Universal rule on chirality-dependent bandgaps in graphene antidot lattices

Chirality in porous self-assembled monolayer networks at liquid/solid interfaces: induction, reversion, recognition and transfer

Chirality in two dimensions (2D) has attracted increasing attention with regard to interesting fundamental aspects as well as potential applications. This article reports several aspects of supramolecular chirality control as exemplified by self-assembled monolayer networks (SAMNs) formed by a class of chiral building blocks consisting of a triangular conjugated core and alkoxy chains on the periphery. It highlights 2D chirality induction phenomena through a classic "sergeants-and-soldiers" mechanism, in which the inducer is incorporated into a network component, as well as through a "supramolecular host-guest" mechanism, in which the inducer is entrapped in the porous space, leading to counterintuitive chirality reversal. Stereochemical control can be extended to three dimensions too, based on interlayer hydrogen bonding of the same class of building blocks bearing hydroxy groups, exhibiting diastereospecific bilayer formation at both single molecule level and supramolecular level arising from orientation between the top and bottom layers. Finally, we showcase that homochiral SAMNs can also be used as templates for the grafting of in situ generated aryl radicals, by covalent bond formation to the basal graphitic surface, thereby yielding topologically chiral functionalized graphite, and thus extending the potential of chiral SAMNs.

Electric field effect in bilayered graphene nanomeshes

The effect of applying an external electric field on the electronic properties of nanoporous bilayered graphene is reported. Such an effect was demonstrated on bilayered graphene structures with various types of stacking and relative arrangements of nanopores. The direct-indirect band gap transformation combined with significant changes of electronic band structure behavior was predicted. The obtained effects are of significant importance for further engineering the optical properties of such materials and open new prospects for using nanoporous bilayered graphene in electronic and optoelectronic device applications.

Graphene Foam: Hole-Flake Network for Uniaxial Supercompression and Recovery Behavior

We employed the coarse-grained molecular dynamics simulation method to systematically study the uniaxial supercompression and recovery behavior of multiporous graphene foam, in which a mesoscopic three-dimensional network with hole-graphene flakes was proposed. The network model not only considers the physical cross-links and interlayer van der Waals interactions, but also introduces a hole in the flake to approach the imperfection of pristine graphene and the hierarchical porous configuration of real foam material. We first recreated a typical two-stage supercompression stress-strain relationship and the corresponding time-dependent recovery as well as a U-type nominal Poisson ratio. Then the recovery unloading at different strains and multicycle compression-uncompression were both conducted; the initial elastic moduli in the multicycles were found to be the same, and a multilevel residual strain was disclosed. Importantly, the residual strain is not exactly the plastic one, part of which can resurrect in the subsequent loading-unloading-holding. The mesoscopic mechanism of viscoelastic and residual deformation for the recovery can be attributed to the van der Waals repulsion and mechanical interlocking among the hole-flakes; interestingly, the local tensile stress was observed in the virial stress distribution. Particularly, an abnormal turning point in the length-time curve for the mean bead-bond length was captured during the supercompression. After the point, the length abnormally increases for different size ratios of the hole to the flake, which is in line with the mesostructure evolution. The finding may provide a mesoscopic criterion for the supercompression of graphene foam related materials.

Interfacial engineering in graphene bandgap

Graphene exhibits superior mechanical strength, high thermal conductivity, strong light-matter interactions, and, in particular, exceptional electronic properties. These merits make graphene an outstanding material for numerous potential applications. However, a graphene-based high-performance transistor, which is the most appealing application, has not yet been produced, which is mainly due to the absence of an intrinsic electronic bandgap in this material. Therefore, bandgap opening in graphene is urgently needed, and great efforts have been made regarding this topic over the past decade. In this review article, we summarise recent theoretical and experimental advances in interfacial engineering to achieve bandgap opening. These developments are divided into two categories: chemical engineering and physical engineering. Chemical engineering is usually destructive to the pristine graphene lattice via chemical functionalization, the introduction of defects, doping, chemical bonds with substrates, and quantum confinement; the latter largely maintains the atomic structure of graphene intact and includes the application of an external field, interactions with substrates, physical adsorption, strain, electron many-body effects and spin-orbit coupling. Although these pioneering works have not met all the requirements for electronic applications of graphene at once, they hold great promise in this direction and may eventually lead to future applications of graphene in semiconductor electronics and beyond.

Periodic Arrays of Phosphorene Nanopores as Antidot Lattices with Tunable Properties

A tunable band gap in phosphorene extends its applicability in nanoelectronic and optoelectronic applications. Here, we propose to tune the band gap in phosphorene by patterning antidot lattices, which are periodic arrays of holes or nanopores etched in the material, and by exploiting quantum confinement in the corresponding nanoconstrictions. We fabricated antidot lattices with radii down to 13 nm in few-layer black phosphorus flakes protected by an oxide layer and observed suppression of the in-plane phonon modes relative to the unmodified material via Raman spectroscopy. In contrast to graphene antidots, the Raman peak positions in few-layer BP antidots are unchanged, in agreement with predicted power spectra. We also use DFT calculations to predict the electronic properties of phosphorene antidot lattices and observe a band gap scaling consistent with quantum confinement effects. Deviations are attributed primarily to self-passivating edge morphologies, where each phosphorus atom has the same number of bonds per atom as the pristine material so that no dopants can saturate dangling bonds. Quantum confinement is stronger for the zigzag edge nanoconstrictions between the holes as compared to those with armchair edges, resulting in a roughly bimodal band gap distribution. Interestingly, in two of the antidot structures an unreported self-passivating reconstruction of the zigzag edge endows the systems with a metallic component. The experimental demonstration of antidots and the theoretical results provide motivation to further scale down nanofabrication of antidots in the few-nanometer size regime, where quantum confinement is particularly important.

Interrelation of Aromaticity and Conductivity of Graphene Dots/Antidots and Related Nanostructures

It is illustrated and computationally verified by ab initio density functional theory and simple but powerful order-of-magnitude arguments, based on deformation energy ΔE_def in relation to the uncertainty principle, that the conductivity and aromaticity of graphene and graphene-based structures, such as graphene dots, antidots, and nanoribbons, are negatively interrelated for π aromatic structures, in agreement with recent experimental data. However, for σ aromaticity, the interrelation could be positive, especially for extended periodic structures. We predict that the conductivity of rectangular graphene dots and antidots, is anisotropic with much larger magnitude along the direction perpendicular to the zigzag edges, compared to the conductivity in direction parallel to them. The same is true for the polarizability and electron mobility. This is directly connected with the much higher aromaticity around the armchair edges compared to the aromaticity near the zigzag edges. Furthermore, contrary to what would be expected on the basis of simple arguments for defect states, we predict that antidot patterning could significantly improve the conductivity (sometimes by 1 order of magnitude) in one or both directions, depending on their number, arrangement, and passivation. For narrow atomically precise armchair nanoribbons (AGNRs) of finite length, both conductivity and energy gaps are dominated by lateral and longitudinal quantum confinement, which decrease with increasing length (for a given width), leading to a peculiar behavior of monotonically increasing "maximum conductivity" as the band gaps monotonically decrease. The electron distribution at the band edges of the AGNRs, in agreement with recent experimental data are well-localized at the zigzag edges. Using the concept of gap-determining LUMO-HOMO frontier states to avoid HOMOs and LUMOs localized at the zigzag edges, we can predict with very high accuracy the recently measured band gaps of AGNRs of widths N = 7 and N = 13. Both the smallest (10^-3-10^-4[Formula: see text]) and the largest (a few 2[Formula: see text]) calculated values of conductance and conductivity for the smaller structures and the larger nanographenes, respectively, are in full accord with the corresponding experimental values of single-molecule junction conductance and the measured minimum conductivity of graphene at 1.6 K.

Tunable electronic and magnetic properties of two-dimensional materials and their one-dimensional derivatives

Low‐dimensional materials exhibit many exceptional properties and functionalities which can be efficiently tuned by externally applied force or fields. Here we review the current status of research on tuning the electronic and magnetic properties of low‐dimensional carbon, boron nitride, metal‐dichalcogenides, phosphorene nanomaterials by applied engineering strain, external electric field and interaction with substrates, etc, with particular focus on the progress of computational methods and studies. We highlight the similarities and differences of the property modulation among one‐ and two‐dimensional nanomaterials. Recent breakthroughs in experimental demonstration of the tunable functionalities in typical nanostructures are also presented. Finally, prospective and challenges for applying the tunable properties into functional devices are discussed. WIREs Comput Mol Sci 2016, 6:324–350. doi: 10.1002/wcms.1251

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Conflict of interest: The authors have declared no conflicts of interest for this article.

Symmetry induced semimetal-semiconductor transition in doped graphene

Substitutional chemical doping is one way of introducing an electronic bandgap in otherwise semimetallic graphene. A small change in dopant arrangement can convert graphene from a semiconducting to a semimetallic state. Based on ab initio Density Functional Theory calculations, we discuss the electron structure of BN-doped graphene with Bravais and non-Bravais lattice-type defect patterns, identifying semiconducting/semimetallic configurations. Semimetallic behavior of graphene with non-Bravais lattice-type defect patterns can be explained by a phase cancellation in the scattering amplitude. Our investigation reveals for the first time that the symmetry of defect islands and the periodicity of defect modulation limit the phase cancellation which controls the semimetal-semiconductor transition in doped graphene.

Predicting Two-Dimensional Silicon Carbide Monolayers

Intrinsic semimetallicity of graphene and silicene largely limits their applications in functional devices. Mixing carbon and silicon atoms to form two-dimensional (2D) silicon carbide (SixC1-x) sheets is promising to overcome this issue. Using first-principles calculations combined with the cluster expansion method, we perform a comprehensive study on the thermodynamic stability and electronic properties of 2D SixC1-x monolayers with 0 ≤ x ≤ 1. Upon varying the silicon concentration, the 2D SixC1-x presents two distinct structural phases, a homogeneous phase with well dispersed Si (or C) atoms and an in-plane hybrid phase rich in SiC domains. While the in-plane hybrid structure shows uniform semiconducting properties with widely tunable band gap from 0 to 2.87 eV due to quantum confinement effect imposed by the SiC domains, the homogeneous structures can be semiconducting or remain semimetallic depending on a superlattice vector which dictates whether the sublattice symmetry is topologically broken. Moreover, we reveal a universal rule for describing the electronic properties of the homogeneous SixC1-x structures. These findings suggest that the 2D SixC1-x monolayers may present a new "family" of 2D materials, with a rich variety of properties for applications in electronics and optoelectronics.

Bandgap scaling in bilayer graphene antidot lattices

On the basis of a tight binding model we reveal how the bandgap in bilayer graphene antidot lattices (GALs) follows a different scaling law than in monolayer GALs and we provide an explanation using the Dirac model. We show that previous findings regarding the criteria for the appearance of a bandgap in monolayer GALs are equally applicable to the bilayer case. Furthermore, we briefly investigate the optical properties of bilayer GALs and show that estimates of the bandgap using optical methods could lead to overestimates due to weak oscillator strength of the lowest transitions. Finally, we investigate the effect of imposing an electric field perpendicular to the bilayer GAL structure and find that the bandgap tunability may be extended as compared to pristine bilayer graphene.

Silicene nanomesh

Similar to graphene, zero band gap limits the application of silicene in nanoelectronics despite of its high carrier mobility. By using first-principles calculations, we reveal that a band gap is opened in silicene nanomesh (SNM) when the width W of the wall between the neighboring holes is even. The size of the band gap increases with the reduced W and has a simple relation with the ratio of the removed Si atom and the total Si atom numbers of silicene. Quantum transport simulation reveals that the sub-10 nm single-gated SNM field effect transistors show excellent performance at zero temperature but such a performance is greatly degraded at room temperature.

Dirac point movement and topological phase transition in patterned graphene

The honeycomb lattice of graphene is characterized by linear dispersion and pseudospin chirality of fermions on the Dirac cones. If lattice anisotropy is introduced, the Dirac cones stay intact but move in reciprocal space. Dirac point movement can lead to a topological transition from semimetal to semiconductor when two inequivalent Dirac points merge, an idea that has attracted significant research interest. However, such movement normally requires unrealistically high lattice anisotropy. Here we show that anisotropic defects can break the C3 symmetry of graphene, leading to Dirac point drift in the Brillouin zone. Additionally, the long-range order in periodically patterned graphene can induce intervalley scattering between two inequivalent Dirac points, resulting in a semimetal-to-insulator topological phase transition. The magnitude and direction of Dirac point drift are predicted analytically, which are consistent with our first-principles electronic structure calculations. Thus, periodically patterned graphene can be used to study the fascinating physics associated with Dirac point movement and the corresponding phase transition.

With the same Clar formulas, do the two-dimensional sandwich nanostructures X-Cr-X (X = C4H, NC3 and BC3) behave similarly?

The "perturbation" effects (i.e. hyperconjugation, electronegativity, and conjugation) on the structural, electronic, and magnetic properties of three kinds of two-dimensional (2D) X-Cr-X (X = C4H, NC3 and BC3 monolayers) sandwich nanostructures were systematically investigated by means of spin-polarized density functional theory (DFT) computations. Although all these 2D sandwich systems energetically prefer the same structural pattern and are featured with the same Clar formulas, their electronic and magnetic properties are significantly influenced by the "perturbations". Especially, a very strong π conjugation through the vacant p orbital of the B atom in BC3 leads to its sandwich structure with antiferromagnetic and conducting characters, which are in stark contrast to the non-magnetic and semiconducting characters of C4H-Cr-C4H and NC3-Cr-NC3. These findings reveal that simple counting Clar formulas alone are insufficient to fully understand the electronic and magnetic properties of graphene-related materials, and more attention should be given to such "perturbation" effects.