A few-layer covalent network of fullerenes.

The two natural allotropes of carbon, diamond and graphite, are extended networks of sp3-hybridized and sp2-hybridized atoms, respectively1. By mixing different hybridizations and geometries of carbon, one could conceptually construct countless synthetic allotropes. Here we introduce graphullerene, a two-dimensional crystalline polymer of C60 that bridges the gulf between molecular and extended carbon materials. Its constituent fullerene subunits arrange hexagonally in a covalently interconnected molecular sheet. We report charge-neutral, purely carbon-based macroscopic crystals that are large enough to be mechanically exfoliated to produce molecularly thin flakes with clean interfaces-a critical requirement for the creation of heterostructures and optoelectronic devices2. The synthesis entails growing single crystals of layered polymeric (Mg4C60)∞ by chemical vapour transport and subsequently removing the magnesium with dilute acid. We explore the thermal conductivity of this material and find it to be much higher than that of molecular C60, which is a consequence of the in-plane covalent bonding. Furthermore, imaging few-layer graphullerene flakes using transmission electron microscopy and near-field nano-photoluminescence spectroscopy reveals the existence of moiré-like superlattices3. More broadly, the synthesis of extended carbon structures by polymerization of molecular precursors charts a clear path to the systematic design of materials for the construction of two-dimensional heterostructures with tunable optoelectronic properties.

Accelerated Nano-Optical Imaging through Sparse Sampling.

The integration time and signal-to-noise ratio are inextricably linked when performing scanning probe microscopy based on raster scanning. This often yields a large lower bound on the measurement time, for example, in nano-optical imaging experiments performed using a scanning near-field optical microscope (SNOM). Here, we utilize sparse scanning augmented with Gaussian process regression to bypass the time constraint. We apply this approach to image charge-transfer polaritons in graphene residing on ruthenium trichloride (α-RuCl3) and obtain key features such as polariton damping and dispersion. Critically, nano-optical SNOM imaging data obtained via sparse sampling are in good agreement with those extracted from traditional raster scans but require 11 times fewer sampled points. As a result, Gaussian process-aided sparse spiral scans offer a major decrease in scanning time.

Topological band engineering of graphene nanoribbons.

Topological insulators are an emerging class of materials that host highly robust in-gap surface or interface states while maintaining an insulating bulk1,2. Most advances in this field have focused on topological insulators and related topological crystalline insulators3 in two dimensions4-6 and three dimensions7-10, but more recent theoretical work has predicted the existence of one-dimensional symmetry-protected topological phases in graphene nanoribbons (GNRs)11. The topological phase of these laterally confined, semiconducting strips of graphene is determined by their width, edge shape and terminating crystallographic unit cell and is characterized by a [Formula: see text] invariant12 (that is, an index of either 0 or 1, indicating two topological classes-similar to quasi-one-dimensional solitonic systems13-16). Interfaces between topologically distinct GNRs characterized by different values of [Formula: see text] are predicted to support half-filled, in-gap localized electronic states that could, in principle, be used as a tool for material engineering11. Here we present the rational design and experimental realization of a topologically engineered GNR superlattice that hosts a one-dimensional array of such states, thus generating otherwise inaccessible electronic structures. This strategy also enables new end states to be engineered directly into the termini of the one-dimensional GNR superlattice. Atomically precise topological GNR superlattices were synthesized from molecular precursors on a gold surface, Au(111), under ultrahigh-vacuum conditions and characterized by low-temperature scanning tunnelling microscopy and spectroscopy. Our experimental results and first-principles calculations reveal that the frontier band structure (the bands bracketing filled and empty states) of these GNR superlattices is defined purely by the coupling between adjacent topological interface states. This manifestation of non-trivial one-dimensional topological phases presents a route to band engineering in one-dimensional materials based on precise control of their electronic topology, and is a promising platform for studies of one-dimensional quantum spin physics.

Polaritonic Probe of an Emergent 2D Dipole Interface.

The use of work-function-mediated charge transfer has recently emerged as a reliable route toward nanoscale electrostatic control of individual atomic layers. Using α-RuCl3 as a 2D electron acceptor, we are able to induce emergent nano-optical behavior in hexagonal boron nitride (hBN) that arises due to interlayer charge polarization. Using scattering-type scanning near-field optical microscopy (s-SNOM), we find that a thin layer of α-RuCl3 adjacent to an hBN slab reduces the propagation length of hBN phonon polaritons (PhPs) in significant excess of what can be attributed to intrinsic optical losses. Concomitant nano-optical spectroscopy experiments reveal a novel resonance that aligns energetically with the region of excess PhP losses. These experimental observations are elucidated by first-principles density-functional theory and near-field model calculations, which show that the formation of a large interfacial dipole suppresses out-of-plane PhP propagation. Our results demonstrate the potential utility of charge-transfer heterostructures for tailoring optoelectronic properties of 2D insulators.

Nanometer-Scale Lateral p-n Junctions in Graphene/α-RuCl3 Heterostructures.

The ability to create nanometer-scale lateral p-n junctions is essential for the next generation of two-dimensional (2D) devices. Using the charge-transfer heterostructure graphene/α-RuCl3, we realize nanoscale lateral p-n junctions in the vicinity of graphene nanobubbles. Our multipronged experimental approach incorporates scanning tunneling microscopy (STM) and spectroscopy (STS) and scattering-type scanning near-field optical microscopy (s-SNOM) to simultaneously probe the electronic and optical responses of nanobubble p-n junctions. Our STM/STS results reveal that p-n junctions with a band offset of ∼0.6 eV can be achieved with widths of ∼3 nm, giving rise to electric fields of order 108 V/m. Concurrent s-SNOM measurements validate a point-scatterer formalism for modeling the interaction of surface plasmon polaritons (SPPs) with nanobubbles. Ab initio density functional theory (DFT) calculations corroborate our experimental data and reveal the dependence of charge transfer on layer separation. Our study provides experimental and conceptual foundations for generating p-n nanojunctions in 2D materials.

Synergetic Bottom-Up Synthesis of Graphene Nanoribbons by Matrix-Assisted Direct Transfer.

The scope of graphene nanoribbon (GNR) structures accessible through bottom-up approaches is defined by the intrinsic limitations of either all-on-surface or all-solution-based synthesis. Here, we report a hybrid bottom-up synthesis of GNRs based on a Matrix-Assisted Direct (MAD) transfer technique that successfully leverages technical advantages inherent to both solution-based and on-surface synthesis while sidestepping their drawbacks. Critical structural parameters tightly controlled in solution-based polymerization reactions can seamlessly be translated into the structure of the corresponding GNRs. The transformative potential of the synergetic bottom-up approaches facilitated by the MAD transfer techniques is highlighted by the synthesis of chevron-type GNRs (cGNRs) featuring narrow length distributions and a nitrogen core-doped armchair GNR (N4-7-ANGR) that remains inaccessible using either a solution-based or an on-surface bottom-up approach alone.

Revealing the Local Electronic Structure of a Single-Layer Covalent Organic Framework through Electronic Decoupling.

Covalent organic frameworks (COFs) are molecule-based 2D and 3D materials that possess a wide range of mechanical and electronic properties. We have performed a joint experimental and theoretical study of the electronic structure of boroxine-linked COFs grown under ultrahigh vacuum conditions and characterized using scanning tunneling spectroscopy on Au(111) and hBN/Cu(111) substrates. Our results show that a single hBN layer electronically decouples the COF from the metallic substrate, thus suppressing substrate-induced broadening and revealing new features in the COF electronic local density of states (LDOS). The resulting sharpening of LDOS features allows us to experimentally determine the COF band gap, bandwidths, and the electronic hopping amplitude between adjacent COF bridge sites. These experimental parameters are consistent with the results of first-principles theoretical predictions.

Charge-Transfer Plasmon Polaritons at Graphene/α-RuCl3 Interfaces.

Nanoscale charge control is a key enabling technology in plasmonics, electronic band structure engineering, and the topology of two-dimensional materials. By exploiting the large electron affinity of α-RuCl3, we are able to visualize and quantify massive charge transfer at graphene/α-RuCl3 interfaces through generation of charge-transfer plasmon polaritons (CPPs). We performed nanoimaging experiments on graphene/α-RuCl3 at both ambient and cryogenic temperatures and discovered robust plasmonic features in otherwise ungated and undoped structures. The CPP wavelength evaluated through several distinct imaging modalities offers a high-fidelity measure of the Fermi energy of the graphene layer: EF = 0.6 eV (n = 2.7 × 1013 cm-2). Our first-principles calculations link the plasmonic response to the work function difference between graphene and α-RuCl3 giving rise to CPPs. Our results provide a novel general strategy for generating nanometer-scale plasmonic interfaces without resorting to external contacts or chemical doping.

Bottom-up Assembly of Nanoporous Graphene with Emergent Electronic States.

The incorporation of nanoscale pores into a sheet of graphene allows it to switch from an impermeable semimetal to a semiconducting nanosieve. Nanoporous graphenes are desirable for applications ranging from high-performance semiconductor device channels to atomically thin molecular sieve membranes, and their performance is highly dependent on the periodicity and reproducibility of pores at the atomic level. Achieving precise nanopore topologies in graphene using top-down lithographic approaches has proven to be challenging due to poor structural control at the atomic level. Alternatively, atomically precise nanometer-sized pores can be fabricated via lateral fusion of bottom-up synthesized graphene nanoribbons. This technique, however, typically requires an additional high temperature cross-coupling step following the nanoribbon formation that inherently yields poor lateral conjugation, resulting in 2D materials that are weakly connected both mechanically and electronically. Here, we demonstrate a novel bottom-up approach for forming fully conjugated nanoporous graphene through a single, mild annealing step following the initial polymer formation. We find emergent interface-localized electronic states within the bulk band gap of the graphene nanoribbon that hybridize to yield a dispersive two-dimensional low-energy band of states. We show that this low-energy band can be rationalized in terms of edge states of the constituent single-strand nanoribbons. The localization of these 2D states around pores makes this material particularly attractive for applications requiring electronically sensitive molecular sieves.

Length-Dependent Evolution of Type II Heterojunctions in Bottom-Up-Synthesized Graphene Nanoribbons.

The ability to tune the band-edge energies of bottom-up graphene nanoribbons (GNRs) via edge dopants creates new opportunities for designing tailor-made GNR heterojunctions and related nanoscale electronic devices. Here we report the local electronic characterization of type II GNR heterojunctions composed of two different nitrogen edge-doping configurations (carbazole and phenanthridine) that separately exhibit electron-donating and electron-withdrawing behavior. Atomically resolved structural characterization of phenanthridine/carbazole GNR heterojunctions was performed using bond-resolved scanning tunneling microscopy and noncontact atomic force microscopy. Scanning tunneling spectroscopy and first-principles calculations reveal that carbazole and phenanthridine dopant configurations induce opposite upward and downward orbital energy shifts owing to their different electron affinities. The magnitude of the energy offsets observed in carbazole/phenanthridine heterojunctions is dependent on the length of the GNR segments comprising each heterojunction with longer segments leading to larger heterojunction energy offsets. Using a new on-site energy analysis based on Wannier functions, we find that the origin of this behavior is a charge transfer process that reshapes the electrostatic potential profile over a long distance within the GNR heterojunction.

Concentration Dependence of Dopant Electronic Structure in Bottom-up Graphene Nanoribbons.

Bottom-up fabrication techniques enable atomically precise integration of dopant atoms into the structure of graphene nanoribbons (GNRs). Such dopants exhibit perfect alignment within GNRs and behave differently from bulk semiconductor dopants. The effect of dopant concentration on the electronic structure of GNRs, however, remains unclear despite its importance in future electronics applications. Here we use scanning tunneling microscopy and first-principles calculations to investigate the electronic structure of bottom-up synthesized N = 7 armchair GNRs featuring varying concentrations of boron dopants. First-principles calculations of freestanding GNRs predict that the inclusion of boron atoms into a GNR backbone should induce two sharp dopant states whose energy splitting varies with dopant concentration. Scanning tunneling spectroscopy experiments, however, reveal two broad dopant states with an energy splitting greater than expected. This anomalous behavior results from an unusual hybridization between the dopant states and the Au(111) surface, with the dopant-surface interaction strength dictated by the dopant orbital symmetry.

Heterostructures through Divergent Edge Reconstruction in Nitrogen-Doped Segmented Graphene Nanoribbons.

Atomically precise engineering of defined segments within individual graphene nanoribbons (GNRs) represents a key enabling technology for the development of advanced functional device architectures. Here, the bottom-up synthesis of chevron GNRs decorated with reactive functional groups derived from 9-methyl-9H-carbazole is reported. Scanning tunneling and non-contact atomic force microscopy reveal that a thermal activation of GNRs induces the rearrangement of the electron-rich carbazole into an electron-deficient phenanthridine. The selective chemical edge-reconstruction of carbazole-substituted chevron GNRs represents a practical strategy for the controlled fabrication of spatially defined GNR heterostructures from a single molecular precursor.

Site-Specific Substitutional Boron Doping of Semiconducting Armchair Graphene Nanoribbons.

A fundamental requirement for the development of advanced electronic device architectures based on graphene nanoribbon (GNR) technology is the ability to modulate the band structure and charge carrier concentration by substituting specific carbon atoms in the hexagonal graphene lattice with p- or n-type dopant heteroatoms. Here we report the atomically precise introduction of group III dopant atoms into bottom-up fabricated semiconducting armchair GNRs (AGNRs). Trigonal-planar B atoms along the backbone of the GNR share an empty p-orbital with the extended π-band for dopant functionality. Scanning tunneling microscopy (STM) topography reveals a characteristic modulation of the local density of states along the backbone of the GNR that is superimposable with the expected position and concentration of dopant B atoms. First-principles calculations support the experimental findings and provide additional insight into the band structure of B-doped 7-AGNRs.

Visualizing Atomically Layered Magnetism in CrSBr.

2D materials can host long-range magnetic order in the presence of underlying magnetic anisotropy. The ability to realize the full potential of 2D magnets necessitates systematic investigation of the role of individual atomic layers and nanoscale inhomogeneity (i.e., strain) on the emergence of stable magnetic phases. Here, spatially dependent magnetism in few-layer CrSBr is revealed using magnetic force microscopy (MFM) and Monte Carlo-based simulations. Nanoscale visualization of the magnetic sheet susceptibility is extracted from MFM data and force-distance curves, revealing a characteristic onset of both intra- and interlayer magnetic correlations as a function of temperature and layer-thickness. These results demonstrate that the presence of a single uncompensated layer in odd-layer terraces significantly reduces the stability of the low-temperature antiferromagnetic (AFM) phase and gives rise to multiple coexisting magnetic ground states at temperatures close to the bulk Néel temperature (TN ). Furthermore, the AFM phase can be reliably suppressed using modest fields (≈16 mT) from the MFM probe, behaving as a nanoscale magnetic switch. This prototypical study of few-layer CrSBr demonstrates the critical role of layer parity on field-tunable 2D magnetism and validates MFM for use in nanomagnetometry of 2D materials (despite the ubiquitous absence of bulk zero-field magnetism in magnetized sheets).

Surface plasmons induce topological transition in graphene/α-MoO3 heterostructures.

Polaritons in hyperbolic van der Waals materials-where principal axes have permittivities of opposite signs-are light-matter modes with unique properties and promising applications. Isofrequency contours of hyperbolic polaritons may undergo topological transitions from open hyperbolas to closed ellipse-like curves, prompting an abrupt change in physical properties. Electronically-tunable topological transitions are especially desirable for future integrated technologies but have yet to be demonstrated. In this work, we present a doping-induced topological transition effected by plasmon-phonon hybridization in graphene/α-MoO3 heterostructures. Scanning near-field optical microscopy was used to image hybrid polaritons in graphene/α-MoO3. We demonstrate the topological transition and characterize hybrid modes, which can be tuned from surface waves to bulk waveguide modes, traversing an exceptional point arising from the anisotropic plasmon-phonon coupling. Graphene/α-MoO3 heterostructures offer the possibility to explore dynamical topological transitions and directional coupling that could inspire new nanophotonic and quantum devices.

Pseudo-atomic orbital behavior in graphene nanoribbons with four-membered rings.

The incorporation of nonhexagonal rings into graphene nanoribbons (GNRs) is an effective strategy for engineering localized electronic states, bandgaps, and magnetic properties. Here, we demonstrate the successful synthesis of nanoribbons having four-membered ring (cyclobutadienoid) linkages by using an on-surface synthesis approach involving direct contact transfer of coronene-type precursors followed by thermally assisted [2 + 2] cycloaddition. The resulting coronene-cyclobutadienoid nanoribbons feature a narrow 600-meV bandgap and novel electronic frontier states that can be interpreted as linear chains of effective px and py pseudo-atomic orbitals. We show that these states give rise to exceptional physical properties, such as a rigid indirect energy gap. This provides a previously unexplored strategy for constructing narrow gap GNRs via modification of precursor molecules whose function is to modulate the coupling between adjacent four-membered ring states.

Deep Learning Analysis of Polaritonic Wave Images.

Deep learning (DL) is an emerging analysis tool across the sciences and engineering. Encouraged by the successes of DL in revealing quantitative trends in massive imaging data, we applied this approach to nanoscale deeply subdiffractional images of propagating polaritonic waves in complex materials. Utilizing the convolutional neural network (CNN), we developed a practical protocol for the rapid regression of images that quantifies the wavelength and the quality factor of polaritonic waves. Using simulated near-field images as training data, the CNN can be made to simultaneously extract polaritonic characteristics and material parameters in a time scale that is at least 3 orders of magnitude faster than common fitting/processing procedures. The CNN-based analysis was validated by examining the experimental near-field images of charge-transfer plasmon polaritons at graphene/α-RuCl3 interfaces. Our work provides a general framework for extracting quantitative information from images generated with a variety of scanning probe methods.

Rationally Designed Topological Quantum Dots in Bottom-Up Graphene Nanoribbons.

Bottom-up graphene nanoribbons (GNRs) have recently been shown to host nontrivial topological phases. Here, we report the fabrication and characterization of deterministic GNR quantum dots whose orbital character is defined by zero-mode states arising from nontrivial topological interfaces. Topological control was achieved through the synthesis and on-surface assembly of three distinct molecular precursors designed to exhibit structurally derived topological electronic states. Using a combination of low-temperature scanning tunneling microscopy and spectroscopy, we have characterized two GNR topological quantum dot arrangements synthesized under ultrahigh vacuum conditions. Our results are supported by density-functional theory and tight-binding calculations, revealing that the magnitude and sign of orbital hopping between topological zero-mode states can be tuned based on the bonding geometry of the interconnecting region. These results demonstrate the utility of topological zero modes as components for designer quantum dots and advanced electronic devices.

Inducing metallicity in graphene nanoribbons via zero-mode superlattices.

The design and fabrication of robust metallic states in graphene nanoribbons (GNRs) are challenging because lateral quantum confinement and many-electron interactions induce electronic band gaps when graphene is patterned at nanometer length scales. Recent developments in bottom-up synthesis have enabled the design and characterization of atomically precise GNRs, but strategies for realizing GNR metallicity have been elusive. Here we demonstrate a general technique for inducing metallicity in GNRs by inserting a symmetric superlattice of zero-energy modes into otherwise semiconducting GNRs. We verify the resulting metallicity using scanning tunneling spectroscopy as well as first-principles density-functional theory and tight-binding calculations. Our results reveal that the metallic bandwidth in GNRs can be tuned over a wide range by controlling the overlap of zero-mode wave functions through intentional sublattice symmetry breaking.

Role of geometrical cues in neuronal growth.

Geometrical cues play an essential role in neuronal growth. Here, we quantify axonal growth on surfaces with controlled geometries and report a general stochastic approach that quantitatively describes the motion of growth cones. We show that axons display a strong directional alignment on micropatterned surfaces when the periodicity of the patterns matches the dimension of the growth cone. The growth cone dynamics on surfaces with uniform geometry is described by a linear Langevin equation with both deterministic and stochastic contributions. In contrast, axonal growth on surfaces with periodic patterns is characterized by a system of two generalized Langevin equations with both linear and quadratic velocity dependence and stochastic noise. We combine experimental data with theoretical analysis to measure the key parameters of the growth cone motion: angular distributions, correlation functions, diffusion coefficients, characteristics speeds, and damping coefficients. We demonstrate that axonal dynamics displays a crossover from an Ornstein-Uhlenbeck process to a nonlinear stochastic regime when the geometrical periodicity of the pattern approaches the linear dimension of the growth cone. Growth alignment is determined by surface geometry, which is fully quantified by the deterministic part of the Langevin equation. These results provide insight into the role of curvature sensing proteins and their interactions with geometrical cues.