Coupled Spin States in Armchair Graphene Nanoribbons with Asymmetric Zigzag Edge Extensions

Coupling of Nondegenerate Topological Modes in Nitrogen Core-Doped Graphene Nanoribbons

Nitrogen core-doping of graphene nanoribbons (GNRs) allows trigonal planar carbon atoms along the backbone of GNRs to be substituted by higher-valency nitrogen atoms. The excess valence electrons are injected into the π-orbital system of the GNR, thereby changing not only its electronic occupation but also its topological properties. We have observed this topological change by synthesizing dilute nitrogen core-doped armchair GNRs with a width of five atoms (N2-5-AGNRs). The incorporation of pairs of trigonal planar nitrogen atoms results in the emergence of topological boundary states at the interface between doped and undoped segments of the GNR. These topological boundary states are offset in energy by approximately ΔE = 300 meV relative to the topological end states at the termini of finite 5-AGNRs. Scanning tunneling microscopy (STM) and spectroscopy (STS) reveal that for finite GNRs the two types of topological states can interact through a linear combination of orbitals, resulting in a pair of asymmetric hybridized states. This behavior is captured by an effective Hamiltonian of nondegenerate diatomic molecules, where the analogous interatomic hybridization interaction strength is tuned by the distance between GNR topological modes.

On-surface synthesis of Heisenberg spin-1/2 antiferromagnetic molecular chains

Magnetic exchange interactions between localized spins in π-electron magnetism of carbon-based nanostructures have attracted tremendous interest due to their great potential for nano spintronics. Unique many-body quantum characteristics, such as gaped excitations, strong spin entanglement, and fractionalized excitations, have been demonstrated, but the spin-1/2 Heisenberg model with a single antiferromagnetic coupling J value remained unexplored. Here, we realized the entangled antiferromagnetic quantum spin-1/2 Heisenberg model with diazahexabenzocoronene oligomers (up to 7 units) on Au(111). Extensive low-temperature scanning tunneling microscopy/spectroscopy measurements and density functional theory and many-body calculations show that even-numbered spin chains host a collective state with gapped excitations, while odd-numbered chains feature a Kondo excitation. We found that a given antiferromagnetic coupling J value between first neighbors in the entangled quantum states is responsible for the quantum phenomena, strongly relating to their parities of the chain. The tunable molecular building blocks act as an ideal platform for the experimental realization of topological spin lattices.

Janus graphene nanoribbons with localized states on a single zigzag edge

Topological design of π electrons in zigzag-edged graphene nanoribbons (ZGNRs) leads to a wealth of magnetic quantum phenomena and exotic quantum phases1-10. Symmetric ZGNRs typically show antiferromagnetically coupled spin-ordered edge states1,2. Eliminating cross-edge magnetic coupling in ZGNRs not only enables the realization of a class of ferromagnetic quantum spin chains11, enabling the exploration of quantum spin physics and entanglement of multiple qubits in the one-dimensional limit3,12, but also establishes a long-sought-after carbon-based ferromagnetic transport channel, pivotal for ultimate scaling of GNR-based quantum electronics1-3,9,13. Here we report a general approach for designing and fabricating such ferromagnetic GNRs in the form of Janus GNRs (JGNRs) with two distinct edge configurations. Guided by Lieb's theorem and topological classification theory14-16, we devised two JGNRs by asymmetrically introducing a topological defect array of benzene motifs to one zigzag edge, while keeping the opposing zigzag edge unchanged. This breaks the structural symmetry and creates a sublattice imbalance within each unit cell, initiating a spin-symmetry breaking. Three Z-shaped precursors are designed to fabricate one parent ZGNR and two JGNRs with an optimal lattice spacing of the defect array for a complete quench of the magnetic edge states at the 'defective' edge. Characterization by scanning probe microscopy and spectroscopy and first-principles density functional theory confirms the successful fabrication of JGNRs with a ferromagnetic ground-state localized along the pristine zigzag edge.

Atomically Precise Control of Topological State Hybridization in Conjugated Polymers

Realization of topological quantum states in carbon nanostructures has recently emerged as a promising platform for hosting highly coherent and controllable quantum dot spin qubits. However, their adjustable manipulation remains elusive. Here, we report the atomically accurate control of the hybridization level of topologically protected quantum edge states emerging from topological interfaces in bottom-up-fabricated π-conjugated polymers. Our investigation employed a combination of low-temperature scanning tunneling microscopy and spectroscopy, along with high-resolution atomic force microscopy, to effectively modify the hybridization level of neighboring edge states by the selective dehydrogenation reaction of molecular units in a pentacene-based polymer and demonstrate their reversible character. Density functional theory, tight binding, and complete active space calculations for the Hubbard model were employed to support our findings, revealing that the extent of orbital overlap between the topological edge states can be finely tuned based on the geometry and electronic bandgap of the interconnecting region. These results demonstrate the utility of topological edge states as components for designing complex quantum arrangements for advanced electronic devices.

Deposition temperature-mediated growth of helically shaped polymers and chevron-type graphene nanoribbons from a fluorinated precursor

Graphene nanoribbons (GNRs) of precise size and shape, critical for controlling electronic properties and future device applications, can be realized via precision synthesis on surfaces using rationally designed molecular precursors. Fluorine-bearing precursors have the potential to form GNRs on nonmetallic substrates suitable for device fabrication. Here, we investigate the deposition temperature-mediated growth of a new fluorine-bearing precursor, 6,11-diiodo-1,4-bis(2-fluorophenyl)-2,3-diphenyltriphenylene (C42H24F2I2), into helically shaped polymer intermediates and chevron-type GNRs on Au(111) by combining scanning tunneling microscopy, X-ray photoelectron spectroscopy, and density functional theory simulations. The fluorinated precursors do not adsorb on the Au(111) surface at lower temperatures, necessitating an optimum substrate temperature to achieve maximum polymer and GNR lengths. We compare the adsorption behavior with that of pristine chevron precursors and discuss the effects of C-H and C-F bonds. The results elucidate the growth mechanism of GNRs with fluorine-bearing precursors and establish a foundation for future synthesis of GNRs on nonmetallic substrates.

Tunable Magnetic Coupling in Graphene Nanoribbon Quantum Dots

Carbon-based quantum dots (QDs) enable flexible manipulation of electronic behavior at the nanoscale, but controlling their magnetic properties requires atomically precise structural control. While magnetism is observed in organic molecules and graphene nanoribbons (GNRs), GNR precursors enabling bottom-up fabrication of QDs with various spin ground states have not yet been reported. Here the development of a new GNR precursor that results in magnetic QD structures embedded in semiconducting GNRs is reported. Inserting one such molecule into the GNR backbone and graphitizing it results in a QD region hosting one unpaired electron. QDs composed of two precursor molecules exhibit nonmagnetic, antiferromagnetic, or antiferromagnetic ground states, depending on the structural details that determine the coupling behavior of the spins originating from each molecule. The synthesis of these QDs and the emergence of localized states are demonstrated through high-resolution atomic force microscopy (HR-AFM), scanning tunneling microscopy (STM) imaging, and spectroscopy, and the relationship between QD atomic structure and magnetic properties is uncovered. GNR QDs provide a useful platform for controlling the spin-degree of freedom in carbon-based nanostructures.

Delocalized spin states at zigzag termini of armchair graphene nanoribbon

Using scanning tunneling microscopy and spectroscopy we demonstrate a revival of magnetism in 7-armchair nanoribbon by unpassivated atoms at the termini. Namely, a pair of intense Kondo resonances emerges at the peripheries of zigzag terminus revealing the many-body screening effects of local magnetic moments. Although Kondo resonance originates from a missing local orbital, it extends to a distance of 2.5 nm along the edge of the ribbon. The results are complemented by density functional theory calculations which suggest a possible coupling between Kondo states despite screening effects of substrate electrons. These findings indicate a possibility to restore intrinsic magnetic ordering in graphene nanoribbon without major structural modifications.

Topological Structure Realized in Cove-Edged Graphene Nanoribbons via Incorporation of Periodic Pentagon Rings

Cove-edged zigzag graphene nanoribbons are predicted to show metallic, topological, or trivial semiconducting band structures, which are precisely determined by their cove offset positions at both edges as well as the ribbon width. However, due to the challenge of introducing coves into zigzag-edged graphene nanoribbons, only a few cove-edged graphene nanoribbons with trivial semiconducting bandgaps have been realized experimentally. Here, we report that the topological band structure can be realized in cove-edged graphene nanoribbons by embedding periodic pentagon rings on the cove edges through on-surface synthesis. Upon noncontact atomic force microscopy and scanning tunneling spectroscopy measurements, the chemical and electronic structures of cove-edged graphene nanoribbons with periodic pentagon rings have been characterized for different lengths. Combined with theoretical calculations, we find that upon inducing periodic pentagon rings the cove-edged graphene nanoribbons exhibit nontrivial topological structures. Our results provide insights for the design and understanding of the topological character in cove-edged graphene nanoribbons.

Five-Membered Rings Create Off-Zero Modes in Nanographene

The low-energy electronic structure of nanographenes can be tuned through zero-energy π-electron states, typically referred to as zero-modes. Customizable electronic and magnetic structures have been engineered by coupling zero-modes through exchange and hybridization interactions. Manipulation of the energy of such states, however, has not yet received significant attention. We find that attaching a five-membered ring to a zigzag edge hosting a zero-mode perturbs the energy of that mode and turns it into an off-zero mode: a localized state with a distinctive electron-accepting character. Whereas the end states of typical 7-atom-wide armchair graphene nanoribbons (7-AGNRs) lose their electrons when physisorbed on Au(111) (due to its high work function), converting them into off-zero modes by introducing cyclopentadienyl five-membered rings allows them to retain their single-electron occupation. This approach enables the magnetic properties of 7-AGNR end states to be explored using scanning tunneling microscopy (STM) on a gold substrate. We find a gradual decrease of the magnetic coupling between off-zero mode end states as a function of GNR length, and evolution from a more closed-shell to a more open-shell ground state.

Orbital-symmetry effects on magnetic exchange in open-shell nanographenes

Open-shell nanographenes appear as promising candidates for future applications in spintronics and quantum technologies. A critical aspect to realize this potential is to design and control the magnetic exchange. Here, we reveal the effects of frontier orbital symmetries on the magnetic coupling in diradical nanographenes through scanning probe microscope measurements and different levels of theoretical calculations. In these open-shell nanographenes, the exchange energy exhibits a remarkable variation between 20 and 160 meV. Theoretical calculations reveal that frontier orbital symmetries play a key role in affecting the magnetic coupling on such a large scale. Moreover, a triradical nanographene is demonstrated for investigating the magnetic interaction among three unpaired electrons with unequal magnetic exchange, in agreement with Heisenberg spin model calculations. Our results provide insights into both theoretical design and experimental realization of nanographene materials with different exchange interactions through tuning the orbital symmetry, potentially useful for realizing magnetically operable graphene-based nanomaterials.

Engineering Robust Metallic Zero-Mode States in Olympicene Graphene Nanoribbons

Metallic graphene nanoribbons (GNRs) represent a critical component in the toolbox of low-dimensional functional materials technology serving as 1D interconnects capable of both electronic and quantum information transport. The structural constraints imposed by on-surface bottom-up GNR synthesis protocols along with the limited control over orientation and sequence of asymmetric monomer building blocks during the radical step-growth polymerization have plagued the design and assembly of metallic GNRs. Here, we report the regioregular synthesis of GNRs hosting robust metallic states by embedding a symmetric zero-mode (ZM) superlattice along the backbone of a GNR. Tight-binding electronic structure models predict a strong nearest-neighbor electron hopping interaction between adjacent ZM states, resulting in a dispersive metallic band. First-principles density functional theory-local density approximation calculations confirm this prediction, and the robust, metallic ZM band of olympicene GNRs is experimentally corroborated by scanning tunneling spectroscopy.

On-Surface Cross-Coupling Reactions

On-surface synthesis, as a bottom-up synthetic method, has been proven to be a powerful tool for atomically precise fabrication of low-dimensional carbon nanomaterials over the past 15 years. This method relies on covalent coupling reactions that occur on solid substrates such as metal or metal oxide surfaces under ultra-high-vacuum conditions, and the achievements with this method have greatly enriched fundamental science and technology. However, due to the complicated reactivity of organic groups, distinct diffusion of reactants and intermediates, and irreversibility of covalent bonds, achieving the high selectivity of covalent coupling reactions on surfaces remains a great challenge. As a result, only a few on-surface covalent coupling reactions, mainly involving dehalogenation and dehydrogenation homocoupling, are frequently used in the synthesis of low-dimensional carbon nanosystems. In this Perspective, we focus on the development and synthetic applications of on-surface cross-coupling reactions, mainly Ullmann, Sonogashira, Heck, and divergent cross-coupling reactions.

Emergent Spin Frustration in Neutral Mixed-Valence 2D Conjugated Polymers: A Potential Quantum Materials Platform

Two-dimensional conjugated polymers (2DCPs)─organic 2D materials composed of arrays of carbon sp² centers connected by π-conjugated linkers─are attracting increasing attention due to their potential applications in device technologies. This interest stems from the ability of 2DCPs to host a range of correlated electronic and magnetic states (e.g., Mott insulators). Substitution of all carbon sp² centers in 2DCPs by nitrogen or boron results in diamagnetic insulating states. Partial substitution of C sp² centers by B or N atoms has not yet been considered for extended 2DCPs but has been extensively studied in the analogous neutral mixed-valence molecular systems. Here, we employ accurate first-principles calculations to predict the electronic and magnetic properties of a new class of hexagonally connected neutral mixed-valence 2DCPs in which every other C sp² nodal center is substituted by either a N or B atom. We show that these neutral mixed-valence 2DCPs significantly energetically favor a state with emergent superexchange-mediated antiferromagnetic (AFM) interactions between C-based spin-¹/₂ centers on a triangular sublattice. These AFM interactions are surprisingly strong and comparable to those in the parent compounds of cuprate superconductors. The rigid and covalently linked symmetric triangular AFM lattice in these materials thus provides a highly promising and robust basis for 2D spin frustration. As such, extended mixed-valence 2DCPs are a highly attractive platform for the future bottom-up realization of a new class of all-organic quantum materials, which could host exotic correlated electronic states (e.g., unusual magnetic ordering, quantum spin liquids).

Unveiling and Manipulating Hidden Symmetries in Graphene Nanoribbons

Armchair graphene nanoribbons are a highly promising class of semiconductors for all-carbon nanocircuitry. Here, we present a new perspective on their electronic structure from simple model Hamiltonians and ab initio calculations. We focus on a specific set of nanoribbons of width n=3p+2, where n is the number of carbon atoms across the nanoribbon axis and p is a positive integer. We demonstrate that the energy-gap opening in these nanoribbons originates from the breaking of a previously unidentified hidden symmetry by long-ranged hopping of π electrons and structural distortions occurring at the edges. This hidden symmetry can be restored or manipulated through the application of in-plane lattice strain, which enables continuous energy-gap tuning, the emergence of Dirac points at the Fermi level, and topological quantum phase transitions. Our work establishes an original interpretation of the semiconducting character of armchair graphene nanoribbons and offers guidelines for rationally designing their electronic structure.

Dibenzotropylium-Capped Orthogonal Geometry Enabling Isolation and Examination of a Series of Hydrocarbons with Multiple 14π-Aromatic Units

A series of six dications composed of pure hydrocarbons with one to six non-substituted 9,10-anthrylene units end-capped with two dibenzotropyliums were designed and synthesized to elucidate the electronic properties of huge oligo(9,10-anthrylene) backbones. Their structures were successfully determined by X-ray analyses even in the case of eight planar 14π-electron units, revealing that all dications adopt almost orthogonally twisted structures between neighboring units. Spectroscopic and voltammetric analyses show that neither the significant overlap of orbitals nor the delocalization of electrons between 14π-electron units occurs due to the orthogonally twisted geometry even in solution. As a result, sequential oxidation processes were observed with the reversible formation of multivalent cations with the release of the same number of electrons as the number of anthrylene units. Upon two-electron reduction, a closed-shell butterfly-shaped form was obtained from the dication containing one anthrylene unit, whereas open-shell twisted biradicals were isolated as stable entities in the cases of derivatives containing three to six anthrylene units. Notably, from the derivative with two anthrylene units, a metastable open-shell isomer was obtained quantitatively and underwent slow thermal conversion to the most stable closed-shell isomer (E_a = 23.1 kcal mol^-1). There is a drastic change in oxidation potentials between two neutral species (ΔE = 1.32 V in CH₂Cl₂). Since the present dications were regenerated upon oxidation of the isolated reduction products, these systems may contribute to the development of advanced response systems capable of switching color, magnetic properties, and oxidative properties by using a "cation-capped orthogonal geometry".

Gaussian Curvature Effects on Graphene Quantum Dots

In the last few years, much attention has been paid to the exotic properties that graphene nanostructures exhibit, especially those emerging upon deforming the material. Here we present a study of the mechanical and electronic properties of bent hexagonal graphene quantum dots employing density functional theory. We explore three different kinds of surfaces with Gaussian curvature exhibiting different shapes-spherical, cylindrical, and one-sheet hyperboloid-used to bend the material, and several boundary conditions regarding what atoms are forced to lay on the chosen surface. In each case, we study the curvature energy and two quantum regeneration times (classic and revival) for different values of the curvature radius. A strong correlation between Gaussian curvature and these regeneration times is found, and a special divergence is observed for the revival time for the hyperboloid case, probably related to the pseudo-magnetic field generated by this curvature being capable of causing a phase transition.

Carbon-based nanostructures as a versatile platform for tunableπ-magnetism

Emergence ofπ-magnetism in open-shell nanographenes has been theoretically predicted decades ago but their experimental characterization was elusive due to the strong chemical reactivity that makes their synthesis and stabilization difficult. In recent years, on-surface synthesis under vacuum conditions has provided unprecedented opportunities for atomically precise engineering of nanographenes, which in combination with scanning probe techniques have led to a substantial progress in our capabilities to realize localized electron spin states and to control electron spin interactions at the atomic scale. Here we review the essential concepts and the remarkable advances in the last few years, and outline the versatility of carbon-basedπ-magnetic materials as an interesting platform for applications in spintronics and quantum technologies.

Manipulation of Spin Polarization in Boron-Substituted Graphene Nanoribbons

The design of magnetic topological states due to spin polarization in an extended π carbon system has great potential in spintronics application. Although magnetic zigzag edges in graphene nanoribbons (GNRs) have been investigated earlier, real-space observation and manipulation of spin polarization in a heteroatom substituted system remains challenging. Here, we investigate a zero-bias peak at a boron site embedded at the center of an armchair-type GNR on a AuSi_X/Au(111) surface with a combination of low-temperature scanning tunneling microscopy/spectroscopy and density functional theory calculations. After the tip-induced removal of a Si atom connected to two adjacent boron atoms, a clear Kondo resonance peak appeared and was further split by an applied magnetic field of 12 T. This magnetic state can be relayed along the longitudinal axis of the GNR by sequential removal of Si atoms.

Quantum Revivals in Curved Graphene Nanoflakes

Graphene nanostructures have attracted a lot of attention in recent years due to their unconventional properties. We have employed Density Functional Theory to study the mechanical and electronic properties of curved graphene nanoflakes. We explore hexagonal flakes relaxed with different boundary conditions: (i) all atoms on a perfect spherical sector, (ii) only border atoms forced to be on the spherical sector, and (iii) only vertex atoms forced to be on the spherical sector. For each case, we have analysed the behaviour of curvature energy and of quantum regeneration times (classical and revival) as the spherical sector radius changes. Revival time presents in one case a divergence usually associated with a phase transition, probably caused by the pseudomagnetic field created by the curvature. This could be the first case of a phase transition in graphene nanostructures without the presence of external electric or magnetic fields.

Transport properties of MoS2/V7(Bz)8 and graphene/V7(Bz)8 vdW junctions tuned by bias and gate voltages

The MoS2/V7(Bz)8 and graphene/V7(Bz)8 vdW junctions are designed and the transport properties of their four-terminal devices are comparatively investigated based on density functional theory (DFT) and the nonequilibrium Green's function (NEGF) technique. The MoS2 and graphene nanoribbons act as the source-to-drain channel and the spin-polarized one-dimensional (1D) benzene-V multidecker complex nanowire (V7(Bz)8) serves as the gate channel. Gate voltages applied on V7(Bz)8 exert different influences of electron transport on MoS2/V7(Bz)8 and graphene/V7(Bz)8. In MoS2/V7(Bz)8, the interplay of source and gate bias potentials could induce promising properties such as negative differential resistance (NDR) behavior, output/input current switching, and spin-polarized currents. In contrast, the gate bias plays an insignificant effect on the transport along graphene in graphene/V7(Bz)8. This dissimilarity is attributed to the fact that the conductivity follows the sequence of MoS2 < V7(Bz)8 < graphene. These transport characteristics are examined by analyzing the conductivity, the currents, the local density of states (LDOS), and the transmission spectra. These results are valuable in designing multi-terminal nanoelectronic devices.

Unveiling the Multiradical Character of the Biphenylene Network and Its Anisotropic Charge Transport

Recent progress in the on-surface synthesis and characterization of nanomaterials is facilitating the realization of new carbon allotropes, such as nanoporous graphenes, graphynes, and 2D π-conjugated polymers. One of the latest examples is the biphenylene network (BPN), which was recently fabricated on gold and characterized with atomic precision. This gapless 2D organic material presents uncommon metallic conduction, which could help develop innovative carbon-based electronics. Here, using first principles calculations and quantum transport simulations, we provide new insights into some fundamental properties of BPN, which are key for its further technological exploitation. We predict that BPN hosts an unprecedented spin-polarized multiradical ground state, which has important implications for the chemical reactivity of the 2D material under practical use conditions. The associated electronic band gap is highly sensitive to perturbations, as seen in finite temperature (300 K) molecular dynamics simulations, but the multiradical character remains stable. Furthermore, BPN is found to host in-plane anisotropic (spin-polarized) electrical transport, rooted in its intrinsic structural features, which suggests potential device functionality of interest for both nanoelectronics and spintronics.

Magnetic nanoribbons with embedded cobalt grown inside single-walled carbon nanotubes

Molecular magnetism and specifically magnetic molecules have recently gained plenty of attention as key elements for quantum technologies, information processing, and spintronics. Transition to the nanoscale and implementation of ordered structures with defined parameters is crucial for advanced applications. Single-walled carbon nanotubes (SWCNTs) provide natural one-dimensional confinement that can be implemented for encapsulation, nanosynthesis, and polymerization of molecules into nanoribbons. Recently, the formation of atomically precise graphene nanoribbons inside SWCNTs has been reported. However, there have been only a limited amount of approaches to form ordered magnetic structures inside the nanotube channels and the creation of magnetic nanoribbons is still lacking. In this work we synthesize and reveal the properties of cobalt-phthalocyanine based nanoribbons (CoPcNRs) encapsulated in SWCNTs. Raman spectroscopy, transmission electron microscopy, absorption spectroscopy, and density functional theory calculations allowed us to confirm the encapsulation and to reveal the specific fingerprints of CoPcNRs. The magnetic properties were studied by transverse magnetooptical Kerr effect measurements, which indicated a strong difference in comparison with the pristine unfilled SWCNTs due to the impact of Co incorporated atoms. We anticipate that this approach of polymerization of encapsulated magnetic molecules inside SWCNTs will result in a diverse class of protected low-dimensional ordered magnetic materials for various applications.

Magnetic Interactions Between Radical Pairs in Chiral Graphene Nanoribbons

Open-shell graphene nanoribbons have become promising candidates for future applications, including quantum technologies. Here, we characterize magnetic states hosted by chiral graphene nanoribbons (chGNRs). The substitution of a hydrogen atom at the chGNR edge by a ketone effectively adds one p_z electron to the π-electron network, producing an unpaired π-radical. A similar scenario occurs for regular ketone-functionalized chGNRs in which one ketone is missing. Two such radical states can interact via exchange coupling, and we study those interactions as a function of their relative position, which includes a remarkable dependence on the chirality, as well as on the nature of the surrounding ribbon, that is, with or without ketone functionalization. Besides, we determine the parameters whereby this type of system with oxygen heteroatoms can be adequately described within the widely used mean-field Hubbard model. Altogether, we provide insight to both theoretically model and devise GNR-based nanostructures with tunable magnetic properties.

Steering on-surface reactions through molecular steric hindrance and molecule-substrate van der Waals interactions

On-surface synthesis is a rapidly developing field involving chemical reactions on well-defined solid surfaces to access synthesis of low-dimensional organic nanostructures which cannot be achieved via traditional solution chemistry. On-surface reactions critically depend on a high degree of chemoselectivity in order to achieve an optimum balance between target structure and possible side products. Here, we demonstrate synthesis of graphene nanoribbons with a large unit cell based on steric hindrance-induced complete chemoselectivity as revealed by scanning probe microscopy measurements and density functional theory calculations. Our results disclose that combined molecule-substrate van der Waals interactions and intermolecular steric hindrance promote a selective aryl-aryl coupling, giving rise to high-quality uniform graphene nanostructures. The established coupling strategy has been used to synthesize two types of graphene nanoribbons with different edge topologies inducing a pronounced variation of the electronic energy gaps. The demonstrated chemoselectivity is representative for n-anthryl precursor molecules and may be further exploited to synthesize graphene nanoribbons with novel electronic, topological and magnetic properties with implications for electronic and spintronic applications.

Supplementary Information

The online version contains supplementary material available at 10.1007/s44214-022-00023-9.

Electrical control of the spin-Seebeck coefficient in graphene nanoribbons with asymmetric zigzag edge extensions

We investigate the effect of the electric field on the spin-dependent thermoelectric properties of graphene nanoribbons with asymmetric zigzag edge extensions.

Influence of the Radicaloid Character of Polyaromatic Hydrocarbon Couplers on Magnetic Exchange Interactions

The molecular properties of the conjugated spacers, such as the π-conjugation, aromaticity, length of the couplers, etc., that couple two localized spin-centers influence the intramolecular magnetic exchange interactions (2J) mediated...

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.

Role Played by Edge-Defects in the Optical Properties of Armchair Graphene Nanoribbons

We explore the implementation of specific optical properties of armchair graphene nanoribbons (AGNRs) through edge-defect manipulation. This technique employs the tight-binding model in conjunction with the calculated absorption spectral function. Modification of the edge states gives rise to the diverse electronic structures with striking changes in the band gap and special flat bands at low energy. The optical-absorption spectra exhibit unique excitation peaks, and they strongly depend on the type and period of the edge extension. Remarkably, there exist the unusual transition channels associated with the flat bands for selected edge-modified systems. We discovered the special rule governing how the edge-defect influences the electronic and optical properties in AGNRs. Our theoretical prediction demonstrates an efficient way to manipulate the optical properties of AGNRs. This might be of importance in the search for suitable materials designed to have possible technology applications in nano-optical, plasmonic and optoelectronic devices.

Electrically Induced Dirac Fermions in Graphene Nanoribbons

Graphene nanoribbons are widely regarded as promising building blocks for next-generation carbon-based devices. A critical issue to their prospective applications is whether their electronic structure can be externally controlled. Here, we combine simple model Hamiltonians with extensive first-principles calculations to investigate the response of armchair graphene nanoribbons to transverse electric fields. Such fields can be achieved either upon laterally gating the nanoribbon or incorporating ambipolar chemical codopants along the edges. We reveal that the field induces a semiconductor-to-semimetal transition with the semimetallic phase featuring zero-energy Dirac fermions that propagate along the armchair edges. The transition occurs at critical fields that scale inversely with the width of the nanoribbons. These findings are universal to group-IV honeycomb lattices, including silicene and germanene nanoribbons, irrespective of the type of edge termination. Overall, our results create new opportunities to electrically engineer Dirac semimetallic phases in otherwise semiconducting graphene-like nanoribbons.

Novel electrical properties and applications in kaleidoscopic graphene nanoribbons

As one of the representatives of nano-graphene materials, graphene nanoribbons (GNRs) have more novel electrical properties, highly adjustable electronic properties, and optoelectronic properties than graphene due to their diverse geometric structures and atomic precision configurations. The electrical properties and band gaps of GNRs depend on their width, length, boundary configuration and other elemental doping, etc. With the improvement of the preparation technology and level of GNRs with atomic precision, increasing number of GNRs with different configurations are being prepared. They all show novel electrical properties and high tunability, which provides a broad prospect for the application of GNRs in the field of microelectronics. Here, we summarize the latest GNR-based achievements in recent years and summarize the latest electrical properties and potential applications of GNRs.

Topological phase transition in chiral graphene nanoribbons: from edge bands to end states

Precise control over the size and shape of graphene nanostructures allows engineering spin-polarized edge and topological states, representing a novel source of non-conventional π-magnetism with promising applications in quantum spintronics. A prerequisite for their emergence is the existence of robust gapped phases, which are difficult to find in extended graphene systems. Here we show that semi-metallic chiral GNRs (chGNRs) narrowed down to nanometer widths undergo a topological phase transition. We fabricated atomically precise chGNRs of different chirality and size by on surface synthesis using predesigned molecular precursors. Combining scanning tunneling microscopy (STM) measurements and theory simulations, we follow the evolution of topological properties and bulk band gap depending on the width, length, and chirality of chGNRs. Our findings represent a new platform for producing topologically protected spin states and demonstrate the potential of connecting chiral edge and defect structure with band engineering.

Engineering plasmon modes and their loss in armchair graphene nanoribbons by selected edge-extended defects

The effect of edge modification of armchair graphene nanoribbons (AGNRs) on the collective excitations are theoretically investigated. The tight-binding method is employed in conjunction with the dielectric function. Unconventional plasmon modes and their association with the flat bands of the specially designed AGNRs are thoroughly studied. We demonstrate the robust relationship between the novel collective excitations and both the type and period of the edge modification. Additionally, we reveal that the main features displayed in the (momentum, frequency)-phase diagrams for both single-particle and collective excitations of AGNRs can be efficiently tuned by edge-extended defects. Our obtained plasmon modes are found to be analogous to magnetoplasmons associated with collective excitations of Landau-quantized electrons. This work provides a unique way to engineer discrete magnetoplasmon-like modes of AGNRs in the absence of magnetic field.

Evolution of the Topological Energy Band in Graphene Nanoribbons

Topological theory has been recently applied in graphene nanoribbons (GNRs) and predicts the existence of topological quantum states in junctions connecting GNRs of different topological classes. Through the periodic alignment of the topological states along a GNR backbone, frontier GNR electronic bands with tunable band gaps and band widths could be generated. In this work, we demonstrate the evolution of the topological band by fabricating GNR structures hosting a single topological junction, dimerized junctions, and multiple coupled junctions with on-surface synthesis, which guarantees the atomic precision of these nanostructures. Their structural and electronic properties are investigated by scanning tunneling microscopy and spectroscopy supported by tight-binding theory. The 1D superlattice of the topological junction states can be described by an effective two-band tight-binding Su-Schrieffer-Heeger (SSH) type model considering two alternating coupling motifs.

Bottom-up Fabrication and Atomic-Scale Characterization of Triply Linked, Laterally π-Extended Porphyrin Nanotapes*

Porphyrin nanotapes (Por NTs) are promising structures for their use as molecular wires thanks to a high degree of π‐conjugation, low HOMO—LUMO gaps, and exceptional conductance. Such structures have been prepared in solution, but their on‐surface synthesis remains unreported. Here, meso–meso triply fused Por NTs have been prepared through a two‐step synthesis on Au(111). The diradical character of the on‐surface formed building block PorA₂, a phenalenyl π‐extended Zn^IIPor, facilitates intermolecular homocoupling and allows for the formation of laterally π‐extended tapes. The structural and electronic properties of individual Por NTs are addressed, both on Au(111) and on a thin insulating NaCl layer, by high‐resolution scanning probe microscopy/spectroscopy complemented by DFT calculations. These Por NTs carry one unpaired electron at each end, which leads to magnetic end states. Our study provides a versatile route towards Por NTs and the atomic‐scale characterization of such tapes.

Atomically precise graphene nanoribbons: interplay of structural and electronic properties

Graphene nanoribbons hold great promise for future applications in nanoelectronic devices, as they may combine the excellent electronic properties of graphene with the opening of an electronic band gap - not present in graphene but required for transistor applications. With a two-step on-surface synthesis process, graphene nanoribbons can be fabricated with atomic precision, allowing precise control over width and edge structure. Meanwhile, a decade of research has resulted in a plethora of graphene nanoribbons having various structural and electronic properties. This article reviews not only the on-surface synthesis of atomically precise graphene nanoribbons but also how their electronic properties are ultimately linked to their structure. Current knowledge and considerations with respect to precursor design, which eventually determines the final (electronic) structure, are summarized. Special attention is dedicated to the electronic properties of graphene nanoribbons, also in dependence on their width and edge structure. It is exactly this possibility of precisely changing their properties by fine-tuning the precursor design - offering tunability over a wide range - which has generated this vast research interest, also in view of future applications. Thus, selected device prototypes are presented as well.

Investigation of edge states in artificial graphene nano-flakes

Graphene nano-flakes (GNFs) are predicted to host spin-polarized metallic edge states, which are envisioned for exploration of spintronics at the nanometer scale. To date, experimental realization of GNFs is only in its infancy because of the limitation of precise cutting or synthesizing methods at the nanometer scale. Here, we use low temperature scanning tunneling microscope to manipulate coronene molecules on a Cu(111) surface to build artificial triangular and hexagonal GNFs with either zigzag or armchair type of edges. We observe that an electronic state at the Dirac point emerges only in the GNFs with zigzag edges and localizes at the outmost lattice sites. The experimental results agree well with the tight-binding calculations. Our work renders an experimental confirmation of the predicated edge states of the GNFs.

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.

Materials Science Challenges to Graphene Nanoribbon Electronics

Graphene nanoribbons (GNRs) have recently emerged as promising candidates for channel materials in future nanoelectronic devices due to their exceptional electronic, thermal, and mechanical properties and chemical inertness. However, the adoption of GNRs in commercial technologies is currently hampered by materials science and integration challenges pertaining to synthesis and devices. In this Review, we present an overview of the current status of challenges, recent breakthroughs toward overcoming these challenges, and possible future directions for the field of GNR electronics. We motivate the need for exploration of scalable synthetic techniques that yield atomically precise, placed, registered, and oriented GNRs on CMOS-compatible substrates and stimulate ideas for contact and dielectric engineering to realize experimental performance close to theoretically predicted metrics. We also briefly discuss unconventional device architectures that could be experimentally investigated to harness the maximum potential of GNRs in future spintronic and quantum information technologies.

Chemical Stability of (3,1)-Chiral Graphene Nanoribbons

Nanostructured graphene has been widely studied in recent years due to the tunability of its electronic properties and its associated interest for a variety of fields, such as nanoelectronics and spintronics. However, many of the graphene nanostructures of technological interest are synthesized under ultrahigh vacuum, and their limited stability as they are brought out of such an inert environment may compromise their applicability. In this study, a combination of bond-resolving scanning probe microscopy (BR-SPM), along with theoretical calculations, has been employed to study (3,1)-chiral graphene nanoribbons [(3,1)-chGNRs] that were synthesized on a Au(111) surface and then exposed to oxidizing environments. Exposure to the ambient atmosphere, along with the required annealing treatment to desorb a sufficiently large fraction of contaminants to allow for its postexposure analysis by BR-SPM, revealed a significant oxidation of the ribbons, with a dramatically disruptive effect on their electronic properties. More controlled experiments avoiding high temperatures and exposing the ribbons only to low pressures of pure oxygen show that also under these more gentle conditions the ribbons are oxidized. From these results, we obtain additional insights into the preferential reaction sites and the nature of the main defects that are caused by oxygen. We conclude that graphene nanoribbons with zigzag edge segments require forms of protection before they can be used in or transferred through ambient conditions.

Controlling pairing of π-conjugated electrons in 2D covalent organic radical frameworks via in-plane strain

Controlling the electronic states of molecules is a fundamental challenge for future sub-nanoscale device technologies. π-conjugated bi-radicals are very attractive systems in this respect as they possess two energetically close, but optically and magnetically distinct, electronic states: the open-shell antiferromagnetic/paramagnetic and the closed-shell quinoidal diamagnetic states. While it has been shown that it is possible to statically induce one electronic ground state or the other by chemical design, the external dynamical control of these states in a rapid and reproducible manner still awaits experimental realization. Here, via quantum chemical calculations, we demonstrate that in-plane uniaxial strain of 2D covalently linked arrays of radical units leads to smooth and reversible conformational changes at the molecular scale that, in turn, induce robust transitions between the two kinds of electronic distributions. Our results pave a general route towards the external control, and thus technological exploitation, of molecular-scale electronic states in organic 2D materials.

Controlling the electronic states of molecules is a fundamental challenge for future sub-nanoscale device technologies but the external dynamical control of these states still awaits experimental realization. Here, via quantum chemical calculations, the authors demonstrate that in-plane uniaxial strain of 2D covalently linked arrays of radical units induces controlled pairing of π-conjugated electrons in a reversible way.

Imprinting Tunable π-Magnetism in Graphene Nanoribbons via Edge Extensions

Magnetic carbon nanostructures are currently under scrutiny for a wide spectrum of applications. Here, we theoretically investigate armchair graphene nanoribbons patterned with asymmetric edge extensions consisting of laterally fused naphtho groups, as recently fabricated via on-surface synthesis. We show that an individual edge extension acts as a spin-12 center and develops a sizable spin-polarization of the conductance around the band edges. The Heisenberg exchange coupling between a pair of edge extensions is dictated by the position of the second naphtho group in the carbon backbone, thus enabling ferromagnetic, antiferromagnetic, or nonmagnetic states. The periodic arrangement of edge extensions yields full spin-polarization at the band extrema, and the accompanying ferromagnetic ground state can be driven into nonmagnetic or antiferromagnetic phases through external stimuli. Overall, our work reveals a precise tunability of the π-magnetism in graphene nanoribbons induced by naphtho groups, thereby establishing these one-dimensional architectures as suitable platforms for logic spintronics.

Highly Aligned Polymeric Nanowire Etch-Mask Lithography Enabling the Integration of Graphene Nanoribbon Transistors

Graphene nanoribbons are a greatly intriguing form of nanomaterials owing to their unique properties that overcome the limitations associated with a zero bandgap of two-dimensional graphene at room temperature. Thus, the fabrication of graphene nanoribbons has garnered much attention for building high-performance field-effect transistors. Consequently, various methodologies reported previously have brought significant progress in the development of highly ordered graphene nanoribbons. Nonetheless, easy control in spatial arrangement and alignment of graphene nanoribbons on a large scale is still limited. In this study, we explored a facile, yet effective method for the fabrication of graphene nanoribbons by employing orientationally controlled electrospun polymeric nanowire etch-mask. We started with a thermal chemical vapor deposition process to prepare graphene monolayer, which was conveniently transferred onto a receiving substrate for electrospun polymer nanowires. The polymeric nanowires act as a robust etching barrier underlying graphene sheets to harvest arrays of the graphene nanoribbons. On varying the parametric control in the process, the size, morphology, and width of electrospun polymer nanowires were easily manipulated. Upon O₂ plasma etching, highly aligned arrays of graphene nanoribbons were produced, and the sacrificial polymeric nanowires were completely removed. The graphene nanoribbons were used to implement field-effect transistors in a bottom-gated configuration. Such approaches could realistically yield a relatively improved current on–off ratio of ~30 higher than those associated with the usual micro-ribbon strategy, with the clear potential to realize reproducible high-performance devices.

Manipulation of Molecular Spin State on Surfaces Studied by Scanning Tunneling Microscopy

The adsorbed magnetic molecules with tunable spin states have drawn wide attention for their immense potential in the emerging fields of molecular spintronics and quantum computing. One of the key issues toward their application is the efficient controlling of their spin state. This review briefly summarizes the recent progress in the field of molecular spin state manipulation on surfaces. We focus on the molecular spins originated from the unpaired electrons of which the Kondo effect and spin excitation can be detected by scanning tunneling microscopy and spectroscopy (STM and STS). Studies of the molecular spin-carriers in three categories are overviewed, i.e., the ones solely composed of main group elements, the ones comprising 3d-metals, and the ones comprising 4f-metals. Several frequently used strategies for tuning molecular spin state are exemplified, including chemical reactions, reversible atomic/molecular chemisorption, and STM-tip manipulations. The summary of the successful case studies of molecular spin state manipulation may not only facilitate the fundamental understanding of molecular magnetism and spintronics but also inspire the design of the molecule-based spintronic devices and materials.