Electromigration Forces on Atoms on Graphene Nanoribbons: The Role of Adsorbate-Surface Bonding.

The synthesis of the two-dimensional (2D) material graphene and nanostructures derived from graphene has opened up an interdisciplinary field at the intersection of chemistry, physics, and materials science. In this field, it is an open question whether intuition derived from molecular or extended solid-state systems governs the physical properties of these materials. In this work, we study the electromigration force on atoms on 2D armchair graphene nanoribbons in an electric field using ab initio simulation techniques. Our findings show that the forces are related to the induced charges in the adsorbate-surface bonds rather than only to the induced atomic charges, and the left and right effective bond order can be used to predict the force direction. Focusing in particular on 3d transition metal atoms, we show how a simple model of a metal atom on benzene can explain the forces in an inorganic chemistry picture. This study demonstrates that atom migration on 2D surfaces in electric fields is governed by a picture that is different from the commonly used electrostatic description of a charged particle in an electric field as the underlying bonding and molecular orbital structure become relevant for the definition of electromigration forces. Accordingly extended models including the ligand field of the atoms might provide a better understanding of adsorbate diffusion on surfaces under nonequilibrium conditions.

Quantum Transport in Large-Scale Patterned Nitrogen-Doped Graphene.

It has recently been demonstrated how the nitrogen dopant concentration in graphene can be controlled spatially on the nano-meter scale using a molecular mask. This technique may be used to create ballistic electron optics-like structures of high/low doping regions; for example, to focus electron beams, harnessing the quantum wave nature of the electronic propagation. Here, we employ large-scale Greens function transport calculations based on a tight-binding approach. We first benchmark different tight-binding models of nitrogen in graphene with parameters based on density functional theory (DFT) and the virtual crystal approximation (VCA). Then, we study theoretically how the random distribution within the masked regions and the discreteness of the nitrogen scattering centers impact the transport behavior of sharp n-p and n-n' interfaces formed by different, realistic nitrogen concentrations. We investigate how constrictions for the current can be realized by patterned high/low doping regions with experimentally feasible nitrogen concentrations. The constrictions can guide the electronic current, while the quantized conductance is significantly washed out due to the nitrogen scattering. The implications for device design is that a p-n junction with nitrogen corrugation should still be viable for current focusing. Furthermore, a guiding channel with less nitrogen in the conducting canal preserves more features of quantized conductance and, therefore, its low-noise regime.

Mach-Zehnder-like interferometry with graphene nanoribbon networks.

We study theoretically electron interference in a Mach-Zehnder-like geometry formed by four zigzag graphene nanoribbons 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 eight-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.

Enhancement of Graphene Phonon Excitation by a Chemically Engineered Molecular Resonance.

The abstraction of pyrrolic hydrogen from a single phthalocyanine on graphene turns the molecule into a sensitive probe for graphene phonons. The inelastic electron transport measured with a scanning tunneling microscope across the molecular adsorbate and graphene becomes strongly enhanced for a graphene out-of-plane acoustic phonon mode. Supporting density functional and transport calculations elucidate the underlying physical mechanism. A molecular orbital resonance close to the Fermi energy controls the inelastic current while specific phonon modes of graphene are magnified due to their coupling to symmetry-equivalent vibrational quanta of the molecule.

Molecular Bridge Engineering for Tuning Quantum Electronic Transport and Anisotropy in Nanoporous Graphene.

Recent advances on surface-assisted synthesis have demonstrated that arrays of nanometer wide graphene nanoribbons can be laterally coupled with atomic precision to give rise to a highly anisotropic nanoporous graphene structure. Electronically, this graphene nanoarchitecture can be conceived as a set of weakly coupled semiconducting 1D nanochannels with electron propagation characterized by substantial interchannel quantum interferences. Here, we report the synthesis of a new nanoporous graphene structure where the interribbon electronic coupling can be controlled by the different degrees of freedom provided by phenylene bridges that couple the conducting channels. This versatility arises from the multiplicity of phenylene cross-coupling configurations, which provides a robust chemical knob, and from the interphenyl twist angle that acts as a fine-tunable knob. The twist angle is significantly altered by the interaction with the substrate, as confirmed by a combined bond-resolved scanning tunneling microscopy (STM) and ab initio analysis, and should accordingly be addressable by other external stimuli. Electron propagation simulations demonstrate the capability of either switching on/off or modulating the interribbon coupling by the corresponding use of the chemical or the conformational knob. Molecular bridges therefore emerge as efficient tools to engineer quantum transport and anisotropy in carbon-based 2D nanoarchitectures.

Characterization and Manipulation of Intervalley Scattering Induced by an Individual Monovacancy in Graphene.

Intervalley scattering involves microscopic processes that electrons are scattered by atomic-scale defects on the nanoscale. Although central to our understanding of electronic properties of materials, direct characterization and manipulation of range and strength of the intervalley scattering induced by an individual atomic defect have so far been elusive. Using scanning tunneling microscope, we visualize and control intervalley scattering from an individual monovacancy in graphene. By directly imaging the affected range of monovacancy-induced intervalley scattering, we demonstrate that it is inversely proportional to the energy; i.e., it is proportional to the wavelength of massless Dirac fermions. A giant electron-hole asymmetry of the intervalley scattering is observed because the monovacancy is charged. By further charging the monovacancy, the bended electronic potential around the monovacancy softens the scattering potential, which, consequently, suppresses the intervalley scattering of the monovacancy.

Negative Differential Resistance in Spin-Crossover Molecular Devices.

We demonstrate, based on low-temperature scanning tunneling microscopy (STM) and spectroscopy, a pronounced negative differential resistance (NDR) in spin-crossover (SCO) molecular devices, where a FeII SCO molecule is deposited on surfaces. The STM measurements reveal that the NDR is robust with respect to substrate materials, temperature, and the number of SCO layers. This indicates that the NDR is intrinsically related to the electronic structure of the SCO molecule. Experimental results are supported by density functional theory (DFT) with nonequilibrium Green's function (NEGF) calculations and a generic theoretical model. While the DFT+NEGF calculations reproduce NDR for a special atomically sharp STM tip, the effect is attributed to the energy-dependent tip density of states rather than the molecule itself. We, therefore, propose a Coulomb blockade model involving three molecular orbitals with very different spatial localization as suggested by the molecular electronic structure.

Proposal for All-Electrical Spin Manipulation and Detection for a Single Molecule on Boron-Substituted Graphene.

All-electrical writing and reading of spin states attract considerable attention for their promising applications in energy-efficient spintronics devices. Here we show, based on rigorous first-principles calculations, that the spin properties can be manipulated and detected in molecular spinterfaces, where an iron tetraphenyl porphyrin (FeTPP) molecule is deposited on boron-substituted graphene (BG). Notably, a reversible spin switching between the S=1 and S=3/2 states is achieved by a gate electrode. We can trace the origin to a strong hybridization between the Fe-d_{z^{2}} and B-p_{z} orbitals. Combining density functional theory with nonequilibrium Green's function formalism, we propose an experimentally feasible three-terminal setup to probe the spin state. Furthermore, we show how the in-plane quantum transport for the BG, which is non-spin polarized, can be modified by FeTPP, yielding a significant transport spin polarization near the Fermi energy (>10% for typical coverage). Our work paves the way to realize all-electrical spintronics devices using molecular spinterfaces.

Spin-Polarizing Electron Beam Splitter from Crossed Graphene Nanoribbons.

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.

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.

Acetylene-Mediated Electron Transport in Nanostructured Graphene and Hexagonal Boron Nitride.

The discovery of graphene has catalyzed the search for other 2D carbon allotropes, such as graphynes, graphdiynes, and 2D π-conjugated polymers, which have been theoretically predicted or experimentally synthesized during the past decade. These materials exhibit a conductive nature bound to their π-conjugated sp2 electronic system. Some cases include sp-hybridized moieties in their nanostructure, such as acetylenes in graphynes; however, these act merely as electronic couplers between the conducting π-orbitals of sp2 centers. Herein, via first-principles calculations and quantum transport simulations, we demonstrate the existence of an acetylene-meditated transport mechanism entirely hosted by sp-hybridized orbitals. For that we propose a series of nanostructured 2D materials featuring linear arrangements of closely packed acetylene units which function as sp-nanowires. Because of the very distinct nature of this unique transport mechanism, it appears to be highly complementary with π-conjugation, thus potentially becoming a key tool for future carbon nanoelectronics.

Intraconfigurational Transition due to Surface-Induced Symmetry Breaking in Noncovalently Bonded Molecules.

The interaction of molecules with surfaces plays a crucial role in the electronic and chemical properties of supported molecules and needs a comprehensive description of interfacial effects. Here, we unveil the effect of the substrate on the electronic configuration of iron porphyrin molecules on Au(111) and graphene, and we provide a physical picture of the molecule-surface interaction. We show that the frontier orbitals derive from different electronic states depending on the substrate. The origin of this difference comes from molecule-substrate orbital selective coupling caused by reduced symmetry and interaction with the substrate. The weak interaction on graphene keeps a ground state configuration close to the gas phase, while the stronger interaction on gold stabilizes another electronic solution. Our findings reveal the origin of the energy redistribution of molecular states for noncovalently bonded molecules on surfaces.

Siesta: Recent developments and applications.

A review of the present status, recent enhancements, and applicability of the Siesta program is presented. Since its debut in the mid-1990s, Siesta's flexibility, efficiency, and free distribution have given advanced materials simulation capabilities to many groups worldwide. The core methodological scheme of Siesta combines finite-support pseudo-atomic orbitals as basis sets, norm-conserving pseudopotentials, and a real-space grid for the representation of charge density and potentials and the computation of their associated matrix elements. Here, we describe the more recent implementations on top of that core scheme, which include full spin-orbit interaction, non-repeated and multiple-contact ballistic electron transport, density functional theory (DFT)+U and hybrid functionals, time-dependent DFT, novel reduced-scaling solvers, density-functional perturbation theory, efficient van der Waals non-local density functionals, and enhanced molecular-dynamics options. In addition, a substantial effort has been made in enhancing interoperability and interfacing with other codes and utilities, such as wannier90 and the second-principles modeling it can be used for, an AiiDA plugin for workflow automatization, interface to Lua for steering Siesta runs, and various post-processing utilities. Siesta has also been engaged in the Electronic Structure Library effort from its inception, which has allowed the sharing of various low-level libraries, as well as data standards and support for them, particularly the PSeudopotential Markup Language definition and library for transferable pseudopotentials, and the interface to the ELectronic Structure Infrastructure library of solvers. Code sharing is made easier by the new open-source licensing model of the program. This review also presents examples of application of the capabilities of the code, as well as a view of on-going and future developments.

QuantumATK: an integrated platform of electronic and atomic-scale modelling tools.

QuantumATK is an integrated set of atomic-scale modelling tools developed since 2003 by professional software engineers in collaboration with academic researchers. While different aspects and individual modules of the platform have been previously presented, the purpose of this paper is to give a general overview of the platform. The QuantumATK simulation engines enable electronic-structure calculations using density functional theory or tight-binding model Hamiltonians, and also offers bonded or reactive empirical force fields in many different parametrizations. Density functional theory is implemented using either a plane-wave basis or expansion of electronic states in a linear combination of atomic orbitals. The platform includes a long list of advanced modules, including Green's-function methods for electron transport simulations and surface calculations, first-principles electron-phonon and electron-photon couplings, simulation of atomic-scale heat transport, ion dynamics, spintronics, optical properties of materials, static polarization, and more. Seamless integration of the different simulation engines into a common platform allows for easy combination of different simulation methods into complex workflows. Besides giving a general overview and presenting a number of implementation details not previously published, we also present four different application examples. These are calculations of the phonon-limited mobility of Cu, Ag and Au, electron transport in a gated 2D device, multi-model simulation of lithium ion drift through a battery cathode in an external electric field, and electronic-structure calculations of the composition-dependent band gap of SiGe alloys.

Graphene-Subgrain-Defined Oxidation of Copper.

The correlation between the crystal structure of chemical vapor deposition (CVD)-grown graphene and the crystal structure of the Cu growth substrate and their mutual effect on the oxidation of the underlying Cu are systematically explored. We report that natural oxygen or water intercalation along the graphene-Cu interface results in an orientation-dependent oxidation rate of the Cu surface, particularly noticeable for bicrystal graphene domains on the same copper grain, suggesting that the relative crystal orientation of subgrains determines the degree of Cu oxidation. Atomistic force field calculations support these observations, showing that graphene domains have preferential alignment with the Cu(111) with a smaller average height above the global Cu surface as compared to intermediate orientations, and that this is the origin of the heterogeneous oxidation rate of Cu. This work demonstrates that the natural oxidation resistance of Cu coated by graphene is highly dependent on the crystal orientation and lattice alignment of Cu and graphene, which is key information for engineering the interface configuration of the graphene-Cu system for specific functionalities in mechanical, anticorrosion, and electrical applications of CVD-grown graphene.

Nonequilibrium Bond Forces in Single-Molecule Junctions.

Passing a current across two touching C60 molecules imposes a nonequilibrium population of bonding and antibonding molecular orbitals, which changes the equilibrium bond character and strength. A current-induced bond force therefore contributes to the total force at chemical-bond distances. The combination of first-principles calculations with scanning probe experiments exploring currents and forces in a wide C60-C60 distance range consistently evidences the presence of current-induced attraction that occurs when the two molecules are on the verge of forming a chemical bond. The unique opportunity to arrange matter at the atomic scale with the atomic force and scanning tunneling microscope tip has enabled closely matching molecular junctions in theory and experiment. The findings consequently represent the first report of current-induced bond forces at the single-molecule level and further elucidate the intimate relation between charge transport and force. The results are relevant to molecular electronics and chemical reactions in the presence of a current.

Quantum Interference Engineering of Nanoporous Graphene for Carbon Nanocircuitry.

Bottom-up prepared carbon nanostructures appear as promising platforms for future carbon-based nanoelectronics due to their atomically precise and versatile structure. An important breakthrough is the recent preparation of nanoporous graphene (NPG) as an ordered covalent array of graphene nanoribbons (GNRs). Within NPG, the GNRs may be thought of as 1D electronic nanochannels through which electrons preferentially move, highlighting NPG's potential for carbon nanocircuitry. However, the π-conjugated bonds bridging the GNRs give rise to electronic crosstalk between the individual 1D channels, leading to spatially dispersing electronic currents. Here, we propose a chemical design of the bridges resulting in destructive quantum interference, which blocks the crosstalk between GNRs in NPG, electronically isolating them. Our multiscale calculations reveal that injected currents can remain confined within a single, 0.7 nm wide, GNR channel for distances as long as 100 nm. The concepts developed in this work thus provide an important ingredient for the quantum design of future carbon nanocircuitry.

Multi-scale approach to first-principles electron transport beyond 100 nm.

Multi-scale computational approaches are important for studies of novel, low-dimensional electronic devices since they are able to capture the different length-scales involved in the device operation, and at the same time describe critical parts such as surfaces, defects, interfaces, gates, and applied bias, on a atomistic, quantum-chemical level. Here we present a multi-scale method which enables calculations of electronic currents in two-dimensional devices larger than 100 nm2, where multiple perturbed regions described by density functional theory (DFT) are embedded into an extended unperturbed region described by a DFT-parametrized tight-binding model. We explain the details of the method, provide examples, and point out the main challenges regarding its practical implementation. Finally we apply it to study current propagation in pristine, defected and nanoporous graphene devices, injected by chemically accurate contacts simulating scanning tunneling microscopy probes.

Electron Transport in Nanoporous Graphene: Probing the Talbot Effect.

Electrons in graphene can show diffraction and interference phenomena fully analogous to light thanks to their Dirac-like energy dispersion. However, it is not clear how this optical analogy persists in nanostructured graphene, for example, with pores. Nanoporous graphene (NPG) consisting of linked graphene nanoribbons has recently been fabricated using molecular precursors and bottom-up assembly (Moreno et al. Science 2018, 360, 199). We predict that electrons propagating in NPG exhibit the interference Talbot effect, analogous to photons in coupled waveguides. Our results are obtained by parameter-free atomistic calculations of real-sized NPG samples based on seamlessly integrated density functional theory and tight-binding regions. We link the origins of this interference phenomenon to the band structure of the NPG. Most importantly, we demonstrate how the Talbot effect may be detected experimentally using dual-probe scanning tunneling microscopy. Talbot interference of electron waves in NPG or other related materials may open up new opportunities for future quantum electronics, computing, or sensing.

Stacked Janus Device Concepts: Abrupt pn-Junctions and Cross-Plane Channels.

Janus transition metal dichalcogenides with a built-in structural cross-plane (cp) asymmetry have recently emerged as a new class of two-dimensional materials with a large cp dipole. Using first-principles calculations, and a tailored transport method, we demonstrate that stacking graphene and MoSSe Janus structures result in record high homogeneous doping of graphene and abrupt, atomically thin, cross-plane pn-junctions. We show how graphene in contrast to metals can act as electrodes to Janus stacks without screening the cp dipole and predict a large photocurrent response dominated by a cp transport channel in a few-layer stacked device. The photocurrent is above that of a corresponding thin-film silicon device illustrating the great potential of Janus stacks, for example, in photovoltaic devices.