Graphene nanostructures can be engineered with atomic precision to display customized electronic states with application in spintronics or quantum technologies. In order to take advantage of their full potential, their charge and spin state must be precisely controlled. Graphene systems exchange charge to reach thermodynamic equilibrium with their environment, requiring external gating potentials to tune their ground state. Alternative strategies like intrinsic doping or substrate modifications provided small variations of their equilibrium charge and poor control over their spin. Here, we show systematic manipulation of the electron occupation in graphene nanoribbons (GNRs) laying on MgO layers grown on Ag(001). Owing to the extraordinary decoupling properties of MgO, and the electropositive character of the substrate, GNRs are found to host an integer number of electron charges that depend on their length and shape. This results in the alternation between a non-magnetic closed-shell state and an open-shell paramagnetic system for even and odd electron occupations respectively. For the odd case, we found the spectral fingerprint of a narrow Coulomb correlation gap, which is the smoking gun of its spin 1/2 paramagnetic state. Comparisons of scanning tunnelling microscopy (STM) data with mean-field Hubbard (MFH) simulations confirm the practical discretization of the GNR electronic states and point to charge excess of up to 19 electrons in a single ribbon. We anticipate that GNRs supported by MgO ultra-thin insulating films can open the door to customized devices for quantum sensing and quantum processing applications..

Here, we analyze the electron transport properties of a device formed of two crossed graphene nanoribbons with zigzag edges (ZGNRs) in a spin state with total magnetization different from zero. While the ground state of ZGNRs has been shown to display antiferromagnetic ordering between the electrons at the edges, for wide ZGNRs—where the localized spin states at the edges are decoupled and the exchange interaction is close to zero—in the presence of relatively small magnetic fields, the ferromagnetic (FM) spin configuration can become the state of lowest energy due to the Zeeman effect. In these terms, by comparing the total energy of a periodic ZGNR as a function of the magnetization per unit cell, we obtain the FM-like solution of the lowest energy for the perfect ribbon, the corresponding FM-like configuration of the lowest energy for the four-terminal device formed of crossed ZGNRs, and the critical magnetic field needed to excite the system to this spin configuration. By performing transport calculations, we analyze the role of the distance between layers and the crossing angle of this device in the electrical conductance, at small gate voltages. The problem is approached employing the mean-field Hubbard Hamiltonian in combination with non-equilibrium Green’s functions. We find that ZGNR devices subject to transverse magnetic fields may acquire a high-spin configuration that ensures a metallic response and tunable beam-splitting properties, making this setting promising for studying electron quantum optics with single-electron excitations.

Low dimensional carbon-based materials can show intrinsic magnetism associated to p-electrons in open-shell π -conjugated systems. Chemical design provides atomically precise control of the π -electron cloud, which makes them promising for nanoscale magnetic devices. However, direct verification of their spatially resolved spin-moment remains elusive. Here, we report the spin-polarization of chiral graphene nanoribbons (one-dimensional strips of graphene with alternating zig-zag and arm-chair boundaries), obtained by means of spin-polarized scanning tunnelling microscopy. We extract the energy-dependent spin-moment distribution of spatially extended edge states with π -orbital character, thus beyond localized magnetic moments at radical or defective carbon sites. Guided by mean-field Hubbard calculations, we demonstrate that electron correlations are responsible for the spin-splitting of the electronic structure. Our versatile platform utilizes a ferromagnetic substrate that stabilizes the organic magnetic moments against thermal and quantum fluctuations, while being fully compatible with on-surface synthesis of the rapidly growing class of nanographenes.

This work compares two approaches to characterize the sooting propensity of liquid fuels, namely, the Threshold Soot Index (TSI) obtained from smoke point measurements and the Isolated Droplet Soot Yield (IDSY), an original metric expressing the mass of soot collected from single droplets vaporizing under a hot atmosphere representative of conventional flames. The TSI of different fuels was experimentally obtained by means of a computer-vision method, whereas their IDSY was extracted using a free-falling droplet combustion facility. The results clearly pointed to a linear dependency of the IDSY with mass fraction, allowing to propose a mixture rule for this index for a significantly broader measuring range than that allowed by the smoke point lamp. A nonlinear correlation was found between IDSY and TSI, with relevant deviations for some compounds. These deviations could advise to consider which of the available indices (TSI, IDSY, others) would be more adequate to emulate the sooting behavior.

Organic diradicals are envisioned as elementary building blocks for designing a new generation of spintronic devices and have been used in constructing prototypical field effect transistors and nonlinear optical devices. Open-shell systems, however, are also reactive, thus requiring design strategies to "protect" their radical character from the environment, especially when they are embedded in solid-state devices. Here, we report the persistence on a metallic surface of the diradical character of a diindeno[b,i]anthracene (DIAn) core protected by bulky end-groups. Our scanning tunneling spectroscopy measurements on single-molecules detected singlet-triplet excitations that were absent for DIAn species packed in assembled structures. Density functional theory simulations unravel that the molecular geometry on the metal substrate can crucially modify the value of the singlet-triplet gap via the delocalization of the radical sites. The persistence of the diradical character over metallic substrates is a promising finding for integrating radical-based materials into functional devices.

We study theoretically electron interference in a Mach–Zehnder-like geometry formed by four zigzag graphene nanoribbons (ZGNRs) arranged in parallel pairs, one on top of the other, such that they form intersection angles of 60˚ Depending on the interribbon separation, each intersection can be tuned to act either as an electron beam splitter or as a mirror, enabling tuneable circuitry with interfering pathways. Based on the mean-field Hubbard model and Green's function techniques, we evaluate the electron transport properties of such 8-terminal devices and identify pairs of terminals that are subject to self-interference. We further show that the scattering matrix formalism in the approximation of independent scattering at the four individual junctions provides accurate results as compared with the Green's function description, allowing for a simple interpretation of the interference process between two dominant pathways. This enables us to characterize the device sensitivity to phase shifts from an external magnetic flux according to the Aharonov–Bohm effect as well as from small geometric variations in the two path lengths. The proposed devices could find applications as magnetic field sensors and as detectors of phase shifts induced by local scatterers on the different segments, such as adsorbates, impurities or defects. The setup could also be used to create and study quantum entanglement.

OPEN DATA related to the research publication: S. Sanz, N. Papior, G. Giedke, D. Sánchez-Portal, M. Brandbyge, and T. Frederiksen, Spin-polarizing electron beam splitter from crossed graphene nanoribbons, Phys. Rev. Lett. 129, 037701 (2022) [arXiv:2201.07147] Abstract: Junctions composed of two crossed graphene nanoribbons (GNRs) have been theoretically proposed as electron beam splitters where incoming electron waves in one GNR can be split coherently into propagating waves in two outgoing terminals with nearly equal amplitude and zero back-scattering. Here we scrutinize this effect for devices composed of narrow zigzag GNRs taking explicitly into account the role of Coulomb repulsion that leads to spin-polarized edge states within mean-field theory. We show that the beam-splitting effect survives the opening of the well-known correlation gap and, more strikingly, that a spin-dependent scattering potential emerges which spin polarizes the transmitted electrons in the two outputs. By studying different ribbons and intersection angles we provide evidence that this is a general feature with edge-polarized nanoribbons. A near-perfect polarization can be achieved by joining several junctions in series. Our findings suggest that GNRs are interesting building blocks in spintronics and quantum technologies with applications for interferometry and entanglement.

Junctions composed of two crossed graphene nanoribbons (GNRs) have been theoretically proposed as electron beam splitters where incoming electron waves in one GNR can be split coherently into propagating waves in two outgoing terminals with nearly equal amplitude and zero back-scattering. Here we scrutinize this effect for devices composed of narrow zigzag GNRs taking explicitly into account the role of Coulomb repulsion that leads to spin-polarized edge states within mean-field theory. We show that the beam-splitting effect survives the opening of the well-known correlation gap and, more strikingly, that a spin-dependent scattering potential emerges which spin polarizes the transmitted electrons in the two outputs. By studying different ribbons and intersection angles we provide evidence that this is a general feature with edge-polarized nanoribbons. A near-perfect polarization can be achieved by joining several junctions in series. Our findings suggest that GNRs are interesting building blocks in spintronics and quantum technologies with applications for interferometry and entanglement.

Triangulene nanographenes are open-shell molecules with predicted high spin state due to the frustration of their conjugated network. Their long-sought synthesis became recently possible over a metal surface. Here, we present a macrocycle formed by six [3]triangulenes, which was obtained by combining the solution synthesis of a dimethylphenyl-anthracene cyclic hexamer and the on-surface cyclodehydrogenation of this precursor over a gold substrate. The resulting triangulene nanostar exhibits a collective spin state generated by the interaction of its 12 unpaired π-electrons along the conjugated lattice, corresponding to the antiferromagnetic ordering of six S=1 sites (one per triangulene unit). Inelastic electron tunneling spectroscopy resolved three spin excitations connecting the singlet ground state with triplet states. The nanostar behaves close to predictions from the Heisenberg model of an S=1 spin ring, representing a unique system to test collective spin modes in cyclic systems.

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.

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 pz 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.

Graphene can develop large magnetic moments in custom-crafted open-shell nanostructures such as triangulene, a triangular piece of graphene with zigzag edges. Current methods of engineering graphene nanosystems on surfaces succeeded in producing atomically precise open-shell structures, but demonstration of their net spin remains elusive to date. Here, we fabricate triangulenelike graphene systems and demonstrate that they possess a spin S=1 ground state. Scanning tunneling spectroscopy identifies the fingerprint of an underscreened S=1 Kondo state on these flakes at low temperatures, signaling the dominant ferromagnetic interactions between two spins. Combined with simulations based on the meanfield Hubbard model, we show that this S=1 π paramagnetism is robust and can be turned into an S=1/2 state by additional H atoms attached to the radical sites. Our results demonstrate that π paramagnetism of high-spin graphene flakes can survive on surfaces, opening the door to study the quantum behavior of interacting π spins in graphene systems.

We analyze theoretically four-terminal electronic devices composed of two crossed graphene nanoribbons (GNRs) and show that they can function as beam splitters or mirrors. These features are identified for electrons in the low-energy region where a single valence or conduction band is present. Our modeling is based on p(z) orbital tight binding with Slater-Koster-type matrix elements fitted to accurately reproduce the low-energy bands from density functional theory calculations. We analyze systematically all devices that can be constructed with either zigzag or armchair GNRs in AA and AB stackings. From Green's function theory the elastic electron transport properties are quantified as a function of the ribbon width. We find that devices composed of relatively narrow zigzag GNRs and AA-stacked armchair GNRs are the most interesting candidates to realize electron beam splitters with a close to 50:50 ratio in the two outgoing terminals. Structures with wider ribbons instead provide electron mirrors, where the electron wave is mostly transferred into the outgoing terminal of the other ribbon, or electron filters where the scattering depends sensitively on the wavelength of the propagating electron. We also test the robustness of these transport properties against variations in the intersection angle, stacking pattern, lattice deformation (uniaxial strain), inter-GNR separation, and electrostatic potential differences between the layers. These generic features show that GNRs are interesting basic components to construct electronic quantum optical setups.

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.

Resumen del trabajo presentado a la International conference on: Novel 2D materials explored via scanning probe microscopy & spectroscopy; celebrada en Donostia.San Sebastian (Pais Vasco, Espana) del 25 al 29 de junio de 2018.

Resumen del trabajo presentado a la International conference on: Novel 2D materials explored via scanning probe microscopy & spectroscopy; celebrada en Donostia.San Sebastian (Pais Vasco, Espana) del 25 al 29 de junio de 2018.