One-Dimensional Magnetic Conduction Channels across Zigzag Graphene Nanoribbon/Hexagonal Boron Nitride Heterojunctions.

We examine the electronic structure of recently fabricated in-plane heterojunctions of zigzag graphene nanoribbons embedded in hexagonal boron nitride. We focus on hitherto unexplored interface configurations in which both edges of the nanoribbon are bonded to the same chemical species, either boron or nitrogen atoms. Using ab initio and mean-field Hubbard model calculations, we reveal the emergence of one-dimensional magnetic conducting channels at these interfaces. These channels originate from the energy shift of the magnetic interface states that is induced by charge transfer between the nanoribbon and hexagonal boron nitride. We further address the response of these heterojunctions to external electric and magnetic fields, demonstrating the tunability of energy and spin splittings in the electronic structure. Our findings establish that zigzag graphene nanoribbon/hexagonal boron nitride heterojunctions are a suitable platform for exploring and engineering spin transport in the atomically thin limit, with potential applications in integrated spintronic devices.

One-Dimensional Moiré Physics and Chemistry in Heterostrained Bilayer Graphene.

Twisted bilayer graphene (tBLG) has emerged as a promising platform for exploring exotic electronic phases. However, the formation of moiré patterns in tBLG has thus far been confined to the introduction of twist angles between the layers. Here, we propose heterostrained bilayer graphene (hBLG), as an alternative avenue for accessing twist angle-free moiré physics via lattice mismatch. Using atomistic and first-principles calculations, we demonstrate that the uniaxial heterostrain can promote isolated flat electronic bands around the Fermi level. Furthermore, the heterostrain-induced out-of-plane lattice relaxation may lead to a spatially modulated reactivity of the surface layer, paving the way for moiré-driven chemistry and magnetism. We anticipate that our findings can be readily generalized to other layered materials.

Dirac Half-Semimetallicity and Antiferromagnetism in Graphene Nanoribbon/Hexagonal Boron Nitride Heterojunctions.

Half-metals have been envisioned as active components in spintronic devices by virtue of their completely spin-polarized electrical currents. Actual materials hosting half-metallic phases, however, remain scarce. Here, we predict that recently fabricated heterojunctions of zigzag nanoribbons embedded in two-dimensional hexagonal boron nitride are half-semimetallic, featuring fully spin-polarized Dirac points at the Fermi level. The half-semimetallicity originates from the transfer of charges from hexagonal boron nitride to the embedded graphene nanoribbon. These charges give rise to opposite energy shifts of the states residing at the two edges, while preserving their intrinsic antiferromagnetic exchange coupling. Upon doping, an antiferromagnetic-to-ferrimagnetic phase transition occurs in these heterojunctions, with the sign of the excess charge controlling the spatial localization of the net magnetic moments. Our findings demonstrate that such heterojunctions realize tunable one-dimensional conducting channels of spin-polarized Dirac fermions seamlessly integrated into a two-dimensional insulator, thus holding promise for the development of carbon-based spintronics.

Domain-Dependent Surface Adhesion in Twisted Few-Layer Graphene: Platform for Moiré-Assisted Chemistry.

Twisted van der Waals multilayers are widely regarded as a rich platform to access novel electronic phases thanks to the multiple degrees of freedom available for controlling their electronic and chemical properties. Here, we propose that the stacking domains that form naturally due to the relative twist between successive layers act as an additional "knob" for controlling the behavior of these systems and report the emergence and engineering of stacking domain-dependent surface chemistry in twisted few-layer graphene. Using mid-infrared near-field optical microscopy and atomic force microscopy, we observe a selective adhesion of metallic nanoparticles and liquid water at the domains with rhombohedral stacking configurations of minimally twisted double bi- and trilayer graphene. Furthermore, we demonstrate that the manipulation of nanoparticles located at certain stacking domains can locally reconfigure the moiré superlattice in their vicinity at the micrometer scale. Our findings establish a new approach to controlling moiré-assisted chemistry and nanoengineering.

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.

Quantum nanomagnets in on-surface metal-free porphyrin chains.

Unlike classic spins, quantum magnets are spin systems that interact via the exchange interaction and exhibit collective quantum behaviours, such as fractional excitations. Molecular magnetism often stems from d/f-transition metals, but their spin-orbit coupling and crystal field induce a significant magnetic anisotropy, breaking the rotation symmetry of quantum spins. Thus, it is of great importance to build quantum nanomagnets in metal-free systems. Here we have synthesized individual quantum nanomagnets based on metal-free multi-porphyrin systems. Covalent chains of two to five porphyrins were first prepared on Au(111) under ultrahigh vacuum, and hydrogen atoms were then removed from selected carbons using the tip of a scanning tunnelling microscope. The conversion of specific porphyrin units to their radical or biradical state enabled the tuning of intra- and inter-porphyrin magnetic coupling. Characterization of the collective magnetic properties of the resulting chains showed that the constructed S = 1/2 antiferromagnets display a gapped excitation, whereas the S = 1 antiferromagnets exhibit distinct end states between even- and odd-numbered spin chains, consistent with Heisenberg model calculations.

Hydrogen Atoms on Zigzag Graphene Nanoribbons: Chemistry and Magnetism Meet at the Edge.

Although the unconventional π-magnetism at the zigzag edges of graphene holds promise for a wide array of applications, whether and to what degree it plays a role in their chemistry remains poorly understood. Here, we investigate the addition of a hydrogen atom─the simplest yet the most experimentally relevant adsorbate─to zigzag graphene nanoribbons (ZGNRs). We show that the π-magnetism governs the chemistry of ZGNRs, giving rise to a site-dependent reactivity of the carbon atoms and driving the hydrogenation process to the nanoribbon edges. Conversely, the chemisorbed hydrogen atom governs the π-magnetism of ZGNRs, acting as a spin-1/2 paramagnetic center in the otherwise antiferromagnetic ground state and spin-polarizing the charge carriers at the band extrema. Our findings establish a comprehensive picture of the peculiar interplay between chemistry and magnetism that emerges at the zigzag edges of graphene.

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.

Edge Disorder in Bottom-Up Zigzag Graphene Nanoribbons: Implications for Magnetism and Quantum Electronic Transport.

We unveil the nature of the structural disorder in bottom-up zigzag graphene nanoribbons along with its effect on the magnetism and electronic transport on the basis of scanning probe microscopies and first-principles calculations. We find that edge-missing m-xylene units emerging during the cyclodehydrogenation step of the on-surface synthesis are the most common point defects. These "bite" defects act as spin-1 paramagnetic centers, severely disrupt the conductance spectrum around the band extrema, and give rise to spin-polarized charge transport. We further show that the electronic conductance across graphene nanoribbons is more sensitive to "bite" defects forming at the zigzag edges than at the armchair ones. Our work establishes a comprehensive understanding of the low-energy electronic properties of disordered bottom-up graphene nanoribbons.

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.

Probing magnetism in atomically thin semiconducting PtSe2.

Atomic-scale disorder in two-dimensional transition metal dichalcogenides is often accompanied by local magnetic moments, which can conceivably induce long-range magnetic ordering into intrinsically non-magnetic materials. Here, we demonstrate the signature of long-range magnetic orderings in defective mono- and bi-layer semiconducting PtSe2 by performing magnetoresistance measurements under both lateral and vertical measurement configurations. As the material is thinned down from bi- to mono-layer thickness, we observe a ferromagnetic-to-antiferromagnetic crossover, a behavior which is opposite to the one observed in the prototypical 2D magnet CrI3. Our first-principles calculations, supported by aberration-corrected transmission electron microscopy imaging of point defects, associate this transition to the interplay between the defect-induced magnetism and the interlayer interactions in PtSe2. Furthermore, we show that graphene can be effectively used to probe the magnetization of adjacent semiconducting PtSe2. Our findings in an ultimately scaled monolayer system lay the foundation for atom-by-atom engineering of magnetism in otherwise non-magnetic 2D materials.

To bend or not to bend, the dilemma of multiple bonds.

Beyond the second row of the periodic table, the nature of the multiple bonds between the elements of the main groups remains yet elusive, and "non-classical" bonding schemes are often invoked for their description. Here, focusing on group 14, we have performed an accurate modeling of the Si-Si and C-C double bonds, including electron correlation effects. We have shown that Si[double bond, length as m-dash]Si bonds are "classical" and closely resemble C[double bond, length as m-dash]C ones, being similarly subjected to a sort of tug of war in which the σ bond favors distortion and the π bond opposes it. The essential difference between Si and C boils down to the sizes of their valence shells, which determine the π-bending stiffness. In carbon, such a stiffness is large because, upon bending, the atomic s orbitals interfere destructively with the p ones. In silicon, the s shell is smaller than the p one, the bending stiffness is reduced and the π bonds typically succumb, distort, and weaken. Electron correlation plays a major role in this context, since π bonds are far from their molecular orbital limit. Hence, we have further shown that upon weakening the effective repulsion between π electrons one may remove any structural instability, strengthen the π bonds and turn Si into a closer relative of C than it used to be.

Manipulating Topological Domain Boundaries in the Single-Layer Quantum Spin Hall Insulator 1T'-WSe2.

We report the creation and manipulation of structural phase boundaries in the single-layer quantum spin Hall insulator 1T'-WSe2 by means of scanning tunneling microscope tip pulses. We observe the formation of one-dimensional interfaces between topologically nontrivial 1T' domains having different rotational orientations, as well as induced interfaces between topologically nontrivial 1T' and topologically trivial 1H phases. Scanning tunneling spectroscopy measurements show that 1T'/1T' interface states are localized at domain boundaries, consistent with theoretically predicted unprotected interface modes that form dispersive bands in and around the energy gap of this quantum spin Hall insulator. We observe a qualitative difference in the experimental spectral line shape between topologically "unprotected" states at 1T'/1T' domain boundaries and protected states at 1T'/1H and 1T'/vacuum boundaries in single-layer WSe2.

Defect induced, layer-modulated magnetism in ultrathin metallic PtSe2.

Defects are ubiquitous in solids and often introduce new properties that are absent in pristine materials. One of the opportunities offered by these crystal imperfections is an extrinsically induced long-range magnetic ordering1, a long-time subject of theoretical investigations1-3. Intrinsic, two-dimensional (2D) magnetic materials4-7 are attracting increasing attention for their unique properties, which include layer-dependent magnetism4 and electric field modulation6. Yet, to induce magnetism into otherwise non-magnetic 2D materials remains a challenge. Here we investigate magneto-transport properties of ultrathin PtSe2 crystals and demonstrate an unexpected magnetism. Our electrical measurements show the existence of either ferromagnetic or antiferromagnetic ground-state orderings that depends on the number of layers in this ultrathin material. The change in the device resistance on the application of a ~25 mT magnetic field is as high as 400 Ω with a magnetoresistance value of 5%. Our first-principles calculations suggest that surface magnetism induced by the presence of Pt vacancies and the Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange couplings across ultrathin films of PtSe2 are responsible for the observed layer-dependent magnetism. Given the existence of such unavoidable growth-related vacancies in 2D materials8,9, these findings can expand the range of 2D ferromagnets into materials that would otherwise be overlooked.

Picture of the wet electron: a localized transient state in liquid water.

A transient state of the excess electron in liquid water preceding the development of the solvation shell, the so-called wet electron, has been invoked to explain spectroscopic observations, but its binding energy and atomic structure have remained highly elusive. Here, we carry out hybrid functional molecular dynamics to unveil the ultrafast solvation mechanism leading to the hydrated electron. In the pre-hydrated regime, the electron is found to repeatedly switch between a quasi-free electron state in the conduction band and a localized state with a binding energy of 0.26 eV, which we assign to the wet electron. This transient state self-traps in a region of the liquid which extends up to ∼4.5 Šand involves a severe disruption of the hydrogen-bond network. Our picture provides an unprecedented view on the nature of the wet electron, which is instrumental to understanding the properties of this fundamental species in liquid water.

Electronic Properties of Transferable Atomically Thin MoSe2/h-BN Heterostructures Grown on Rh(111).

Vertically stacked two-dimensional (2D) heterostructures composed of 2D semiconductors have attracted great attention. Most of these include hexagonal boron nitride (h-BN) as either a substrate, an encapsulant, or a tunnel barrier. However, reliable synthesis of large-area and epitaxial 2D heterostructures incorporating BN remains challenging. Here, we demonstrate the epitaxial growth of nominal monolayer (ML) MoSe2 on h-BN/Rh(111) by molecular beam epitaxy, where the MoSe2/h-BN layer system can be transferred from the growth substrate onto SiO2. The valence band structure of ML MoSe2/h-BN/Rh(111) revealed by photoemission electron momentum microscopy ( kPEEM) shows that the valence band maximum located at the K point is 1.33 eV below the Fermi level ( EF), whereas the energy difference between K and Γ points is determined to be 0.23 eV, demonstrating that the electronic properties, such as the direct band gap and the effective mass of ML MoSe2, are well preserved in MoSe2/h-BN heterostructures.

Highly Oriented Atomically Thin Ambipolar MoSe2 Grown by Molecular Beam Epitaxy.

Transition metal dichalcogenides (TMDCs), together with other two-dimensional (2D) materials, have attracted great interest due to the unique optical and electrical properties of atomically thin layers. In order to fulfill their potential, developing large-area growth and understanding the properties of TMDCs have become crucial. Here, we have used molecular beam epitaxy (MBE) to grow atomically thin MoSe2 on GaAs(111)B. No intermediate compounds were detected at the interface of as-grown films. Careful optimization of the growth temperature can result in the growth of highly aligned films with only two possible crystalline orientations due to broken inversion symmetry. As-grown films can be transferred onto insulating substrates, allowing their optical and electrical properties to be probed. By using polymer electrolyte gating, we have achieved ambipolar transport in MBE-grown MoSe2. The temperature-dependent transport characteristics can be explained by the 2D variable-range hopping (2D-VRH) model, indicating that the transport is strongly limited by the disorder in the film.

Hydrogen on silicene: like or unlike graphene?

Hydrogenation of free-standing silicene, the two-dimensional allotrope of silicon, is investigated in detail using first-principles methods and compared with the adsorption of H atoms on graphene. Similarly to graphene, chemisorption of a single H atom on silicene induces the formation of a semilocalized state around the adatom, a sharp peak in the density of states at the Fermi level which acts as a strong resonant scatterer for charge carriers. This state hosts an unpaired electron, the itinerant electron of the resonating valence bond picture which primarily resides on the "majority" sublattice and biases the reactivity towards specific lattice positions. Contrary to graphene, sticking of hydrogen atoms is barrierless, on both the pristine and the hydrogenated surface. As a consequence, hydrogen adsorption on silicene is expected to proceed randomly under typical laboratory conditions, and preferential binding to form balanced dimers (or clusters) only occurs when thermodynamic equilibrium conditions prevail. The absence of clustering can be experimentally confirmed using scanning tunneling microscopy techniques since simulated imaging shows that the investigated structures provide distinguishable features that should allow their easy identification, if present on the surface. Overall, our findings can be rationalized by the fact that in silicene π bonds are weaker and the lattice is softer than in graphene and suggest that in silicene adatoms may severely limit carrier mobility.

Hydrogen adsorption on nitrogen and boron doped graphene.

Hydrogen adsorption on boron and nitrogen doped graphene is investigated in detail by means of first-principles calculations. A comprehensive study is performed of the structural, electronic, and magnetic properties of chemisorbed hydrogen atoms and atom pairs near the dopant sites. The main effect of the substitutional atoms is charge doping which is found to greatly affect the adsorption process by increasing the binding energy at the sites closest to the substitutional species. It is also found that doping does not induce magnetism despite the odd number of electrons per atom introduced by the foreign species, and that it quenches the paramagnetic response of chemisorbed H atoms on graphene. Overall, the effects are similar for B and N doping, with only minor differences in the adsorption energetics due to different sizes of the dopant atoms and the accompanying lattice distortions.