Scattering and Interference in Epitaxial Graphene

Scanning Probe Microscopies for Characterizations of 2D Materials

2D materials are intriguing due to their remarkably thin and flat structure. This unique configuration allows the majority of their constituent atoms to be accessible on the surface, facilitating easier electron tunneling while generating weak surface forces. To decipher the subtle signals inherent in these materials, the application of techniques that offer atomic resolution (horizontal) and sub-Angstrom (z-height vertical) sensitivity is crucial. Scanning probe microscopy (SPM) emerges as the quintessential tool in this regard, owing to its atomic-level spatial precision, ability to detect unitary charges, responsiveness to pico-newton-scale forces, and capability to discern pico-ampere currents. Furthermore, the versatility of SPM to operate under varying environmental conditions, such as different temperatures and in the presence of various gases or liquids, opens up the possibility of studying the stability and reactivity of 2D materials in situ. The characteristic flatness, surface accessibility, ultra-thinness, and weak signal strengths of 2D materials align perfectly with the capabilities of SPM technologies, enabling researchers to uncover the nuanced behaviors and properties of these advanced materials at the nanoscale and even the atomic scale.

Hyperbolic response and low-frequency ultra-flat plasmons in inhomogeneous charge-distributed transition-metal monohalides

Plasmon, the collective oscillations of free electron gas in materials, determines the long-wavelength excitation spectrum and optical response, are pivotal in the realm of nanophotonics and optoelectronics. In this study, using the first-principles calculations, we systematically investigated the dielectric response and plasmon properties of bulk transition-metal monohalides MXs (M = Zr, Mo; X = Cl, F). Due to the strong electronic anisotropy, MXs exhibit a broadband type-II hyperbolic response and direction-dependent plasmon modes. Particularly, local field effect (LFE) driven by the charge distribution inhomogeneity, significantly modifies the optical response and excitation spectra in MX along the out-of-plane direction. Taking into account LFE, the energy dissipation along the out-of-plane direction is almost completely suppressed, and an ultra-flat and long-lived plasmon mode with a slow group velocity is introduced. This finding reveals the role of charge density in modifying the optical response and excitation behavior, shedding light on potential applications in plasmonics.

Multimode Friedel oscillations in monolayer and bilayer graphene

This study systematically explores the influence of charged impurities on static screening in monolayer graphene and extends the investigation to AA-stacked and AB-stacked bilayer graphene (BLG). Applying the random phase approximation (RPA), monolayer graphene displays unique beating Friedel oscillations (FOs) in inter-valley and intra-valley channels. Shifting to BLG, the study emphasizes layer-specific responses on each layer by considering self-consistent field interactions between layers. It also explores the derived multimode FOs, elucidating distinctions from monolayer behavior. In AA-stacked BLG, distinct metallic screening behaviors are revealed, uncovering unique oscillatory patterns in induced charge density, providing insights into static Coulomb scattering effects between two Dirac cones. The exploration extends to AB-stacked BLG, unveiling layer-specific responses of parabolic bands in multimode FOs with increasing Fermi energy. This comprehensive investigation, integrating RPA considerations, significantly advances our understanding of layer-dependent static screening in the broader context of FOs in graphene, providing valuable contributions to the field of condensed matter physics.

Analogous electronic states in graphene and planer metallic quantum dots

Graphene nanostructures offer wide range of applications due to their distinguished and tunable electronic properties. Recently, atomic and molecular graphene were modeled following simple free-electron scattering by periodic muffin tin potential leading to remarkable agreement with density functional theory. Here we extend the analogy of the π -electronic structures and quantum effects between atomic graphene quantum dots (QDs) and homogeneous planer metallic counterparts of similar size and shape. Specifically, we show that at high binding energies, below the M ¯ -point gap, graphene QDs enclose confined states and standing wave quasiparticle interference patterns analogous to those reported on coinage metal surfaces for nanoscale confining structures such as vacancy islands and quantum corrals. These confined and quantum corral-like states in graphene QDs can be resolved in tomography experiments using angle-resolved photoemission spectroscopy. Likewise, the shape of near-Fermi frontier orbitals in graphene quantum dots can be reproduced from electron confinement within homogeneous metal QDs of identical size and shape. Furthermore, confined states analogous to those found in metallic quantum stadiums can be realized in coupled QDs of graphene for reduced separation. The present study offer a simple fundamental understanding of graphene electronic structures and also open the way towards efficient modeling of novel graphene-based nanostructures.

Spiral-Driven Vertical Conductivity in Nanocrystalline Graphene

The structure of graphene grown in chemical vapor deposition (CVD) is sensitive to the growth condition, particularly the substrate. The conventional growth of high-quality graphene via the Cu-catalyzed cracking of hydrocarbon species has been extensively studied; however, the direct growth on noncatalytic substrates, for practical applications of graphene such as current Si technologies, remains unexplored. In this study, nanocrystalline graphene (nc-G) spirals are produced on noncatalytic substrates by inductively coupled plasma CVD. The enhanced out-of-plane electrical conductivity is achieved by a spiral-driven continuous current pathway from bottom to top layer. Furthermore, some neighboring nc-G spirals exhibit a homogeneous electrical conductance, which is not common for stacked graphene structure. Klein-edge structure developed at the edge of nc-Gs, which can easily form covalent bonding, is thought to be responsible for the uniform conductance of nc-G aggregates. These results have important implications for practical applications of graphene with vertical conductivity realized through spiral structure.

Determining Band Splitting and Spin-Flip Dynamics in Monolayer MoS2

Femtosecond helicity-resolved pump-probe spectroscopy is performed to study the spin and valley dynamics in monolayer (ML) MoS2. Both the bright to dark intravalley exciton transition (∼50 fs) and the reverse transition process (<50 fs) are directly monitored. It suggests that the bright exciton state of ML MoS2 is lower in energy than the dark one, which is also confirmed by observing the temperature-dependent co-polarized photobleaching dynamics of A and B excitons. Furthermore, the band splitting in the conduction band of ML MoS2 with a value of 15 ± 0.3 meV is determined by fitting the temperature-dependent ratios of the population in bright and dark states using the Boltzmann distribution law. Such minor band splitting allows the phonon-mediated intravalley spin-flip to even occur from the lower to the upper conduction band within tens of femtoseconds, which will have non-negligible effects on the performance of these ML MoS2-based optoelectronic and photonic devices.

Aperiodic Modulation of Graphene Driven by Oxygen-Induced Reconstruction of Rh(110)

Artificial nanostructuring of graphene has served as a platform to induce variations in its structural and electronic properties, fostering the experimental observation of a wide and fascinating phenomenology. Here, we present an approach to graphene tuning, based on Rh(110) surface reconstruction induced by oxygen atoms intercalation. The resulting nanostructured graphene has been characterized by scanning tunneling microscopy (STM) complemented by low-energy electron microscopy (LEEM), micro low-energy electron diffraction (μ-LEED), micro angle-resolved photoemission spectroscopy (μ-ARPES), and micro X-ray photoelectron spectroscopy (μ-XPS) measurements under ultrahigh vacuum (UHV) conditions at room temperature (RT). It is found that by fine-tuning the O2 exposure amount, a mixture of missing row surface reconstructions of the metal surface below the graphene layer can be induced. This atomic rearrangement under the graphene layer results in aperiodic patterning of the two-dimensional (2D) material. The electronic structure of the resulting nanostructured graphene is dominated by a linear dispersion of the Dirac quasiparticles, characteristic of its free-standing state but with a p-doping character. The local effects of the underlying missing rows on the interfacial chemistry and on the quasiparticle scattering processes in graphene are studied using atomically resolved STM images. The possibilities offered by this nanostructuring approach, which consists in inducing surface reconstructions under graphene, could provide a novel tuning strategy for this 2D material.

Quantum textures of the many-body wavefunctions in magic-angle graphene

Interactions among electrons create novel many-body quantum phases of matter with wavefunctions that reflect electronic correlation effects, broken symmetries and collective excitations. Many quantum phases have been discovered in magic-angle twisted bilayer graphene (MATBG), including correlated insulating1, unconventional superconducting2-5 and magnetic topological6-9 phases. The lack of microscopic information10,11 of possible broken symmetries has hampered our understanding of these phases12-17. Here we use high-resolution scanning tunnelling microscopy to study the wavefunctions of the correlated phases in MATBG. The squares of the wavefunctions of gapped phases, including those of the correlated insulating, pseudogap and superconducting phases, show distinct broken-symmetry patterns with a √3 × √3 super-periodicity on the graphene atomic lattice that has a complex spatial dependence on the moiré scale. We introduce a symmetry-based analysis using a set of complex-valued local order parameters, which show intricate textures that distinguish the various correlated phases. We compare the observed quantum textures of the correlated insulators at fillings of ±2 electrons per moiré unit cell to those expected for proposed theoretical ground states. In typical MATBG devices, these textures closely match those of the proposed incommensurate Kekulé spiral order15, whereas in ultralow-strain samples, our data have local symmetries like those of a time-reversal symmetric intervalley coherent phase12. Moreover, the superconducting state of MATBG shows strong signatures of intervalley coherence, only distinguishable from those of the insulator with our phase-sensitive measurements.

Imaging beyond the surface region: Probing hidden materials via atomic force microscopy

Probing material properties at surfaces down to the single-particle scale of atoms and molecules has been achieved, but high-resolution subsurface imaging remains a nanometrology challenge due to electromagnetic and acoustic dispersion and diffraction. The atomically sharp probe used in scanning probe microscopy (SPM) has broken these limits at surfaces. Subsurface imaging is possible under certain physical, chemical, electrical, and thermal gradients present in the material. Of all the SPM techniques, atomic force microscopy has entertained unique opportunities for nondestructive and label-free measurements. Here, we explore the physics of the subsurface imaging problem and the emerging solutions that offer exceptional potential for visualization. We discuss materials science, electronics, biology, polymer and composite sciences, and emerging quantum sensing and quantum bio-imaging applications. The perspectives and prospects of subsurface techniques are presented to stimulate further work toward enabling noninvasive high spatial and spectral resolution investigation of materials including meta- and quantum materials.

Determining spin-orbit coupling in graphene by quasiparticle interference imaging

Inducing and controlling spin-orbit coupling (SOC) in graphene is key to create topological states of matter, and for the realization of spintronic devices. Placing graphene onto a transition metal dichalcogenide is currently the most successful strategy to achieve this goal, but there is no consensus as to the nature and the magnitude of the induced SOC. Here, we show that the presence of backscattering in graphene-on-WSe₂ heterostructures can be used to probe SOC and to determine its strength quantitatively, by imaging quasiparticle interference with a scanning tunneling microscope. A detailed theoretical analysis of the Fourier transform of quasiparticle interference images reveals that the induced SOC consists of a valley-Zeeman (λ_vZ ≈ 2 meV) and a Rashba (λ_R ≈ 15 meV) term, one order of magnitude larger than what theory predicts, but in excellent agreement with earlier transport experiments. The validity of our analysis is confirmed by measurements on a 30 degree twist angle heterostructure that exhibits no backscattering, as expected from symmetry considerations. Our results demonstrate a viable strategy to determine SOC quantitatively by imaging quasiparticle interference.

Observation of Robust and Long-Ranged Superperiodicity of Electronic Density Induced by Intervalley Scattering in Graphene/Transition Metal Dichalcogenide Heterostructures

Two-dimensional (2D) h-BN and transition metal dichalcogenides (TMDs) are widely used as substrates of graphene because they are insulating, atomically flat, and without dangling bonds. Usually, it is believed that such insulating substrates will not affect the electronic properties of graphene, especially when the moiré pattern generated between them is quite small. Here, we present a systematic study of the electronic properties of graphene/TMD heterostructures with the period of the moiré pattern <1 nm, and our results reveal an unexpected sensitivity of electronic properties in graphene to the 2D insulating substrates. We demonstrate that there is a robust and long-ranged superperiodicity of electronic density in graphene, which arises from the scattering of electrons between the two valleys of graphene in the graphene/TMD heterostructures. By using scanning tunneling microscope and spectroscopy, three distinct atomic-scale patterns of the electronic density are directly imaged in every graphene/TMD heterostructure.

Lateral Heterostructures of Graphene and h-BN with Atomic Lattice Coherence and Tunable Rotational Order

In-plane heterostructures of graphene and hexagonal boron nitride (h-BN) exhibit exceptional properties, which are highly sensitive to the structure of the alternating domains. Nevertheless, achieving accurate control over their structural properties, while keeping a high perfection at the graphene-h-BN boundaries, still remains a challenge. Here, the growth of lateral heterostructures of graphene and h-BN on Rh(110) surfaces is reported. The choice of the 2D material, grown firstly, determines the structural properties of the whole heterostructure layer, allowing to have control over the rotational order of the domains. The atomic-scale observation of the boundaries demonstrates a perfect lateral matching. In-plane heterostructures floating over an oxygen layer have been successfully obtained, enabling to observe intervalley scattering processes in graphene regions. The high tuning capabilities of these heterostructures, along with their good structural quality, even around the boundaries, suggest their usage as test beds for fundamental studies aiming at the development of novel nanomaterials with tailored properties.

Structural identification of graphene films and nanoislands on 6H-SiC(0001) by direct height measurement

By combining non-contact atomic force microscopy (nc-AFM) and Kelvin probe microscopy (KPFM) in ultra high vacuum environment (UHV), we directly measure the height and work function of graphene monolayer on the Si-face of 6H-SiC(0001) with a precision that allows us to differentiate three different types of graphene structures : zero layer graphene (ZLG), Quasi free-standing monolayer graphene (QFMLG) and bilayer graphene (BLG). The height and work function of ZLG are 2.62 ± 0.22 Å and 4.42 ± 0.05 eV respectively, when they are 4.09 ± 0.11 Å and 4.63 ± 0.05 eV for QFMLG. The work function is 4.83 ± 0.05 eV for the BLG. Unlike any other available technique, the local nc-AFM/KPFM dual probe makes it possible to directly identify the nature of nanometer-sized graphene islands that constitute the early nuclei of graphene monolayer grown on 6H-SiC(0001) by chemical vapor deposition.

Suppression of Intervalley Coupling in Graphene via Potassium Doping

The quantum interference patterns induced by impurities in graphene can form the (√3 × √3)R30° superlattice with intervalley scattering. This superlattice can lead to the folded Dirac cone at the center of Brillouin zone by coupling two non-equivalent valleys. Using angle-resolved photoemission spectroscopy (ARPES), we report the observation of suppression of the folded Dirac cone in mono- and bilayer graphene upon potassium doping. The intervalley coupling with chiral symmetry broken can persist upon a light potassium-doped level but be ruined at the heavily doped level. Meanwhile, the folded Dirac cone can be suppressed by the renormalization of the Dirac band with potassium doping. Our results demonstrate that the suppression of the intervalley scattering pattern by potassium doping could pave the way toward the realization of novel chiraltronic devices in superlattice graphene.

Characterization and Manipulation of Intervalley Scattering Induced by an Individual Monovacancy in Graphene

Intervalley scattering involves microscopic processes that electrons are scattered by atomic-scale defects on the nanoscale. Although central to our understanding of electronic properties of materials, direct characterization and manipulation of range and strength of the intervalley scattering induced by an individual atomic defect have so far been elusive. Using scanning tunneling microscope, we visualize and control intervalley scattering from an individual monovacancy in graphene. By directly imaging the affected range of monovacancy-induced intervalley scattering, we demonstrate that it is inversely proportional to the energy; i.e., it is proportional to the wavelength of massless Dirac fermions. A giant electron-hole asymmetry of the intervalley scattering is observed because the monovacancy is charged. By further charging the monovacancy, the bended electronic potential around the monovacancy softens the scattering potential, which, consequently, suppresses the intervalley scattering of the monovacancy.

Two-Way Twisting of a Confined Monolayer: Orientational Ordering within the van der Waals Gap between Graphene and Its Crystalline Substrate

Two-dimensional confinement of lattices produces a variety of order and disorder phenomena. When the confining walls have atomic granularity, unique structural phases are expected, of relevance in nanotribology, porous materials, or intercalation compounds where, e.g., electronic states can emerge accordingly. The interlayer's own order is frustrated by the competing interactions exerted by the two confining surfaces. We revisit the concept of orientational ordering, introduced by Novaco and McTague to describe the twist of incommensurate monolayers on crystalline surfaces. We predict a two-way twist of the monolayer as its density increases. We discover such a behavior in alkali atom monolayers (sodium, cesium) confined between graphene and an iridium surface, using scanning tunneling microscopy and electron diffraction.

Ubiquitous defect-induced density wave instability in monolayer graphene

Quantum materials are notoriously sensitive to their environments, where small perturbations can tip a system toward one of several competing ground states. Graphene hosts a rich assortment of such competing phases, including a bond density wave instability ("Kekulé distortion") that couples electrons at the K/K' valleys and breaks the lattice symmetry. Here, we report observations of a ubiquitous Kekulé distortion across multiple graphene systems. We show that extremely dilute concentrations of surface atoms (less than three adsorbed atoms every 1000 graphene unit cells) can self-assemble and trigger the onset of a global Kekulé density wave phase. Combining complementary momentum-sensitive angle-resolved photoemission spectroscopy (ARPES) and low-energy electron diffraction (LEED) measurements, we confirm the presence of this density wave phase and observe the opening of an energy gap. Our results reveal an unexpected sensitivity of the graphene lattice to dilute surface disorder and show that adsorbed atoms offer an attractive route toward designing novel phases in two-dimensional materials.

Atomic Simulations of (8,0)CNT-Graphene by SCC-DFTB Algorithm

Self-consistent density functional tight binding (SCC-DFTB) approaches were used to study optimized structures, energy, differential charge density, and Mülliken populations for the (8,0) carbon nanotubes (CNTs) connected to the graphene having different topology defects. Based on the calculations, nine seamless (8,0)CNT-graphenes were selected. For these connected systems, geometric configurations of the graphene and nanotubes were characterized, and the nearest neighbor length of C-C atoms and average length were obtained. The intrinsic energy, energy gap, and chemical potential were analyzed, and they presented apparent differences for different connection modes. Differential charge densities of these connection modes were analyzed to present covalent bonds between the atoms. We have also thoroughly analyzed the Mülliken charge transfer among the C atoms at the junctions.

Functionalization and exfoliation of graphite with low temperature pulse plasma in distilled water

Graphene materials exhibit extraordinary properties, but are difficult to produce. The present work describes the possibility of using a plasma process to exfoliate and functionalize graphite flakes. An impulse plasma phase is generated at a liquid surface to produce chemical species and shock waves in order to modify the reactive liquid as well as the graphite flakes. With this process, industrial graphite was treated. 20% thickness diminution was observed, and the formation of a random turbostratic structure. The exfoliation occurs with small amount of functionalization of the surface. Even after treatment, the graphite flakes present a low defect density compared with other treated graphite obtained by more conventional chemical treatments. This process is a new way to exfoliate graphite and to produce functionalized graphenic materials.

Two-dimensional carbon materials with an anisotropic Dirac cone: high stability and tunable Fermi velocity

A new 2D Dirac carbon allotrope is proposed, which has unique self-doping properties and a tunable Fermi velocity via the applied strain.

Quantum Sensing of Thermoelectric Power in Low-Dimensional Materials

Thermoelectric power, has been extensively studied in low-dimensional materials where quantum confinement and spin textures can largely modulate thermopower generation. In addition to classical and macroscopic values, thermopower also varies locally over a wide range of length scales, and is fundamentally linked to electron wave functions and phonon propagation. Various experimental methods for the quantum sensing of localized thermopower have been suggested, particularly based on scanning probe microscopy. Here, critical advances in the quantum sensing of thermopower are introduced, from the atomic to the several-hundred-nanometer scales, including the unique role of low-dimensionality, defects, spins, and relativistic effects for optimized power generation. Investigating the microscopic nature of thermopower in quantum materials can provide insights useful for the design of advanced materials for future thermoelectric applications. Quantum sensing techniques for thermopower can pave the way to practical and novel energy devices for a sustainable society.

High-Throughput Screening of Two-Dimensional Planar sp2 Carbon Space Associated with a Labeled Quotient Graph

The configurational space of two-dimensional planar sp² carbon has been systematically scanned by a random strategy combined with group and graph theory, and 1114 new carbon allotropes have been identified. These allotropes are energetically more favorable than most of the previously predicted 120 carbon allotropes. By fitting the HSE06 band structures of six old structures, we optimize the parameters for a general and transferable tight-binding model for high-throughput band structure calculations. We identified that there are 190 Dirac semimetals, 241 semiconductors, and 683 normal metals among the new allotropes. Interestingly, several stable low-energy carbon systems with exotic electronic properties are proposed, such as type III, type I/II mixed, and type I/III mixed semimetals, which are very rare in planar carbon systems. In particular, one nodal-line semimetal has been discovered among these thousands of allotropes, which is the first nodal-line semimetal in sp² carbon systems. Our discoveries greatly enrich our knowledge of the structures and electronic properties of the two-dimensional carbon family.

Epitaxial Growth of Uniform Single-Layer and Bilayer Graphene with Assistance of Nitrogen Plasma

Graphene was reported as the first-discovered two-dimensional material, and the thermal decomposition of SiC is a feasible route to prepare graphene films. However, it is difficult to obtain a uniform single-layer graphene avoiding the coexistence of multilayer graphene islands or bare substrate holes, which give rise to the degradation of device performance and becomes an obstacle for the further applications. Here, with the assistance of nitrogen plasma, we successfully obtained high-quality single-layer and bilayer graphene with large-scale and uniform surface via annealing 4H-SiC(0001) wafers. The highly flat surface and ordered terraces of the samples were characterized using in situ scanning tunneling microscopy. The Dirac bands in single-layer and bilayer graphene were measured using angle-resolved photoemission spectroscopy. X-ray photoelectron spectroscopy combined with Raman spectroscopy were used to determine the composition of the samples and to ensure no intercalation or chemical reaction of nitrogen with graphene. Our work has provided an efficient way to obtain the uniform single-layer and bilayer graphene films grown on a semiconductive substrate, which would be an ideal platform for fabricating two-dimensional devices based on graphene.

Dirac Fermions in Graphene with Stacking Fault Induced Periodic Line Defects

The exploration of carbon phases with intact massless Dirac fermions in the presence of defects is critical for practical applications to nanoelectronics. Here, we identify by first-principles calculations that the Dirac cones can exist in graphene with stacking fault (SF) induced periodic line defects. These structures are width (n)-dependent to graphene nanoribbon and are thus termed as (SF)_n-graphene. The electronic properties reveal that the semimetallic features with Dirac cones occur in (SF)_n-graphene with n = 3m + 1, where m is a positive integer, and then lead to a quasi-one-dimensional conducting channel. Importantly, it is found that the twisted Dirac cone in the (SF)₄-graphene is tunable among type-I, type-II, and type-III through a small uniaxial strain. The further stability analysis shows that (SF)_n-graphene is thermodynamic stable. Our findings provide an artificial avenue for exploring Dirac Ffermions in carbon-allotropic structures in the presence of defects.

Direct Observation of Global Elastic Intervalley Scattering Induced by Impurities on Graphene

The scattering process induced by impurities in graphene plays a key role in transport properties. Especially, the disorder impurities can drive the ordered state with a hexagonal superlattice on graphene by electron-mediated interaction at a transition temperature. Using angle-resolved photoemission spectroscopy (ARPES), we reveal that the epitaxial monolayer and bilayer graphene with various impurities display global elastic intervalley scattering and quantum interference below the critical temperature (34 K), which leads to a set of new folded Dirac cones at the Brillouin-zone center by mixing two inequivalent Dirac cones. The Dirac electrons generated from intervalley scattering without chirality can be due to the breaking of the sublattice symmetry. In addition, the temperature-dependent ARPES measurements indicate the thermal damping of quantum interference patterns from Dirac electron scattering on impurities. Our results demonstrate that the electron scattering and interference induced by impurities can completely modulate the Dirac bands of graphene.

Direct Visualization of Native Defects in Graphite and Their Effect on the Electronic Properties of Bernal-Stacked Bilayer Graphene

Graphite crystals used to prepare graphene-based heterostructures are generally assumed to be defect free. We report here scanning tunneling microscopy results that show graphite commonly used to prepare graphene devices can contain a significant amount of native defects. Extensive scanning of the surface allows us to determine the concentration of native defects to be 6.6 × 10⁸ cm^-2. We further study the effects of these native defects on the electronic properties of Bernal-stacked bilayer graphene. We observe gate-dependent intravalley scattering and successfully compare our experimental results to T-matrix-based calculations, revealing a clear carrier density dependence in the distribution of the scattering vectors. We also present a technique for evaluating the spatial distribution of short-scale scattering. Finally, we present a theoretical analysis based on the Boltzmann transport equation that predicts that the dilute native defects identified in our study are an important extrinsic source of scattering, ultimately setting the charge carrier mobility at low temperatures.

Traction-separation laws of graphene grain boundaries

Molecular dynamics simulations are used to extract the traction-separation laws (TSLs) of symmetric grain boundaries of graphene. Grain boundaries with realistic atomic structures are constructed using different types of dislocations. The TSLs of grain boundaries are extracted by using cohesive zone volume elements (CZVEs) ahead of the crack tip. The traction and separation of each cohesive zone volume element are calculated during the crack growth. The traction and separation values obtained for the cohesive elements predict that the TSLs of grain boundaries have a bilinear form. The areas under the traction-separation curves are used to calculate the separation energy of the grain boundaries. The results show that as the grain boundary misorientation angle increases the separation energy of the grain boundaries decreases. The impact of temperature on the traction separation laws is studied. The results show that, with an increase of the temperature from 0.1 K to 300 K, the separation energy first increases to reach its peak at around 25 K and then slightly decreases.

Measuring and Tuning the Potential Landscape of Electrostatically Defined Quantum Dots in Graphene

We use Kelvin probe force microscopy (KPFM) to probe the carrier-dependent potential of an electrostatically defined quantum dot (QD) in a graphene/hexagonal boron nitride (hBN) heterostructure. We show that gate-dependent measurements enable a calibration scheme that corrects for uncertainty inherent in typical KPFM measurements and accurately reconstructs the potential well profile. Our measurements reveal how the well changes with carrier concentration, which we associate with the nonlinear dependence of graphene's work function on carrier density. These changes shift the energy levels of quasi-bound states in the QD which we can measure via scanning tunneling spectroscopy (STS). We show that the experimentally extracted energy levels closely compare with wave functions calculated from the reconstructed KPFM data. This methodology, where KPFM and STS data are simultaneously acquired from 2D materials, allows the quasiparticle response to an electrostatic potential to be determined in a self-consistent way.

Anomalous thermopower oscillations in graphene-nanowire vertical heterostructures

Thermoelectric measurements have the potential to uncover the density of states (DOSs) of low-dimensional materials. Here, we present the anomalous thermoelectric behavior of monolayer graphene-nanowire (NW) heterostructures, showing large oscillations as a function of the doping concentration. Our devices consist of InAs NW and graphene vertical heterostructures, which are electrically isolated by thin (∼10 nm) hexagonal boron nitride (hBN) layers. In contrast to conventional thermoelectric measurements, where a heater is placed on one side of a sample, we use the InAs NW (diameter ∼50 nm) as a local heater placed in the middle of the graphene channel. We measure the thermoelectric voltage induced in graphene due to Joule heating in the NW as a function of temperature (1.5-50 K) and carrier concentration. The thermoelectric voltage in bilayer graphene (BLG)-NW heterostructures shows sign change around the Dirac point, as predicted by Mott's formula. In contrast, the thermoelectric voltage measured across monolayer graphene (MLG)-NW heterostructures shows anomalous large-amplitude oscillations around the Dirac point, not seen in the Mott response derived from the electrical conductivity measured on the same device. The anomalous oscillations are a signature of the modified DOSs in MLG by the electrostatic potential of the NW, which is much weaker in the NW-BLG devices. Thermal calculations of the heterostructure stack show that the temperature gradient is dominant in the graphene region underneath the NW, and thus sensitive to the modified DOSs resulting in anomalous oscillations in the thermoelectric voltage. Furthermore, with the application of a magnetic field, we detect modifications in the DOSs due to the formation of Landau levels in both MLG and BLG.

Quantum Interferences of Pseudospin-Mediated Atomic-Scale Vortices in Monolayer Graphene

A vortex is a universal and significant phenomenon that has been known for centuries. However, creating vortices to the atomic limit has remained elusive. Very recently, it was demonstrated that intervalley scattering induced by the single carbon defect of graphene leads to phase winding over a closed path surrounding the defect. Motivated by this, we demonstrate that the single carbon defects at A and B sublattices of graphene can be regarded as pseudospin-mediated atomic-scale vortices with angular momenta l = +2 and -2, respectively. The quantum interference measurements of the vortices indicate that the vortices cancel each other, resulting in zero total angular momentum, in the |A| = |B| case, and they show aggregate chirality and angular momenta similar to a single vortex of the majority in the |A| ≠ |B| case, where |A| (|B|) is the number of vortices with angular momenta l = +2 (l = -2).

Progress in Epitaxial Thin-Film Na3 Bi as a Topological Electronic Material

Trisodium bismuthide (Na₃ Bi) is the first experimentally verified topological Dirac semimetal, and is a 3D analogue of graphene hosting relativistic Dirac fermions. Its unconventional momentum-energy relationship is interesting from a fundamental perspective, yielding exciting physical properties such as chiral charge carriers, the chiral anomaly, and weak anti-localization. It also shows promise for realizing topological electronic devices such as topological transistors. Herein, an overview of the substantial progress achieved in the last few years on Na₃ Bi is presented, with a focus on technologically relevant large-area thin films synthesized via molecular beam epitaxy. Key theoretical aspects underpinning the unique electronic properties of Na₃ Bi are introduced. Next, the growth process on different substrates is reviewed. Spectroscopic and microscopic features are illustrated, and an analysis of semiclassical and quantum transport phenomena in different doping regimes is provided. The emergent properties arising from confinement in two dimensions, including thickness-dependent and electric-field-driven topological phase transitions, are addressed, with an outlook toward current challenges and expected future progress.

Encapsulation of metal nanoparticles at the surface of a prototypical layered material

Encapsulation of metal nanoparticles just below the surface of a prototypical layered material, graphite, is a recently discovered phenomenon. These encapsulation architectures have potential for tuning the properties of two-dimensional or layered materials, and additional applications might exploit the properties of the encapsulated metal nanoclusters themselves. The encapsulation process produces novel surface nanostructures and can be achieved for a variety of metals. Given that these studies of near-surface intercalation are in their infancy, these systems provide a rich area for future studies. This Review presents the current progress on the encapsulation, including experimental strategies and characterization, as well as theoretical understanding which leads to the development of predictive capability. The Review closes with future opportunities where further understanding of the encapsulation is desired to exploit its applications.

Two-Dimensional Carbon Allotropes and Nanoribbons based on 2,6-Polyazulene Chains: Stacking Stabilities and Electronic Properties

The previously predicted phagraphene [Wang et al., Nano Lett. 15, 6182 (2015)] and a recently proposed TPH-graphene have been synthesized from fusion of 2,6-polyazulene chain (5-7 chain) in a recent experiment [Fan et al., J. Am. Chem. Soc., 141, 17713 (2019)]. Theoretically, phagraphene and TPH-graphene can be considered as the combinations of the 5-7 chains with distinct 6-6-6 and 4-7-7 interfacial stacking manners, respectively. In this work, we propose another new graphene allotrope, named as penta-hex-hepta-graphene (PHH-graphene), which can be constructed by coupling the synthesized 5-7 chains with a new type of 5-7-6 stacking interface. It is found that the PHH-graphene is dynamically and thermally stable, and especially notable, the total energy of PHH-graphene is lower than that of synthesized TPH-graphene. Thus, it is highly possible that PHH-graphene can be realized through assembly of 5-7 chains. We have systematically investigated the electronic properties of these three graphene allotropes and their nanoribbons. The results show that PHH-graphene is a type-I semimetal with a highly anisotropic Dirac cone similar to phagraphene, while TPH-graphene is a metal. Their nanoribbons exhibit different electronic band structures as the number (n) of 5-7 chains increases. For TPH-graphene nanoribbons, they become metal rapidly as n ≥ 2. The nanoribbons of the semimetallic phagraphene and PHH-graphene are narrow band gap semiconductors with gaps decreasing as n increases, which are similar to the graphene nanoribbons. We also find that the band gaps of PHH-graphene nanoribbons exhibit two distinct families with n = 2i and n = 2i + 1, which can be understood by the width-dependent symmetries of the system.

Local Berry Phase Signatures of Bilayer Graphene in Intervalley Quantum Interference

Chiral quasiparticles in Bernal-stacked bilayer graphene have valley-contrasting Berry phases of ±2π. This nontrivial topological structure, associated with the pseudospin winding along a closed Fermi surface, is responsible for various novel electronic properties. Here we show that the quantum interference due to intervalley scattering induced by single-atom vacancies or impurities provides insights into the topological nature of the bilayer graphene. The scattered chiral quasiparticles between distinct valleys with opposite chirality undergo a rotation of pseudospin that results in the Friedel oscillation with wavefront dislocations. The number of dislocations reflects the information about pseudospin texture and hence can be used to measure the Berry phase. As demonstrated both experimentally and theoretically, the Friedel oscillation, depending on the single-atom vacancy or impurity at different sublattices, can exhibit N=4, 2, or 0 additional wavefronts, characterizing the 2π Berry phase of the bilayer graphene. Our results provide a comprehensive study of the intervalley quantum interference in bilayer graphene and can be extended to multilayer graphene, shedding light on the pseudospin physics.

Structural and magnetic properties of a defective graphene buffer layer grown on SiC(0001): a DFT study

Understanding the role of defects in the magnetic properties of the graphene buffer layer (BL) grown on substrates should be important to provide hints for manufacturing future graphene-based spintronic devices in a controlled fashion. Herein, density functional theory was applied to assess the structure and magnetic properties of defective BL on 6H-SiC(0001). Particularly, we conducted a thorough study of one and two vacancies and Stone-Wales defects in the BL. Our results reveal that the removal of a carbon atom in the BL framework that was originally bonded to a Si atom in the substrate is preferred over that of a sp2-bonded atom. As a result, a hexacoordinated silicon atom is formed with a slightly deviated octahedral geometry. A stable antiferromagnetic (AF) state was verified for the single vacancy system, with a quite different spin-density distribution to the one obtained for the perfect BL. Also, this AF state is nearly degenerate with the non-magnetic and low magnetic states. As for the Stone-Wales defect, the AF sate is almost degenerate with the most stable M = 2 μB magnetic configuration. However, the introduction of two vacancies in the carbon network of BL causes the loss of magnetism of the BL-SiC system. Our theoretical calculations support experimental predictions favoring the BL as the site for single vacancy formation rather than the epitaxial monolayer graphene, by 4.3 eV.

Weak localization in graphene sandwiched by aligned h-BN flakes

Charge carriers in graphene exhibit distinct characteristics from those in other two-dimensional materials because of their chiral nature. Additionally, multiple Dirac cones that emerge in graphene superlattices have been regarded as an interesting point in condensed-matter physics in recent years. Here, we report an investigation of the magneto-conductance in graphene encapsulated on the top and bottom by aligned h-BN. The bottom h-BN is precisely aligned with graphene, while the top h-BN is rotated a very small angle relative to it. Such a heterostructure could spoil the commensurate state existing in precisely aligned graphene while the giant moiré superlattice remains. A clear signature of weak localization and weak anti-localization is observed at multiple Dirac cones. Both the weak (anti)localization and the universal conductance fluctuations exhibit strong dependencies on the carrier density, temperature and channel length. This artificial heterostructure allows one to explore quantum interference in graphene with a wide spectrum of electronic properties.

Strain Modulated Superlattices in Graphene

Numerous theoretically proposed devices and novel phenomena have sought to take advantage of the intense pseudogauge fields that can arise in strained graphene. Many of these proposals, however, require fields to oscillate with a spatial frequency smaller than the magnetic length, while to date only the generation and effects of fields varying at a much larger length scale have been reported. Here, we describe the creation of short wavelength, periodic pseudogauge-fields using rippled graphene under extreme (>10%) strain and study of its effects on Dirac electrons. Combining scanning tunneling microscopy and atomistic calculations, we find that spatially oscillating strain generates a new quantization different from the familiar Landau quantization. Graphene ripples also cause large variations in carbon-carbon bond length, creating an effective electronic superlattice within a single graphene sheet. Our results thus also establish a novel approach of synthesizing effective 2D lateral heterostructures by periodically modulating lattice strain.

Dictionary learning in Fourier-transform scanning tunneling spectroscopy

Modern high-resolution microscopes are commonly used to study specimens that have dense and aperiodic spatial structure. Extracting meaningful information from images obtained from such microscopes remains a formidable challenge. Fourier analysis is commonly used to analyze the structure of such images. However, the Fourier transform fundamentally suffers from severe phase noise when applied to aperiodic images. Here, we report the development of an algorithm based on nonconvex optimization that directly uncovers the fundamental motifs present in a real-space image. Apart from being quantitatively superior to traditional Fourier analysis, we show that this algorithm also uncovers phase sensitive information about the underlying motif structure. We demonstrate its usefulness by studying scanning tunneling microscopy images of a Co-doped iron arsenide superconductor and prove that the application of the algorithm allows for the complete recovery of quasiparticle interference in this material.

Aperiodic structure imaging suffers limitations when utilizing Fourier analysis. The authors report an algorithm that quantitatively overcomes these limitations based on nonconvex optimization, demonstrated by studying aperiodic structures via the phase sensitive interference in STM images.

Interlayer Decoupling in 30° Twisted Bilayer Graphene Quasicrystal

Stacking order has a strong influence on the coupling between the two layers of twisted bilayer graphene (BLG), which in turn determines its physical properties. Here, we report the investigation of the interlayer coupling of the epitaxially grown single-crystal 30°-twisted BLG on Cu(111) at the atomic scale. The stacking order and morphology of BLG is controlled by a rationally designed two-step growth process, that is, the thermodynamically controlled nucleation and kinetically controlled growth. The crystal structure of the 30°-twisted bilayer graphene (30°-tBLG) is determined to have quasicrystal-like symmetry. The electronic properties and interlayer coupling of the 30°-tBLG are investigated using scanning tunneling microscopy and spectroscopy. The energy-dependent local density of states with in situ electrostatic doping shows that the electronic states in two graphene layers are decoupled near the Dirac point. A linear dispersion originated from the constituent graphene monolayers is discovered with doubled degeneracy. This study contributes to controlled growth of twist-angle-defined BLG and provides insights on the electronic properties and interlayer coupling in this intriguing system.

Intercalation-Mediated Synthesis and Interfacial Coupling Effect Exploration of Unconventional Graphene/PtSe2 Vertical Heterostructures

Vertical heterostructures formed by stacks of two-dimensional (2D) layered materials with disparate electronic properties have attracted tremendous attention for their versatile applications. The targeted fabrication of such vertical stacks with clean interfaces and a specific stacking sequence remains challenging. Herein, we design a two-step chemical vapor deposition route for the direct synthesis of unconventional graphene/PtSe₂ vertical stacks (Gr/PtSe₂) on conductive Au foil substrates. Monolayer PtSe₂ (1L-PtSe₂) was detected to preferentially grow at the interface of the predeposited Gr layer and the Au foil substrate rather than on the Gr surface. The concurrent effect from the strong interaction of PtSe₂/Au and the space confinement effect of Gr/Au are proposed to be the essential mechanisms. Particularly, this unique growth system allows us to uncover the intrinsic property of 1L-PtSe₂ and the interfacial coupling effect using scanning tunneling microscopy/spectroscopy. Our work should hereby enable significant advances in the synthesis of 2D-based vertical heterostructures and in the exploration of their intrinsic interface properties.

Local electronic structure of doping defects on Tl/Si(111)1x1

The Tl/Si(111)1 × 1 surface is a representative of a 2D layer with Rashba-type spin-split electronic bands. To utilize the spin polarization, doping of the system should be understood on atomic level. We present a study of two types of atomic defects predicted to dope the considered electronic system – Si-induced vacancies and defects associated with the presence of extra Tl atoms. Structural calculations based on density functional theory (DFT) confirm the stability of the proposed defect structure consisting of an extra Si atom and missing seven Tl atoms as proposed in an earlier experimental study. The calculated spatial charge distributions indicate an enhancement of the charge around the extra Si atom, which correctly reproduces topographies of the corresponding scanning tunneling microscopy images while the calculated local densities of states of this system explain obtained scanning tunneling spectra. The DFT structural calculations let us determine the atomic structure of the defect caused by the presence of an extra Tl atom. The calculated spatial charge distributions show a ring-like feature around the extra Tl atom. The obtained results indicate a charge transfer from the central extra Tl atom to its vicinity in the agreement with earlier photoemission measurements.

Measuring the Berry phase of graphene from wavefront dislocations in Friedel oscillations

Electronic band structures dictate the mechanical, optical and electrical properties of crystalline solids. Their experimental determination is therefore crucial for technological applications. Although the spectral distribution in energy bands is routinely measured by various techniques¹, it is more difficult to access the topological properties of band structures such as the quantized Berry phase, γ, which is a gauge-invariant geometrical phase accumulated by the wavefunction along an adiabatic cycle². In graphene, the quantized Berry phase γ = π accumulated by massless relativistic electrons along cyclotron orbits is evidenced by the anomalous quantum Hall effect^4,5. It is usually thought that measuring the Berry phase requires the application of external electromagnetic fields to force the charged particles along closed trajectories³. Contradicting this belief, here we demonstrate that the Berry phase of graphene can be measured in the absence of any external magnetic field. We observe edge dislocations in oscillations of the charge density ρ (Friedel oscillations) that are formed at hydrogen atoms chemisorbed on graphene. Following Nye and Berry⁶ in describing these topological defects as phase singularities of complex fields, we show that the number of additional wavefronts in the dislocation is a real-space measure of the Berry phase of graphene. Because the electronic dispersion relation can also be determined from Friedel oscillations⁷, our study establishes the charge density as a powerful observable with which to determine both the dispersion relation and topological properties of wavefunctions. This could have profound consequences for the study of the band-structure topology of relativistic and gapped phases in solids.

Chemical-Vapor-Deposited Graphene as a Thermally Conducting Coating

We performed scanning thermal microscopy measurements on single layers of chemical-vapor-deposited (CVD) graphene supported by different substrates, namely, SiO₂, Al₂O₃, and PET using a double-scan technique to remove the contribution to the heat flux through the air and the cantilever. Then, by adopting a simple lumped-elements model, we developed a new method that allows determining, through a multistep numerical analysis, the equivalent thermal properties of thermally conductive coatings of nanometric thickness. In this specific case we found that our CVD graphene is "thermally equivalent", for heat injection perpendicular to the graphene planes, to a coating material of conductivity k _eff = 2.5 ± 0.3 W/m K and thickness t _eff = 3.5 ± 0.3 nm in perfect contact with the substrate. For the SiO₂ substrate, we also measured stacks made of 2- and 4-CVD monolayers, and we found that the effective thermal conductivity increases with increasing number of layers and, with a technologically achievable number of layers, is expected to be comparable to that of 1 order of magnitude-thicker metallic thin films. This study provides a powerful method for characterizing the thermal properties of graphene in view of several thermal management applications.

Layer-Stacking, Defects, and Robust Superconductivity on the Mo-Terminated Surface of Ultrathin Mo2C Flakes Grown by CVD

Materials can exhibit exotic properties when they approach the two-dimensional (2D) limit. Because of promising applications in catalysis and energy storage, 2D transition-metal carbides (TMCs) have attracted considerable attention in recent years. Among these TMCs, ultrathin crystalline α-Mo₂C flakes have been fabricated by chemical vapor deposition on Cu/Mo bilayer foils, and their 2D superconducting property was revealed by transport measurements. Herein, we studied the ultrathin α-Mo₂C flakes by atomic-resolved scanning tunneling microscopy/spectroscopy (STM/S). Strain-related structural modulation and the coexistence of different layer-stacking modes are observed on the Mo-terminated surface of α-Mo₂C flakes as well as various lattice defects. Furthermore, an enhanced superconductivity with shorter correlation length was observed by STS technique, and such superconductivity is very robust despite the appearance of the defects. A mechanism of superconducting enhancement is proposed based on the strain-induced strong coupling and the increased disordering originated from lattice defects. Our results provide a comprehensive understanding of the correlations between atomic structure, defects, and enhanced superconductivity of this emerging 2D material.

Mxenes Derived Laminated and Magnetic Composites with Excellent Microwave Absorbing Performance

Two dimensional materials have been widely identified as promising microwave absorbers, owing to their large surface area and abundant interfaces. Here, a novel laminated and magnetic composite derived from Mxene was designed and successfully synthesized via facile hydrothermal oxidization of nickel ion intercalated Ti3C2. Highly disordered carbon sheets were obtained by low temperature hydrothermal oxidization, and the in-situ produced TiO2 and NiO nanoparticles embedded closely between them. This layered hybrid exhibits excellent microwave absorbing performance with an effective absorbing bandwidth as high as 11.1 GHz (6.9-18 GHz) and 9 GHz (9-18 GHz) when the thickness is 3 and 2 mm, respectively. Besides the high dielectric loss, magnetic loss and ohmic loss of the composite, the amorphous nature of obtained carbon sheets and multi-reflections between them are believed to play a decisive role in achieving such superior microwave absorbing performance.

Interaction-disorder-driven characteristic momentum in graphene, approach of multi-body distribution functions

Multi-point probability measures along with the dielectric function of Dirac Fermions in mono-layer graphene containing particle-particle and white-noise (out-plane) disorder interactions on an equal footing in the Thomas-Fermi-Dirac approximation is investigated. By calculating the one-body carrier density probability measure of the graphene sheet, we show that the density fluctuation (ζ-1) is related to the disorder strength (ni), the interaction parameter (rs) and the average density ([Formula: see text]) via the relation [Formula: see text] for which [Formula: see text] leads to strong density inhomogeneities, i.e. electron-hole puddles (EHPs), in agreement with the previous works. The general equation governing the two-body distribution probability is obtained and analyzed. We present the analytical solution for some limits which is used for calculating density-density response function. We show that the resulting function shows power-law behaviors in terms of ζ with fractional exponents which are reported. The disorder-averaged polarization operator is shown to be a decreasing function of momentum like ordinary 2D parabolic band systems. It is seen that a disorder-driven momentum qch emerges in the system which controls the behaviors of the screened potential. We show that in small densities an instability occurs in which imaginary part of the dielectric function becomes negative and the screened potential changes sign. Corresponding to this instability, some oscillations in charge density along with a screening-anti-screening transition are observed. These effects become dominant in very low densities, strong disorders and strong interactions, the state in which EHPs appear. The total charge probability measure is another quantity which has been investigated in this paper. The resulting equation is analytically solved for large carrier densities, which admits the calculation of arbitrary-point correlation function.