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.

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.

Highly sensitive and low-power consumption metalloporphyrin-based junctions for COx detection with excellent recovery.

The development of cost-effective and eco-friendly sensor materials is needed to realize the application of detectors in daily life-such as in the internet of things. In this regard, monitoring air pollutants such as carbon monoxide (CO) and carbon dioxide (CO2), mainly emitted by anthropogenic sources from daily human activities, is of great importance. In particular, developing a susceptible and portable CO2 sensor raises a dilemma because of the chemical inertness and non-polarity of CO2 molecules. We find that porphyrin-based materials, exploited by nature in biological systems, are a playground to search for such sensor materials. Using density functional non-equilibrium Green's function formalism, we fully screen all 3d metalloporphyrin (MPor) based devices to find efficient CO and CO2 gas sensors. Our detailed analysis of the adsorption energy, molecular orbitals, transmission spectra, sensitivity, and recovery time reveals that the nature of central M alters the efficiency of MPor gas detectors. We find that CO and CO2 can be monitored using, respectively, CoPor- and TiPor-based devices. The estimated sensitivity is around 100%, along with a fast recovery time at very low bias voltages (V ≥ 0.5 V), which turn metalloporphyrins into promising candidates for the widespread development of enhanced CO and CO2 sensors awaiting further experimental validations.

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.

Towards developing efficient metalloporphyrin-based hybrid photocatalysts for CO2 reduction; an ab initio study.

A series of thiophene-based donor-acceptor-donor (D-A-D) oligomer substituted metalloporphyrins (MPors) with different 3d central metal-ions (M = Co, Ni, Cu, and Zn) were systematically investigated to screen efficient hybrid photocatalysts for CO2 reduction based on density functional theory (DFT) and time-dependent DFT simulations. Compared with base MPors, the newly designed hybrid photocatalysts have a lower bandgap energy, stronger and broader absorption spectra, and enhanced intermolecular charge transfer, exciton lifetime, and light-harvesting efficiency. Then, the introduction of D-A-D electron donor (ED) groups into the meso-positions of MPors is a promising method for the construction of efficient photocatalysts. According to the calculated adsorption distance, adsorption energy, Hirshfeld charge and electrostatic potential analysis, it was revealed that CO2 physically adsorbed on the designed photocatalyst surface. In addition, among the studied model systems the ZnPor(ED)4 catalyst with four D-A-D electron donors exhibits the best photocatalytic performance due to its broadest absorption spectra with λmax = 500.12 nm and the highest adsorption energy of about 26 kJ mol-1. Finally, the sensing ability of the ZnPor(ED)4-based multi-terminal molecular junction for CO2 gas detection is determined using Green's functions. The transmission plots of this molecular junction are barely changed due to the physical adsorption of CO2 on the molecular surface, leading to the low sensitivity of the device. We believe that such a theoretical design can provide a general approach for further experimental and computational studies of photocatalysts used in the CO2 reduction process.

The CECAM electronic structure library and the modular software development paradigm.

First-principles electronic structure calculations are now accessible to a very large community of users across many disciplines, thanks to many successful software packages, some of which are described in this special issue. The traditional coding paradigm for such packages is monolithic, i.e., regardless of how modular its internal structure may be, the code is built independently from others, essentially from the compiler up, possibly with the exception of linear-algebra and message-passing libraries. This model has endured and been quite successful for decades. The successful evolution of the electronic structure methodology itself, however, has resulted in an increasing complexity and an ever longer list of features expected within all software packages, which implies a growing amount of replication between different packages, not only in the initial coding but, more importantly, every time a code needs to be re-engineered to adapt to the evolution of computer hardware architecture. The Electronic Structure Library (ESL) was initiated by CECAM (the European Centre for Atomic and Molecular Calculations) to catalyze a paradigm shift away from the monolithic model and promote modularization, with the ambition to extract common tasks from electronic structure codes and redesign them as open-source libraries available to everybody. Such libraries include "heavy-duty" ones that have the potential for a high degree of parallelization and adaptation to novel hardware within them, thereby separating the sophisticated computer science aspects of performance optimization and re-engineering from the computational science done by, e.g., physicists and chemists when implementing new ideas. We envisage that this modular paradigm will improve overall coding efficiency and enable specialists (whether they be computer scientists or computational scientists) to use their skills more effectively and will lead to a more dynamic evolution of software in the community as well as lower barriers to entry for new developers. The model comes with new challenges, though. The building and compilation of a code based on many interdependent libraries (and their versions) is a much more complex task than that of a code delivered in a single self-contained package. Here, we describe the state of the ESL, the different libraries it now contains, the short- and mid-term plans for further libraries, and the way the new challenges are faced. The ESL is a community initiative into which several pre-existing codes and their developers have contributed with their software and efforts, from which several codes are already benefiting, and which remains open to the community.

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.

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.

Large-scale tight-binding simulations of quantum transport in ballistic graphene.

Graphene has proven to host outstanding mesoscopic effects involving massless Dirac quasiparticles travelling ballistically resulting in the current flow exhibiting light-like behaviour. A new branch of 2D electronics inspired by the standard principles of optics is rapidly evolving, calling for a deeper understanding of transport in large-scale devices at a quantum level. Here we perform large-scale quantum transport calculations based on a tight-binding model of graphene and the non-equilibrium Green's function method and include the effects of p-n junctions of different shape, magnetic field, and absorptive regions acting as drains for current. We stress the importance of choosing absorbing boundary conditions in the calculations to correctly capture how current flows in the limit of infinite devices. As a specific application we present a fully quantum-mechanical framework for the '2D Dirac fermion microscope' recently proposed by Bøggild et al (2017 Nat. Commun. 8 10.1038), tackling several key electron-optical effects therein predicted via semiclassical trajectory simulations, such as electron beam collimation, deflection and scattering off Veselago dots. Our results confirm that a semiclassical approach to a large extend is sufficient to capture the main transport features in the mesoscopic limit and the optical regime, but also that a richer electron-optical landscape is to be expected when coherence or other purely quantum effects are accounted for in the simulations.

Simple and efficient LCAO basis sets for the diffuse states in carbon nanostructures.

We present a simple way to describe the lowest unoccupied diffuse states in carbon nanostructures in density functional theory calculations using a minimal LCAO (linear combination of atomic orbitals) basis set. By comparing plane wave basis calculations, we show how these states can be captured by adding long-range orbitals to the standard LCAO basis sets for the extreme cases of planar sp 2 (graphene) and curved carbon (C60). In particular, using Bessel functions with a long range as additional basis functions retain a minimal basis size. This provides a smaller and simpler atom-centered basis set compared to the standard pseudo-atomic orbitals (PAOs) with multiple polarization orbitals or by adding non-atom-centered states to the basis.

Unconventional Current Scaling and Edge Effects for Charge Transport through Molecular Clusters.

Metal-molecule-metal junctions are the key components of molecular electronics circuits. Gaining a microscopic understanding of their conducting properties is central to advancing the field. In the present contribution, we highlight the fundamental differences between single-molecule and ensemble junctions focusing on the fundamentals of transport through molecular clusters. In this way, we elucidate the collective behavior of parallel molecular wires, bridging the gap between single molecule and large-area monolayer electronics, where even in the latter case transport is usually dominated by finite-size islands. On the basis of first-principles charge-transport simulations, we explain why the scaling of the conductivity of a junction has to be distinctly nonlinear in the number of molecules it contains. Moreover, transport through molecular clusters is found to be highly inhomogeneous with pronounced edge effects determined by molecules in locally different electrostatic environments. These effects are most pronounced for comparably small clusters, but electrostatic considerations show that they prevail also for more extended systems.

Enhanced Cooperativity in Supported Spin-Crossover Metal-Organic Frameworks.

The impact of surface deposition on cooperativity is explored in Au(111)-supported self-assembled metal-organic frameworks (MOFs) based on Fe(II) ions. Using a thermodynamic model, we first demonstrate that dimensionality reduction combined with deposition on a metal surface is likely to deeply enhance the spin-crossover cooperativity, going from γ3D = 16 K for the bulk material to γ2Dsupp = 386 K for its 2D supported derivative. On the basis of density functional theory, we then elucidate the electronic structure of a promising Fe-based MOF. A chemical strategy is proposed to turn a weakly interacting magnetic system into a strongly cooperative spin-crossover monolayer with γMOFAu(111) = 83 K. These results open a promising route to the fabrication of cooperative materials based on SCO Fe(II) platforms.

A two-dimensional Dirac fermion microscope.

The electron microscope has been a powerful, highly versatile workhorse in the fields of material and surface science, micro and nanotechnology, biology and geology, for nearly 80 years. The advent of two-dimensional materials opens new possibilities for realizing an analogy to electron microscopy in the solid state. Here we provide a perspective view on how a two-dimensional (2D) Dirac fermion-based microscope can be realistically implemented and operated, using graphene as a vacuum chamber for ballistic electrons. We use semiclassical simulations to propose concrete architectures and design rules of 2D electron guns, deflectors, tunable lenses and various detectors. The simulations show how simple objects can be imaged with well-controlled and collimated in-plane beams consisting of relativistic charge carriers. Finally, we discuss the potential of such microscopes for investigating edges, terminations and defects, as well as interfaces, including external nanoscale structures such as adsorbed molecules, nanoparticles or quantum dots.

Field Effect in Graphene-Based van der Waals Heterostructures: Stacking Sequence Matters.

Stacked van der Waals (vdW) heterostructures where semiconducting two-dimensional (2D) materials are contacted by overlaid graphene electrodes enable atomically thin, flexible electronics. We use first-principles quantum transport simulations of graphene-contacted MoS2 devices to show how the transistor effect critically depends on the stacking configuration relative to the gate electrode. We can trace this behavior to the stacking-dependent response of the contact region to the capacitive electric field induced by the gate. The contact resistance is a central parameter and our observation establishes an important design rule for ultrathin devices based on 2D atomic crystals.

Manipulating the voltage drop in graphene nanojunctions using a gate potential.

Graphene is an attractive electrode material to contact nanostructures down to the molecular scale since it can be gated electrostatically. Gating can be used to control the doping and the energy level alignment in the nanojunction, thereby influencing its conductance. Here we investigate the impact of electrostatic gating in nanojunctions between graphene electrodes operating at finite bias. Using quantum transport simulations based on density functional theory, we show that the voltage drop across symmetric junctions changes dramatically and controllably in gated systems compared to non-gated junctions. In particular, for p-type(n-type) carriers the voltage drop is located close to the electrode with positive(negative) polarity, the potential of the junction is pinned to the negative(positive) electrode. We trace this behaviour back to the vanishing density of states of graphene in the proximity of the Dirac point. Due to the electrostatic gating, each electrode exposes different density of states in the bias window between the two different electrode Fermi energies, thereby leading to a non-symmetry in the voltage drop across the device. This selective pinning is found to be independent of device length when carriers are induced either by the gate or dopant atoms, indicating a general effect for electronic circuitry based on graphene electrodes. We envision this could be used to control the spatial distribution of Joule heating in graphene nanostructures, and possibly the chemical reaction rate around high potential gradients.