Electronic and magnetic properties of zigzag graphene nanoribbons on the (111) surface of Cu, Ag, and Au

Ferromagnetic Boundary States in the Hydrogenated Graphene/Nickel Moiré Superlattice

Zigzag graphene nanoribbons (ZGNRs) exhibit spin-polarized edge states, which are key elements for designing graphene-based spintronics devices. The intrinsic ZGNRs have an antiferromagnetic ground state, which can be modified by edge engineering and external field. Here, this work proposes an avenue to realize the zigzag graphene/graphane nanoribbon superlattice (ZGNR-SL) on Ni(100) by selective hydrogenation of the 1D moiré patterns, based on the first-principles calculations. The growth mechanism of the ZGNR-SL is revealed having two steps: first, hydrogen atoms intercalate at the interface of graphene/Ni and form H ribbons in the apex regions of the 1D moiré pattern; second, the intercalated hydrogen ribbons serve as a template for the directed hydrogen adsorption on both sides of the graphene over the hydrogen ribbons. Interestingly, ZGNR-SL on Ni(100) surface exhibit ferromagnetic boundary states, which may be exploited in potential spintronics device applications.

Theoretical insights into the methane catalytic decomposition on graphene nanoribbons edges

Catalytic methane decomposition (CMD) is receiving much attention as a promising application for hydrogen production. Due to the high energy required for breaking the C-H bonds of methane, the choice of catalyst is crucial to the viability of this process. However, atomistic insights for the CMD mechanism on carbon-based materials are still limited. Here, we investigate the viability of CMD under reaction conditions on the zigzag (12-ZGNR) and armchair (AGRN) edges of graphene nanoribbons employing dispersion-corrected density functional theory (DFT). First, we investigated the desorption of H and H₂ at 1200 K on the passivated 12-ZGNR and 12-AGNR edges. The diffusion of hydrogen atom on the passivated edges is the rate determinant step for the most favourable H₂ desorption pathway, with a activation free energy of 4.17 eV and 3.45 eV on 12-ZGNR and 12-AGNR, respectively. The most favourable H₂ desorption occurs on the 12-AGNR edges with a free energy barrier of 1.56 eV, reflecting the availability of bare carbon active sites on the catalytic application. The direct dissociative chemisorption of CH₄ is the preferred pathway on the non-passivated 12-ZGNR edges, with an activation free energy of 0.56 eV. We also present the reaction steps for the complete catalytic dehydrogenation of methane on 12-ZGNR and 12-AGNR edges, proposing a mechanism in which the solid carbon formed on the edges act as new active sites. The active sites on the 12-AGNR edges show more propensity to be regenerated due lower free energy barrier of 2.71 eV for the H₂ desorption from the newly grown active site. Comparison is made between the results obtained here and experimental and computational data available in the literature. We provide fundamental insights for the engineering of carbon-based catalysts for the CMD, showing that the bare carbon edges of graphene nanoribbons have performance comparable to commonly used metallic and bi-metallic catalysts for methane decomposition.

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.

Current-Induced One-Dimensional Diffusion of Co Adatoms on Graphene Nanoribbons

One-dimensional diffusion of Co adatoms on graphene nanoribbons has been induced and investigated by means of scanning tunnelling microscopy (STM). To this end, the nanoribbons and the Co adatoms have been imaged before and after injecting current pulses into the nanoribbons, with the STM tip in direct contact with the ribbon. We observe current-induced motion of the Co atoms along the nanoribbons, which is approximately described by a distribution expected for a thermally activated one-dimensional random walk. This indicates that the nanoribbons reach temperatures far beyond 100 K, which is well above the temperature of the underlying Au substrate. This model system can be developed further for the study of electromigration at the single-atom level.

Realization of Strong Room-Temperature Ferromagnetism in Atomically Thin 2D Carbon Nitride Sheets by Thermal Annealing

The presence of the intrinsic band gap of 3.06 eV makes atomically thin carbon nitride sheets (CNs) a promising spin-based semiconductor material. However, the absence of localized spins makes the pristine CNs intrinsically nonmagnetic. Here we report the realization of strong room-temperature (RT) ferromagnetism with a high Curie temperature of ca. 524.2 K in atomically thin 2D CNs by annealing pristine CNs at 700 °C. In particular, the RT saturated magnetization reaches as high as 0.71 emu/g, which is the highest value reported so far in carbon-based materials. The structural characterization combined with density functional theory calculations reveals that (i) the seven C-C bonds per unit cell were formed after annealing and (ii) the C-C bonds can introduce high-density localized spins and realize the long-range ferromagnetic couplings among these spins.

Dynamics of quantum entanglement in a zigzag graphene nanoribbon

We study the dynamics of entanglement between two edge spins in a zigzag graphene nanoribbon (ZGNR) which is thermalized with a reservoir at temperatureT. The results show that the entanglement evolution displays oscillating behaviors in the presence of an external magnetic field. Such oscillating behaviors of entanglement strongly depend on the field frequency and relative location between two inter-edge coupled spins. At some critical field frequencies, the entanglement exhibits a periodic structure. When the temperature is low, the oscillating patterns of entanglement are quite regular and symmetrical. When the temperature is high, the patterns of entanglement evolution occur irregular distortions due to the thermal fluctuations. However, the entanglement between two inter-edge coupled spins in ZGNR still exists a nontrivial value even at room temperature.

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.

Diversified Phenomena in Metal- and Transition-Metal-Adsorbed Graphene Nanoribbons

Adatom-adsorbed graphene nanoribbons (GNRs) have gained much attention owing to the tunable electronic and magnetic properties. The metal (Bi, Al)/transition metal (Ti, Fe, Co, Ni) atoms could provide various outermost orbitals for the multi-orbital hybridizations with the out-of-plane π bondings on the carbon honeycomb lattice, which dominate the fundamental properties of chemisorption systems. In this study, the significant similarities and differences among Bi-/Al-/Ti-/Fe-/Co-/Ni-adsorbed GNRs are thoroughly investigated by using the first-principles calculations. The main characterizations include the adsorption sites, bond lengths, stability, band structures, charge density distributions, spin- and orbital-projected density of states, and magnetic configurations. Furthermore, there exists a transformation from finite gap semiconducting to metallic behaviors, accompanied by the nonmagnetism, antiferromagnetism, or ferromagnetism. They arise from the cooperative or competitive relations among the significant chemical bonds, finite-size quantum confinement, edge structure, and spin-dependent many-body effects. The proposed theoretical framework could be further improved and generalized to explore other emergent 1D and 2D materials.

Multi-orbital tight binding model for the electronic and optical properties of armchair graphene nanoribbons in the presence of a periodic potential

The influences of an external electric field with uniform or modulated potential on the electronic and optical properties of armchair graphene nanoribbons (GNRs) are explored using the multi-orbital tight-binding Hamiltonian. The interplay between an electric field and interaction between (s,p_x,p_y,p_z) orbitals remarkably enriches the main features of band structures and absorption spectra. The applied electric field can notably alter the energy dispersions ofπandσbands, leading to the deformation of band-edge states, open and close of a band gap, and modification of the Fermi energy. The vertical optical excitations happen among theπbands, while their available channels depend on the Fermi level which is controlled by theσ-edge bands and a finite potential. With the rich and unique properties, GNRs are suitable candidates for applications in the fields of photodetectors, nanoelectronics, and spintronics. The calculated results are expected to be examined by the angle-resolved photoemission spectroscopies and optical spectroscopies.

Rational synthesis of atomically precise graphene nanoribbons directly on metal oxide surfaces

Atomically precise graphene nanoribbons (GNRs) attract great interest because of their highly tunable electronic, optical, and transport properties. However, on-surface synthesis of GNRs is typically based on metal surface–assisted chemical reactions, where metallic substrates strongly screen their designer electronic properties and limit further applications. Here, we present an on-surface synthesis approach to forming atomically precise GNRs directly on semiconducting metal oxide surfaces. The thermally triggered multistep transformations preprogrammed in our precursors’ design rely on highly selective and sequential activations of carbon-bromine (C-Br) and carbon-fluorine (C-F) bonds and cyclodehydrogenation. The formation of planar armchair GNRs terminated by well-defined zigzag ends is confirmed by scanning tunneling microscopy and spectroscopy, which also reveal weak interaction between GNRs and the rutile titanium dioxide substrate.

Scalable and Precise Synthesis of Armchair-Edge Graphene Nanoribbon in Metal-Organic Framework

Graphene nanoribbons (GNRs), narrow and straight-edged stripes of graphene, attract a great deal of attention because of their excellent electronic and magnetic properties. As of yet, there is no fabrication method for GNRs to satisfy both precision at the atomic scale and scalability, which is critical for fundamental research and future technological development. Here, we report a methodology for bulk-scale synthesis of GNRs with atomic precision utilizing a metal-organic framework (MOF). The GNR was synthesized by the polymerization of perylene (PER) or its derivative within the nanochannels of the MOF. Molecular dynamics simulations showed that PER was uniaxially aligned along the nanochannels of the MOF through host-guest interactions, which allowed for regulated growth of the nanoribbons. A series of characterizations of the GNR, including NMR, UV/vis/NIR, and Raman spectroscopy measurements, confirmed the formation of the GNR with well-controlled edge structure and width.

Common surface structures of graphene and Au(111): The effect of rotational angle on adsorption and electronic properties

Graphene adsorption on the Au(111) surface was explored to identify its common surface structures by means of van der Waals corrected density functional theory calculations. The alignment of graphene in the form of certain rotational angles on the gold surface has an important role in lattice matching, which causes Moiré patterns, and in the electronic properties of the resulting common cell structures. Dispersive weak interactions between carbon and gold layers lead to a downward shift of Fermi energy of the adsorption system with respect to the Dirac point of graphene showing a p-type doping character. Moreover, the shift was shown to depend on the rotational angle of graphene on Au(111).

Single spin localization and manipulation in graphene open-shell nanostructures

Turning graphene magnetic is a promising challenge to make it an active material for spintronics. Predictions state that graphene structures with specific shapes can spontaneously develop magnetism driven by Coulomb repulsion of π-electrons, but its experimental verification is demanding. Here, we report on the observation and manipulation of individual magnetic moments in graphene open-shell nanostructures on a gold surface. Using scanning tunneling spectroscopy, we detect the presence of single electron spins localized around certain zigzag sites of the carbon backbone via the Kondo effect. We find near-by spins coupled into a singlet ground state and quantify their exchange interaction via singlet-triplet inelastic electron excitations. Theoretical simulations picture how electron correlations result in spin-polarized radical states with the experimentally observed spatial distributions. Extra hydrogen atoms bound to radical sites quench their magnetic moment and switch the spin of the nanostructure in half-integer amounts. Our work demonstrates the intrinsic π-paramagnetism of graphene nanostructures.

Spin signatures in the electrical response of graphene nanogaps

We analyse the electrical response of narrow graphene nanogaps in search for transport signatures stemming from spin-polarized edge states. We find that the electrical transport across graphene nanogaps having perfectly defined zigzag edges does not carry any spin-related signature. We also analyse the magnetic and electrical properties of nanogaps whose electrodes have wedges that possibly occur in the currently fabricated nanogaps. These wedges can host spin polarized wedge low-energy states due to the bipartite nature of the graphene lattice. We find that these spin-polarized low-energy modes give rise to low-voltage signatures in the differential conductance and to distinctive features in the stability diagrams. These are caused by fully spin-polarized currents.

Emerging chemical strategies for imprinting magnetism in graphene and related 2D materials for spintronic and biomedical applications

Graphene, a single two-dimensional sheet of carbon atoms with an arrangement mimicking the honeycomb hexagonal architecture, has captured immense interest of the scientific community since its isolation in 2004. Besides its extraordinarily high electrical conductivity and surface area, graphene shows a long spin lifetime and limited hyperfine interactions, which favors its potential exploitation in spintronic and biomedical applications, provided it can be made magnetic. However, pristine graphene is diamagnetic in nature due to solely sp2 hybridization. Thus, various attempts have been proposed to imprint magnetic features into graphene. The present review focuses on a systematic classification and physicochemical description of approaches leading to equip graphene with magnetic properties. These include introduction of point and line defects into graphene lattices, spatial confinement and edge engineering, doping of graphene lattice with foreign atoms, and sp3 functionalization. Each magnetism-imprinting strategy is discussed in detail including identification of roles of various internal and external parameters in the induced magnetic regimes, with assessment of their robustness. Moreover, emergence of magnetism in graphene analogues and related 2D materials such as transition metal dichalcogenides, metal halides, metal dinitrides, MXenes, hexagonal boron nitride, and other organic compounds is also reviewed. Since the magnetic features of graphene can be readily masked by the presence of magnetic residues from synthesis itself or sample handling, the issue of magnetic impurities and correct data interpretations is also addressed. Finally, current problems and challenges in magnetism of graphene and related 2D materials and future potential applications are also highlighted.

Controllable conversion of quasi-freestanding polymer chains to graphene nanoribbons

In the bottom-up synthesis of graphene nanoribbons (GNRs) from self-assembled linear polymer intermediates, surface-assisted cyclodehydrogenations usually take place on catalytic metal surfaces. Here we demonstrate the formation of GNRs from quasi-freestanding polymers assisted by hole injections from a scanning tunnelling microscope (STM) tip. While catalytic cyclodehydrogenations typically occur in a domino-like conversion process during the thermal annealing, the hole-injection-assisted reactions happen at selective molecular sites controlled by the STM tip. The charge injections lower the cyclodehydrogenation barrier in the catalyst-free formation of graphitic lattices, and the orbital symmetry conservation rules favour hole rather than electron injections for the GNR formation. The created polymer–GNR intraribbon heterostructures have a type-I energy level alignment and strongly localized interfacial states. This finding points to a new route towards controllable synthesis of freestanding graphitic layers, facilitating the design of on-surface reactions for GNR-based structures.

A key step in the on-surface synthesis of graphene nanoribbons is thermal annealing of polymer precursors on a metal substrate. Here, Ma et al. decouple the cyclodehydrogenation reaction from the catalytic metal substrate and grow graphene nanoribbons by injecting charges at molecular sites.

Orbital Edge States in a Photonic Honeycomb Lattice

We experimentally reveal the emergence of edge states in a photonic lattice with orbital bands. We use a two-dimensional honeycomb lattice of coupled micropillars whose bulk spectrum shows four gapless bands arising from the coupling of p-like photonic orbitals. We observe zero-energy edge states whose topological origin is similar to that of conventional edge states in graphene. Additionally, we report novel dispersive edge states in zigzag and armchair edges. The observations are reproduced by tight-binding and analytical calculations, which we extend to bearded edges. Our work shows the potentiality of coupled micropillars in elucidating some of the electronic properties of emergent two-dimensional materials with orbital bands.

Synthesis of graphene nanoribbons with a defined mixed edge-site sequence by surface assisted polymerization of (1,6)-dibromopyrene on Ag(110)

By a combination of scanning tunneling microscopy, X-ray spectroscopic techniques and density functional theory calculations, we prove the formation of extended patterns of parallel, graphene nanoribbons with alternate zig-zag and armchair edges and selected width by surface-assisted Ullmann coupling polymerization and dehydrogenation of 1,6-dibromopyrene (C₁₆H₈Br₂). Besides the relevance of these nanostructures for their possible application in nanodevices, we demonstrate the peculiarity of halogenated pyrene derivatives for the formation of nanoribbons, in particular on Ag(110). These results open the possibility of tuning the shape and dimension of nanoribbons (and hence the correlated electronic properties) by choosing suitably tailored or on-purpose designed molecular precursors.

On-Surface Synthesis of Atomically Precise Graphene Nanoribbons

The surface-assisted polymerization and cyclodehydrogenation of specifically designed organic precursors provides a route toward atomically precise graphene nanoribbons, which promises to combine the outstanding electronic properties of graphene with a bandgap that is sufficiently large for room-temperature digital-logic applications. Starting from the basic concepts behind the on-surface synthesis approach, this report covers the progress made in understanding the different reaction steps, in synthesizing atomically precise graphene nanoribbons of various widths and edge structures, and in characterizing their properties, ending with an outlook on the challenges that still lie ahead.

Electronic and magnetic properties of H-terminated graphene nanoribbons deposited on the topological insulator Sb2Te3

Magnetism in zigzag graphene nanoribbons (GNRs) has received enormous attention recently, due to the one-dimensional nature of this phenomenon, as well as its potential applications in the field of spintronics. In this work, we present a density functional theory (DFT) investigation of H-passivated GNRs on the (111) surface of the topological insulator Sb2Te3. We show that the chemical interaction between the GNR and the substrate is weak. As a result, the GNR-surface distance is large, of the order of 3.4 Angstrom, doping effects are almost negligible, and the mean-field magnetic properties of the GNR are preserved. Nevertheless, the presence of the substrate affects significantly the magnitude of the exchange coupling constants between the edges. Although our DFT calculations do not properly describe quantum fluctuations that destabilize the edge magnetism in free-standing GNRs, they provide important information about the stabilizing mechanisms which originate from the substrate-induced spin orbit coupling and the decoherence effects due to the surface states of Sb2Te3. We argue that, owing to these mechanisms, Sb2Te3 may be a suitable substrate to investigate experimentally the transition from "quantum" to "classical" magnetism in GNRs.

Sulfur Doping Induces Strong Ferromagnetic Ordering in Graphene: Effect of Concentration and Substitution Mechanism

Imprinting ferromagnetism to a graphene structure by substitution of carbon atoms with sulfur is reported. S-doped graphene (4.2 at%) shows strong ferromagnetic properties with saturation magnetization exceeding 5.5 emu g(-1) at 2 K, which is among the highest values reported for any sp-based system. The remarkable magnetic response is attributed to delocalization of electrons from sulfur injected into the graphene conduction band.

Room-temperature magnetic order on zigzag edges of narrow graphene nanoribbons

The possibility that non-magnetic materials such as carbon could exhibit a novel type of s-p electron magnetism has attracted much attention over the years, not least because such magnetic order is predicted to be stable at high temperatures. It has been demonstrated that atomic-scale structural defects of graphene can host unpaired spins, but it remains unclear under what conditions long-range magnetic order can emerge from such defect-bound magnetic moments. Here we propose that, in contrast to random defect distributions, atomic-scale engineering of graphene edges with specific crystallographic orientation--comprising edge atoms from only one sub-lattice of the bipartite graphene lattice--can give rise to a robust magnetic order. We use a nanofabrication technique based on scanning tunnelling microscopy to define graphene nanoribbons with nanometre precision and well-defined crystallographic edge orientations. Although so-called 'armchair' ribbons display quantum confinement gaps, ribbons with the 'zigzag' edge structure that are narrower than 7 nanometres exhibit an electronic bandgap of about 0.2-0.3 electronvolts, which can be identified as a signature of interaction-induced spin ordering along their edges. Moreover, upon increasing the ribbon width, a semiconductor-to-metal transition is revealed, indicating the switching of the magnetic coupling between opposite ribbon edges from the antiferromagnetic to the ferromagnetic configuration. We found that the magnetic order on graphene edges of controlled zigzag orientation can be stable even at room temperature, raising hopes of graphene-based spintronic devices operating under ambient conditions.

Limited robustness of edge magnetism in zigzag graphene nanoribbons with electrodes

It is shown that apart from well-known factors, like temperature, substrate, and edge reconstruction effects, also the presence of external contacts is destructive for the formation of magnetic moments at the edges of graphene nanoribbons (GNRs). The edge magnetism gradually decreases when graphene/electrode interfaces become more and more transparent for electrons. In addition to the graphene/electrode coupling strength, the aspect ratio parameter, i.e. a width/length ratio of the GNR, is also crucial for the suppression of edge magnetism. The present theory uses a tight-binding method, based on the mean-field Hubbard Hamiltonian for π electrons, and the Green's function technique within the Landauer-Büttiker approach.

Voltage-driven spintronic logic gates in graphene nanoribbons

Electronic devices lose efficacy due to quantum effect when the line-width of gate decreases to sub-10 nm. Spintronics overcome this bottleneck and logic gates are building blocks of integrated circuits. Thus, it is essential to control electronic transport of opposite spins for designing a spintronic logic gate, and spin-selective semiconductors are natural candidates such as zigzag graphene nanoribbons (ZGNR) whose edges are ferromagnetically ordered and antiferromagnetically coupled with each other. Moreover, it is necessary to sandwich ZGNR between two ferromagnetic electrodes for making a spintronic logic gate and also necessary to apply magnetic field to change the spin orientation for modulating the spin transport. By first principle calculations, we propose a method to manipulate the spin transport in graphene nanoribbons with electric field only, instead of magnetic field. We find that metal gates with specific bias nearby edges of ZGNR build up an in-plane inhomogeneous electric field which modulates the spin transport by localizing the spin density in device. The specific manipulation of spin transport we have proposed doesn't need spin-charge conversion for output and suggests a possible base for designing spintronic integrated circuit in atomic scale.

Electronic states at the graphene-hexagonal boron nitride zigzag interface

The electronic properties of graphene edges have been predicted to depend on their crystallographic orientation. The so-called zigzag (ZZ) edges haven been extensively explored theoretically and proposed for various electronic applications. However, their experimental study remains challenging due to the difficulty in realizing clean ZZ edges without disorder, reconstructions, or the presence of chemical functional groups. Here, we propose the ZZ-terminated, atomically sharp interfaces between graphene and hexagonal boron nitride (BN) as experimentally realizable, chemically stable model systems for graphene ZZ edges. Combining scanning tunneling microscopy and numerical methods, we explore the structure of graphene-BN interfaces and show them to host localized electronic states similar to those on the pristine graphene ZZ edge.

First-principles insights into the electronic and magnetic structure of hybrid organic-metal interfaces

In this review we summarize our experience gained from several recent ab initio studies aimed to investigate how the competition between short-ranged chemical and long-ranged dispersion interactions determines the bonding mechanism of a specific set of chemically functionalized π-conjugated organic molecules on non-magnetic and magnetic metal surfaces. A key point of this review is to provide a detailed analysis on the issue of how to tune the strength of the organic molecule-surface interaction, such that the nature of the molecular bonding exhibits the specific electronic features of the physisorption or chemisorption bonding mechanisms. In particular, we discuss in detail how the precise control of these bonding mechanisms can be used to design specific electronic and magnetic properties of hybrid organic-metallic interfaces. Furthermore, our first-principles simulations provide not only the basic insights needed to interpret surface-science experiments, but are also a key tool to design organic-substrate systems with tailored properties that can be integrated into future organic-based devices for molecular electronics and molecular spintronics applications.

In situ fabrication of quasi-free-standing epitaxial graphene nanoflakes on gold

Addressing the multitude of electronic phenomena theoretically predicted for confined graphene structures requires appropriate in situ fabrication procedures yielding graphene nanoflakes (GNFs) with well-defined geometries and accessible electronic properties. Here, we present a simple strategy to fabricate quasi-free-standing GNFs of variable sizes, performing temperature programmed growth of graphene flakes on the Ir(111) surface and subsequent intercalation of gold. Using scanning tunneling microscopy (STM), we show that epitaxial GNFs on a perfectly ordered Au(111) surface are formed while maintaining an unreconstructed, singly hydrogen-terminated edge structure, as confirmed by the accompanying density functional theory (DFT) calculations. Using tip-induced lateral displacement of GNFs, we demonstrate that GNFs on Au(111) are to a large extent decoupled from the Au(111) substrate. The direct accessibility of the electronic states of a single GNF is demonstrated upon analysis of the quasiparticle interference patterns obtained by low-temperature STM. These findings open up an interesting playground for diverse investigations of graphene nanostructures with possible implications for device fabrication.

Quantum nature of edge magnetism in graphene

It is argued that the subtle crossover from decoherence-dominated classical magnetism to fluctuation-dominated quantum magnetism is experimentally accessible in graphene nanoribbons. We show that the width of a nanoribbon determines whether the edge magnetism is on the classical side, on the quantum side, or in between. In the classical regime, decoherence is dominant and leads to static spin polarizations at the ribbon edges, which are well described by mean-field theories. The quantum Zeno effect is identified as the basic mechanism which is responsible for the spin polarization and thereby enables the application of graphene in spintronics. On the quantum side, however, the spin polarization is destroyed by dynamical processes. The great tunability of graphene magnetism thus offers a viable route for the study of the quantum-classical crossover.

Magnetic correlations in short and narrow graphene armchair nanoribbons

Electronic states at the ends of a narrow armchair nanoribbon give rise to a pair of nonlocally entangled spins. We propose two experiments to probe these magnetic states, based on magnetometry and tunneling spectroscopy, in which correlation effects lead to a striking, nonlinear response to external magnetic fields. On the basis of low-energy theories that we derive here, it is remarkably simple to assess these nonlinear signatures for magnetic edge states. The effective theories are especially suitable in parameter regimes where other methods such as quantum Monte Carlo simulations are exceedingly difficult due to exponentially small energy scales. The armchair ribbon setup discussed here provides a promisingly well-controlled (both experimentally and theoretically) environment for studying the principles behind edge magnetism in graphene-based nanostructures.