorder, which was observed through correlative polarization-resolved second harmonic generation and electron microscopy. This connection between the electronic relaxation rates, far-field optical responses, and metal lattice disorder is made possible by the intimate relation between nonlinear optical properties and atomic-level structure in these materials. These studies provided insights into electronic carrier dynamics in 2-D crystalline elemental metals, including resolving contributions from specific components of a 2-D metal-containing heterojunction. The correlative ultrafast spectroscopy and nonlinear microscopy results suggest that the energy dissipation rates can be tuned through atomic-level structures.

Charge Transfer Screening and Energy Level Alignment at Complex Organic-Inorganic Interfaces: A Tractable Ab Initio GW Approach.

Complex organic-inorganic interfaces are important for device and sensing applications. Charge transfer doping is prevalent in such applications and can affect the interfacial energy level alignments (ELA), which are determined by many-body interactions. We develop an approximate ab initio many-body GW approach that can capture many-body interactions due to interfacial charge transfer. The approach uses significantly less resources than a regular GW calculation but gives excellent agreement with benchmark GW calculations on an F4TCNQ/graphene interface. We find that many-body interactions due to charge transfer screening result in gate-tunable F4TCNQ HOMO-LUMO gaps. We further predict the ELA of a large system of experimental interest-4,4'-bis(dimethylamino)bipyridine (DMAP-OED) on monolayer MoS2, where charge transfer screening results in an ∼1 eV reduction of the molecular HOMO-LUMO gap. Comparison with a two-dimensional electron gas model reveals the importance of explicitly considering the intraband transitions in determining the charge transfer screening in organic-inorganic interface systems.

Tunable 2D Group-III Metal Alloys.

Chemically stable quantum-confined 2D metals are of interest in next-generation nanoscale quantum devices. Bottom-up design and synthesis of such metals could enable the creation of materials with tailored, on-demand, electronic and optical properties for applications that utilize tunable plasmonic coupling, optical nonlinearity, epsilon-near-zero behavior, or wavelength-specific light trapping. In this work, it is demonstrated that the electronic, superconducting, and optical properties of air-stable 2D metals can be controllably tuned by the formation of alloys. Environmentally robust large-area 2D-Inx Ga1- x alloys are synthesized byConfinement Heteroepitaxy (CHet). Near-complete solid solubility is achieved with no evidence of phase segregation, and the composition is tunable over the full range of x by changing the relative elemental composition of the precursor. The optical and electronic properties directly correlate with alloy composition, wherein the dielectric function, band structure, superconductivity, and charge transfer from the metal to graphene are all controlled by the indium/gallium ratio in the 2D metal layer.

Chiral Phonons and Giant Magneto-Optical Effect in CrBr3 2D Magnet.

Phonons with chirality determine the optical helicity of inelastic light scattering processes due to their nonzero angular momentum. Here it is shown that 2D magnetic CrBr3 hosts chiral phonons at the Brillouin-zone center. These chiral phonons are linear combinations of the doubly-degenerate Eg phonons, and the phonon eigenmodes exhibit clockwise and counterclockwise rotational vibrations corresponding to angular momenta of l = ± 1. Such Eg chiral phonons completely switch the polarization of incident circularly polarized light. On the other hand, the non-degenerate non-chiral Ag phonons display a giant magneto-optical effect under an external out-of-plane magnetic field, rotating the plane of polarization of the scattered linearly polarized light. The corresponding degree of polarization of the scattered light changes from 91% to -68% as the magnetic field strength increases from 0 to 5 T. In contrast, the chiral Eg modes display no field dependence. The results lay a foundation for the study of phonon chirality and magneto-optical phenomena in 2D magnetic materials, as well as their related applications, such as the phonon Hall effect, topological photonics, and Raman lasing.

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.

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.

Partitioning the interlayer space of covalent organic frameworks by embedding pseudorotaxanes in their backbones.

Mono- or few-layer sheets of covalent organic frameworks (COFs) represent an attractive platform of two-dimensional materials that hold promise for tailor-made functionality and pores, through judicious design of the COF building blocks. But although a wide variety of layered COFs have been synthesized, cleaving their interlayer stacking to obtain COF sheets of uniform thickness has remained challenging. Here, we have partitioned the interlayer space in COFs by incorporating pseudorotaxane units into their backbones. Macrocyclic hosts based on crown ethers were embedded into either a ditopic or a tetratopic acylhydrazide building block. Reaction with a tritopic aldehyde linker led to the formation of acylhydrazone-based layered COFs in which one basal plane is composed of either one layer, in the case of the ditopic macrocyclic component, or two adjacent layers covalently held together by its tetratopic counterpart. When a viologen threading unit is introduced, the formation of a host-guest complex facilitates the self-exfoliation of the COFs into crystalline monolayers or bilayers, respectively.

Spin-Dependent Tunneling Barriers in CoPc/VSe2 from Many-Body Interactions.

Mixed-dimensional magnetic heterostructures are intriguing, newly available platforms to explore quantum physics and its applications. Using state-of-the-art many-body perturbation theory, we predict the energy level alignment for a self-assembled monolayer of cobalt phthalocyanine (CoPc) molecules on magnetic VSe2 monolayers. The predicted projected density of states on CoPc agrees with experimental scanning tunneling spectra. Consistent with experiment, we predict a shoulder in the unoccupied region of the spectra that is absent from mean-field calculations. Unlike the nearly spin-degenerate gas-phase frontier molecular orbitals, the tunneling barriers at the interface are spin-dependent, a finding of interest for quantum information and spintronics applications. Both the experimentally observed shoulder and the predicted spin-dependent tunneling barriers originate from many-body interactions in the interface-hybridized states. Our results showcase the intricate many-body physics that governs the properties of these mixed-dimensional magnetic heterostructures and suggests the possibility of manipulating the spin-dependent tunneling barriers through modifications of interface coupling.

Isolated flat bands and physics of mixed dimensions in a 2D covalent organic framework.

We demonstrate that it is possible to rationally incorporate both an isolated flat band and the physics of zero dimensions (0D), one dimension (1D), and two dimensions (2D) in a single 2D material. Such unique electronic properties are present in a recently synthesized 2D covalent organic framework (COF), where "I"-shaped building blocks and "T"-shaped connectors result in quasi-1D chains that are linked by quasi-0D bridge units arranged in a stable 2D lattice. The lowest unoccupied conduction band is an isolated flat band, and electron-doping gives rise to novel quantum phenomena, such as magnetism and Mott insulating phases. The highest occupied valence band arises from wave functions in the quasi-1D chains. Examples of mixed dimensional physics are illustrated in this system. The strong electron-hole asymmetry in this material results in a large Seebeck coefficient, while the quasi-1D nature of the chains leads to linear dichroism, in conjunction with strongly bound 2D excitons. We elucidate strategies to design and optimize 2D COFs to host both isolated flat bands and quantum-confined 1D subsystems. The properties of the 2D COF discussed here provide a taste of the intriguing possibilities in this open research field.

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.

Room Temperature Commensurate Charge Density Wave on Epitaxially Grown Bilayer 2H-Tantalum Sulfide on Hexagonal Boron Nitride.

The breaking of multiple symmetries by periodic lattice distortion at a commensurate charge density wave (CDW) state is expected to give rise to intriguing interesting properties. However, accessing the commensurate CDW state on bulk TaS2 crystals typically requires cryogenic temperatures (77 K), which precludes practical applications. Here, we found that heteroepitaxial growth of a 2H-tantalum disulfide bilayer on a hexagonal-boron nitride (h-BN) substrate produces a robust commensurate CDW order at room temperature, characterized by a Moiré superlattice of 3 × 3 TaS2 on a 4 × 4 h-BN unit cell. The CDW order is confirmed by scanning transmission electron microscopy and Raman measurements. Theoretical calculations reveal that the stabilizing energy for the CDW phase of the monolayer and bilayer 2H-TaS2-on-h-BN substrates arises primarily from interfacial electrostatic interactions and, to a lesser extent, interfacial strain. Our work shows that engineering interfacial electrostatic interactions in an ultrathin van der Waals heterostructure constitutes an effective way to enhance CDW order in two-dimensional materials.

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.

Quasiparticle Levels at Large Interface Systems from Many-Body Perturbation Theory: The XAF-GW Method.

We present a fully ab initio approach based on many-body perturbation theory in the GW approximation to compute the quasiparticle levels of large interface systems without significant covalent interactions between the different components of the interface (meaning that the different components can be separated without the creation of dangling bonds). The only assumption in our approach is that the polarizability matrix (chi) of the interface can be given by the sum of the polarizability matrices of individual components of the interface. We show analytically, using a two-state hybridized model, that this assumption is valid even in the presence of interface hybridization to form bonding and antibonding states up to first order in the overlap matrix elements involved in the hybridization. We validate our approach by showing that the band structure obtained in our method is almost identical to that obtained using a regular GW calculation for bilayer black phosphorus, where interlayer hybridization is significant. Significant savings in computational time and memory are obtained by computing chi only for the smallest subunit cell of each component and expanding (unfolding) the chi matrix to that in the unit cell of the interface. To treat interface hybridization, the full wave functions of the interface are used in computing the self-energy. We thus call the method XAF-GW (X, eXpand-chi; A, Add-chi; F, Full wave functions). Compared to GW-embedding type approaches in the literature, the XAF-GW approach is not limited to specific screening environments or to nonhybridized interface systems. XAF-GW can also be applied to systems with different dimensionalities, as well as to Moire superlattices such as in twisted bilayers. We illustrate the generality and usefulness of our approach by applying it to self-assembled PTCDA monolayers on Au(111) and Ag(111) and PTCDA monolayers on graphite-supported monolayer WSe2. In all cases, the predicted HOMO and LUMO levels agree well with experimental measurements.