Bandgap opening in graphene antidot lattices: the missing half

The Covalent Functionalization of Surface-Supported Graphene: An Update

In the last decade, the use of graphene supported on solid surfaces has broadened its scope and applications, and graphene has acquire a promising role as a major component of high-performance electronic devices. In this context, the chemical modification of graphene has become essential. In particular, covalent modification offers key benefits, including controllability, stability, and the facility to be integrated into manufacturing operations. In this Review, we critically comment on the latest advances in the covalent modification of supported graphene on substrates. We analyze the different chemical modifications with special attention to radical reactions. In this context, we review the latest achievements in reactivity control, tailoring electronic properties, and introducing active functionalities. Finally, we extended our analysis to other emerging 2D materials supported on surfaces, such as transition metal dichalcogenides, transition metal oxides, and elemental analogs of graphene.

Strain effects in the electron orbital coupling and electric structure of graphene

Graphene is not only a very strong two-dimensional material, but is also able to sustain reversible tensile elastic strain larger than 20%, which yields an interesting possibility to regulate the properties of graphene by applied strain. We have investigated the strain effects in the electron orbital coupling and electric structure of graphene adopting the density functional theory. We found that the Fermi level of graphene is elevated by compressive strain and degraded by tensile strain. But uniaxial strain can give rise to the symmetry breaking of graphene and open the band gap. Furthermore, the tensile uniaxial strain is more beneficial to the band gap opening than the compressive uniaxial strain when the uniaxial strain is perpendicular to the C-C bond, but the compressive uniaxial strain is more than the tensile uniaxial strain when the uniaxial strain is parallel to the C-C bond. Second, the symmetry breaking of graphene resulting from uniaxial strain can be illustrated in that the uniaxial strain weakens the electron orbital coupling of graphene between p_x and p_y orbitals and brings about the splitting of the peak of the p_z orbital density of states (DOS) on the left side of the Fermi level. Finally, whether uniaxial or biaxial strain, the compressive strain widens the pseudogap of graphene and the tensile strain narrows it. This would be useful for greatly broadening its applications in nanoelectronics and optoelectronics.

Local current analysis on defective zigzag graphene nanoribbons devices for biosensor material applications

In this contribution, we aim at investigating the mechanism of biosensing in graphene-based materials from first principles. Inspired by recent experiments, we construct an atomistic model composed of a pyrene molecule serving as a linker fragment, which is used in experiment to attach certain aptamers, and a defective zigzag graphene nanoribbons (ZGNRs). Density functional theory including dispersive interaction is employed to study the energetics of the linker absorption on the defective ZGNRs. Combining non-equilibrium Green's function and the Landauer formalism, the total current-bias voltage dependence through the device is evaluated. Modifying the distance between the linker molecule and the nanojunction plane reveals a quantitative change in the total current-bias voltage dependence, which correlates to the experimental measurements. In order to illuminate the geometric origin of these variation observed in the considered systems, the local currents through the device are investigated using the method originally introduced by Evers and co-workers. In our new implementation, the numerical efficiency is improved by applying sparse matrix storage and spectral filtering techniques, without compromising the resolution of the local currents. Local current density maps qualitatively demonstrate the local variation of the interference between the linker molecule and the nanojunction plane.

Effect of pore-size disorder on the electronic properties of semiconducting graphene nanomeshes

Graphene nanomeshes (GNMs) are novel materials that recently raised a lot of interest. They are fabricated by forming a lattice of pores in graphene. Depending on the pore size and pore lattice constant, GNMs can be either semimetallic or semiconducting with a gap large enough (∼ 0.5 eV) to be considered for transistor applications. The fabrication process is bound to produce some structural disorder due to variations in pore size. Recent electronic transport measurements in GNM devices (ACS Appl. Mater. Interfaces 10, 10 362, 2018) show a degradation of their bandgap in devices having pore-size disorder. It is therefore important to understand the effect of such variability on the electronic properties of semiconducting GNMs. In this work we use the density functional-based tight binding formalism to calculate the electronic properties of GNM structures with different pore sizes, pore densities, and with hydrogen and oxygen pore edge passivations. We find that structural disorder reduces the electronic gap and the carrier group velocity, which may interpret recent transport measurements in GNM devices. Furthermore, the trend of the bandgap with structural disorder is not significantly affected by the change in pore edge passivation. Our results show that even with structural disorder, GNMs are still attractive from a transistor device perspective.

A new photodetector structure based on graphene nanomeshes: an ab initio study

Recent experiments suggest graphene-based materials as candidates in future electronic and optoelectronic devices. In this paper, we propose to investigate new photodetectors based on graphene nanomeshes (GNMs). Density functional theory (DFT) calculations are performed to gain insight into electronic and optical characteristics of various GNM structures. To investigate the device-level properties of GNMs, their current-voltage characteristics are explored by DFT-based tight-binding (DFTB) in combination with non-equilibrium Green's function (NEGF) methods. Band structure analysis shows that GNMs have both metallic and semiconducting properties depending on the arrangements of perforations. Also, absorption spectrum analysis indicates attractive infrared peaks for GNMs with semiconducting characteristics, making them better photodetectors than graphene nanoribbon (GNR)-based alternatives. The results suggest that GNMs can be potentially used in mid-infrared detectors with specific detectivity values that are 100-fold that of graphene-based devices and 1000-fold that of GNR-based devices. Hence, the special properties of graphene combined with the quantum feathers of the perforation makes it suitable for optical devices.

Photoresponse in a Strain-Induced Graphene Wrinkle Superlattice

Applied strain introduces significant changes in the carbon-carbon bond of graphene and thereby forms electronic superlattices. The electron/phonon coupling and existence of pseudogauge fields within these superlattices render unique electronic and magnetism properties. However, the interfacial interactions between strained and pristine graphene have rarely been studied. Herein, we report a prominent increase in photocurrent at the interface between pristine graphene and the strain-induced superlattice (i.e., the graphene wrinkle). The photocurrent distribution indicates a large increase in the bending lattice of graphene. These results demonstrate that the photocurrent enhancement is due to the difference in the Seebeck coefficient between pristine graphene and deformed superlattices, resulting in a significant increase in the photothermoelectric effect at the interface.

Conductance Tunable Suspended Graphene Nanomesh by Helium Ion Beam Milling

This paper demonstrates that the electrical properties of suspended graphene nanomesh (GNM) can be tuned by systematically changing the porosity with helium ion beam milling (HIBM). The porosity of the GNM is well-controlled by defining the pitch of the periodic nanopores. The defective region surrounding the individual nanopores after HIBM, which limits the minimum pitch achievable between nanopores for a certain dose, is investigated and reported. The exponential relationship between the thermal activation energy (E_A) and the porosity is found in the GNM devices. Good E_A tuneability observed from the GNMs provides a new approach to the transport gap engineering beyond the conventional nanoribbon method.

PbE (E = S, Se) Colloidal Quantum Dot-Layered 2D Material Hybrid Photodetectors

Hybrid lead chalcogenide (PbE) (E = S, Se) quantum dot (QD)-layered 2D systems are an emerging class of photodetectors with unique potential to expand the range of current technologies and easily integrate into current complementary metal-oxide-semiconductor (CMOS)-compatible architectures. Herein, we review recent advancements in hybrid PbE QD-layered 2D photodetectors and place them in the context of key findings from studies of charge transport in layered 2D materials and QD films that provide lessons to be applied to the hybrid system. Photodetectors utilizing a range of layered 2D materials including graphene and transition metal dichalcogenides sensitized with PbE QDs in various device architectures are presented. Figures of merit such as responsivity (R) and detectivity (D*) are reviewed for a multitude of devices in order to compare detector performance. Finally, a look to the future considers possible avenues for future device development, including potential new materials and device treatment/fabrication options.

Generating pure spin current with spin-dependent Seebeck effect in ferromagnetic zigzag graphene nanoribbons

Pure spin current is of great importance in spintronics and may be achieved by spin dependent Seebeck effect (SDSE) in magnetic systems. Zigzag-edged graphene nanoribbons (ZGNRs) are very well-known 2D magnetic nanostructures. However, perfect and pristine ZGNRs either in the anti-ferromagnetic ground state or in the ferromagnetic (FM) state are not capable of producing pure spin current by SDSE at low temperature. In this work, by density functional theory calculations, we propose a scheme for generating pure spin current using SDSE in FM-ZGNRs by introducing antidots. Specifically, by creating a hexagonal antidot with either armchair edges or zigzag edges in the scattering region, we can get finite Seebeck thermopower for both spin channels with opposite signs, leading to the opposite flow directions of the two spin channels. The mechanism is well explained by the cooperation of the varying localization features of states around the Fermi level and the antidot induced scattering potential. By slightly tuning the chemical potential, pure spin current can be achieved. The size and edge shape effects have also been systematically studied. The findings indicate a novel scheme for thermally generating pure spin current in zigzag graphene nanoribbons and may find important application in graphene based spintronics.

Recent Advances in 2D Lateral Heterostructures

Recent developments in synthesis and nanofabrication technologies offer the tantalizing prospect of realizing various applications from two-dimensional (2D) materials. A revolutionary development is to flexibly construct many different kinds of heterostructures with a diversity of 2D materials. These 2D heterostructures play an important role in semiconductor and condensed matter physics studies and are promising candidates for new device designs in the fields of integrated circuits and quantum sciences. Theoretical and experimental studies have focused on both vertical and lateral 2D heterostructures; the lateral heterostructures are considered to be easier for planner integration and exhibit unique electronic and photoelectronic properties. In this review, we give a summary of the properties of lateral heterostructures with homogeneous junction and heterogeneous junction, where the homogeneous junctions have the same host materials and the heterogeneous junctions are combined with different materials. Afterward, we discuss the applications and experimental synthesis of lateral 2D heterostructures. Moreover, a perspective on lateral 2D heterostructures is given at the end.

Graphene and graphene nanomesh supported nickel clusters: electronic, magnetic, and hydrogen storage properties

Small-sized nanoparticles are widely used in applications such as catalysis, nanoelectronics, and hydrogen storage. However, the small size causes a common problem: agglomeration on the support template. One solution is to use templates that limit the mobility of the nanoparticles. Graphene nanomeshes (GNMs) are two dimensional porous structures with controllably passivated pores. In this work, we employ first principles calculations to investigate the potential for using GNMs as support templates for Ni clusters and, at the same time, study their magnetic and hydrogen storage properties. We consider two Ni clusters (Ni₆ and Ni₁₃) and two GNMs (O-terminated and N-terminated), comparing our results to those of isolated Ni clusters and those of Ni clusters on graphene. High stability of the Ni clusters is found on the N-GNM in contrast to the O-GNM. We quantify the hydrogen storage capacity by calculating the adsorption energy for multiple H₂ molecules. The values on Ni _x /N-GNM are significantly reduced as compared to the corresponding isolated Ni _x clusters, but a high hydrogen storage capacity is maintained. The fact that Ni _x /N-GNM hosts spin polarization is interesting for spintronic applications.

Bandgap scaling and negative differential resistance behavior of zigzag phosphorene antidot nanoribbons (ZPANRs)

This work examines the prospect of phosphorene antidot nanoribbons (PANRs) using the density functional based tight binding (DFTB) method. Horizontally perforated PANRs with both armchair (A) and zigzag (Z) configurations were considered for electrical simulations. Our simulation results found that the APANRs cannot be scaled down with nanoribbon width, whereas ZPANRs can be scaled easily. Bandgap scaling in terms of ribbon width, length and antidot number was thoroughly analyzed for ZPANRs. In the end, a two-terminal device was constructed and transmission analysis was performed using the non-equilibrium Green's function (NEGF) methodology. A negative differential resistance (NDR) region appeared in the current-voltage characteristics of the ZPANRs, which paved a pathway for nano-device application.

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.

Structurally Controlled Large-Area 10 nm Pitch Graphene Nanomesh by Focused Helium Ion Beam Milling

Graphene nanomesh (GNM) is formed by patterning graphene with nanometer-scale pores separated by narrow necks. GNMs are of interest due to their potential semiconducting characteristics when quantum confinement in the necks leads to an energy gap opening. GNMs also have potential for use in phonon control and water filtration. Furthermore, physical phenomena, such as spin qubit, are predicted at pitches below 10 nm fabricated with precise structural control. Current GNM patterning techniques suffer from either large dimensions or a lack of structural control. This work establishes reliable GNM patterning with a sub-10 nm pitch and an < 4 nm pore diameter by the direct helium ion beam milling of suspended monolayer graphene. Due to the simplicity of the method, no postpatterning processing is required. Electrical transport measurements reveal an effective energy gap opening of up to ∼450 meV. The reported technique combines the highest resolution with structural control and opens a path toward GNM-based, room-temperature semiconducting applications.

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.

Detection of Multiconfigurational States of Hydrogen-Passivated Silicene Nanoclusters

Utilizing density functional theory (DFT) and a complete active space self-consistent field (CASSCF) approach,we study the electronic properties of rectangular silicene nano clusters with hydrogen passivated edges denoted by H-SiNCs (n_z,n_a), with n_z and n_a representing the zigzag and armchair directions, respectively. The results show that in the n_z direction, the H-SiNCs prefer to be in a singlet (S = 0) ground state for n_z > n_a. However, a transition from a singlet (S = 0) to a triplet (S = 1) ground state is revealed for n_a > n_z. Through the calculated Raman spectrum, the S = 0 and S = 1 ground states can be observed by the E_2g (G) and A (D) Raman modes. Furthermore, H-SiNC clusters are shown to have HOMO-LUMO (HL) energy gaps, which decrease as a function of n_a and n_z for S = 0 and S = 1 states. The H-SiNC with a S = 1 ground state can be potentially used for silicene-based spintronic devices.

Tunable Dirac cones in two-dimensional covalent organic materials: C2N6S3 and its analogs

C₂N₆S₃ sustains a biaxial tensile strain up to 24% and its Fermi velocity can be tuned by biaxial strain.

Online Determination of Graphene Lattice Orientation Through Lateral Forces

Rapid progress in graphene engineering has called for a simple and effective method to determine the lattice orientation on graphene before tailoring graphene to the desired edge structures and shapes. In this work, a wavelet transform-based frequency identification method is developed to distinguish the lattice orientation of graphene. The lattice orientation is determined through the different distribution of the frequency power spectrum just from a single scan line. This method is proven both theoretically and experimentally to be useful and controllable. The results at the atomic scale show that the frequencies vary with the lattice orientation of graphene. Thus, an adjusted angle to the desired lattice orientation (zigzag or armchair) can easily be calculated based on the frequency obtained from the single scan line. Ultimately, these results will play a critical role in wafer-size graphene engineering and in the manufacturing of graphene-based nanodevices.

Strain engineering of graphene: a review

Graphene has intrigued the science community by many unique properties not found in conventional materials. In particular, it is the strongest two-dimensional material ever measured, being able to sustain reversible tensile elastic strain larger than 20%, which yields an interesting possibility to tune the properties of graphene by strain and thus opens a new field called "straintronics". In this article, the current progress in the strain engineering of graphene is reviewed. We first summarize the strain effects on the electronic structure and Raman spectra of graphene. We then highlight the electron-phonon coupling greatly enhanced by the biaxial strain and the strong pseudomagnetic field induced by the non-uniform strain with specific distribution. Finally, the potential application of strain-engineering in the self-assembly of foreign atoms on the graphene surface is also discussed. Given the short history of graphene straintronics research, the current progress has been notable, and many further advances in this field are expected.

Organic Covalent Patterning of Nanostructured Graphene with Selectivity at the Atomic Level

Organic covalent functionalization of graphene with long-range periodicity is highly desirable-it is anticipated to provide control over its electronic, optical, or magnetic properties-and remarkably challenging. In this work we describe a method for the covalent modification of graphene with strict spatial periodicity at the nanometer scale. The periodic landscape is provided by a single monolayer of graphene grown on Ru(0001) that presents a moiré pattern due to the mismatch between the carbon and ruthenium hexagonal lattices. The moiré contains periodically arranged areas where the graphene-ruthenium interaction is enhanced and shows higher chemical reactivity. This phenomenon is demonstrated by the attachment of cyanomethyl radicals (CH2CN(•)) produced by homolytic breaking of acetonitrile (CH3CN), which is shown to present a nearly complete selectivity (>98%) binding covalently to graphene on specific atomic sites. This method can be extended to other organic nitriles, paving the way for the attachment of functional molecules.

Hexagonal Boron Nitride-Graphene Heterostructures: Synthesis and Interfacial Properties

Research on in-plane and vertically-stacked heterostructures of graphene and hexagonal boron nitride (h-BN) have attracted intense attentions for energy band engineering and device performance optimization of graphene. In this review article, recent advances in the controlled syntheses, interfacial structures, and electronic properties, as well as novel device constructions of h-BN and graphene heterostructures are highlighted. Firstly, diverse synthesis approaches for in-plane h-BN and graphene (h-BN-G) heterostructures are reviewed, and their applications in nanoelectronics are briefly introduced. Moreover, the interfacial structures and electronic properties of h-BN-G heterojunctions are discussed, and a zigzag type interface is found to preferentially evolve at the linking edge of the two structural analogues. Secondly, several synthetic routes for the vertically-stacked graphene/h-BN (G/h-BN) heterostructures are also reviewed. The role of h-BN as perfect dielectric layers in promoting the device performance of graphene is presented. Finally, future research directions in the synthesis and application of such heterostructures are discussed.

Bilayered graphene as a platform of nanostructures with folded edge holes

The stability and the electronic properties of new AB-stacking and moiré bilayer graphene superlattices with closed edge nanoholes are studied using DFT calculations.

Surface-catalyzed C-C covalent coupling strategies toward the synthesis of low-dimensional carbon-based nanostructures

Carbon-based nanostructures have attracted tremendous interest because of their versatile and tunable properties, which depend on the bonding type of the constituting carbon atoms. Graphene, as the most prominent representative of the π-conjugated carbon-based materials, consists entirely of sp(2)-hybridized carbon atoms and exhibits a zero band gap. Recently, countless efforts were made to open and tune the band gap of graphene for its applications in semiconductor devices. One promising method is periodic perforation, resulting in a graphene nanomesh (GNM), which opens the band gap while maintaining the exceptional transport properties. However, the typically employed lithographic approach for graphene perforation is difficult to control at the atomic level. The complementary bottom-up method using surface-assisted carbon-carbon (C-C) covalent coupling between organic molecules has opened up new possibilities for atomically precise fabrication of conjugated nanostructures like GNM and graphene nanoribbons (GNR), although with limited maturity. A general drawback of the bottom-up approach is that the desired structure usually does not represent the global thermodynamic minimum. It is therefore impossible to improve the long-range order by postannealing, because once the C-C bond formation becomes reversible, graphene as the thermodynamically most stable structure will be formed. This means that only carefully chosen precursors and reaction conditions can lead to the desired (non-graphene) material. One of the most popular and frequently used organic reactions for on-surface C-C coupling is the Ullmann reaction of aromatic halides. While experimentally simple to perform, the irreversibility of the C-C bond formation makes it a challenge to obtain long-range ordered nanostructures. With no postreaction structural improvement possible, the assembly process must be optimized to result in defect-free nanostructures during the initial reaction, requiring complete reaction of the precursors in the right positions. Incomplete connections typically result when mobile precursor monomers are blocked from reaching unsaturated reaction sites of the preformed nanostructures. For example, monomers may not be able to reach a randomly formed internal cavity of a two-dimensional (2D) nanostructure island due to steric hindrance in 2D confinement, leaving reaction sites in the internal cavity unsaturated. Wrong connections between precursor monomers, here defined as intermolecular C-C bonds forcing the monomer into a nonideal position within the structure, are usually irreversible and can induce further structural defects. The relative conformational flexibility of the monomer backbones permits connections between deformed monomers when they encounter strong steric hindrance. This, however, usually leads to heterogeneous structural motifs in the formed nanostructures. This Account reviews some of the latest developments regarding on-surface C-C coupling strategies toward the synthesis of carbon-based nanostructures by addressing the above-mentioned issues. The strategies include Ullmann coupling and other, "cleaner" alternative C-C coupling reactions like Glaser coupling, cyclo-dehydrogenation, and dehydrogenative coupling. The choice of substrate materials and precursor designs is crucial for optimizing substrate reactivity and precursor diffusion rates, and to reduce events of wrong linkage. Hierarchical polymerization is employed to steer the coupling route, which effectively improves the completeness of the reaction. Effects of byproducts on nanostructure formation is comprehended with both experimental and theoretical studies.

The formation mechanism of multiple vacancies and amorphous graphene under electron irradiation

The evolution of multiple vacancies (Vns) in graphene under electron irradiation (EI) was explored systematically by long time non-equilibrium molecular dynamics simulations, with n varying from 4 to 40. The simulations showed that the Vns form haeckelites in the case with small n, while forming holes as n increases. The scale of the haeckelites, characterized by the number of pentagon-heptagon pairs, grows linearly with n. Such a linear relationship can be interpreted as a consequence of compensating the missing area, caused by the Vns, in order to maintain the area of the perfect sp(2) network by self-healing. Beyond that, the scale of the haeckelite vs. the density of missing atoms is predicted to be Sh ∼ 6Dn, where Sh and Dn are the percentage of non-hexagonal rings and missing atoms, respectively. This study provides an intuitive picture of the formation of amorphous graphene under EI and the quantitative understanding of the mechanism.

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.

The rare two-dimensional materials with Dirac cones

Inspired by the great development of graphene, more and more research has been conducted to seek new two-dimensional (2D) materials with Dirac cones. Although 2D Dirac materials possess many novel properties and physics, they are rare compared with the numerous 2D materials. To provide explanation for the rarity of 2D Dirac materials as well as clues in searching for new Dirac systems, here we review the recent theoretical aspects of various 2D Dirac materials, including graphene, silicene, germanene, graphynes, several boron and carbon sheets, transition-metal oxides (VO2)n/(TiO2)m and (CrO2)n/(TiO2)m, organic and organometallic crystals, so-MoS2, and artificial lattices (electron gases and ultracold atoms). Their structural and electronic properties are summarized. We also investigate how Dirac points emerge, move, and merge in these systems. The von Neumann–Wigner theorem is used to explain the scarcity of Dirac cones in 2D systems, which leads to rigorous requirements on the symmetry, parameters, Fermi level, and band overlap of materials to achieve Dirac cones. Connections between existence of Dirac cones and the structural features are also discussed.

Graphene nanomesh: new versatile materials

Graphene, an atomic-scale honeycomb crystal lattice, is increasingly becoming popular because of its excellent mechanical, electrical, chemical, and physical properties. However, its zero bandgap places restrictions on its applications in field-effect transistors (FETs). Graphene nanomesh (GNM), a new graphene nanostructure with a tunable bandgap, shows more excellent performance. It can be widely applied in electronic or photonic devices such as highly sensitive biosensors, new generation of spintronics and energy materials. These illustrate significant opportunities for the industrial use of GNM, and hence they push nanoscience and nanotechnology one step toward practical applications. This review briefly describes the current status of the design, synthesis, and potential applications of GNM. Finally, the perspectives and challenges of GNM development are presented and some suggestions are made for its further development and exploration.

Dirac model of electronic transport in graphene antidot barriers

In order to use graphene for semiconductor applications, such as transistors with high on/off ratios, a band gap must be introduced into this otherwise semimetallic material. A promising method of achieving a band gap is by introducing nanoscale perforations (antidots) in a periodic pattern, known as a graphene antidot lattice (GAL). A graphene antidot barrier (GAB) can be made by introducing a 1D GAL strip in an otherwise pristine sheet of graphene. In this paper, we will use the Dirac equation (DE) with a spatially varying mass term to calculate the electronic transport through such structures. Our approach is much more general than previous attempts to use the Dirac equation to calculate scattering of Dirac electrons on antidots. The advantage of using the DE is that the computational time is scale invariant and our method may therefore be used to calculate properties of arbitrarily large structures. We show that the results of our Dirac model are in quantitative agreement with tight-binding for hexagonal antidots with armchair edges. Furthermore, for a wide range of structures, we verify that a relatively narrow GAB, with only a few antidots in the unit cell, is sufficient to give rise to a transport gap.

Plasmon-phonon coupling in large-area graphene dot and antidot arrays fabricated by nanosphere lithography

Nanostructured graphene on SiO2 substrates paves the way for enhanced light-matter interactions and explorations of strong plasmon-phonon hybridization in the mid-infrared regime. Unprecedented large-area graphene nanodot and antidot optical arrays are fabricated by nanosphere lithography, with structural control down to the sub-100 nm regime. The interaction between graphene plasmon modes and the substrate phonons is experimentally demonstrated, and structural control is used to map out the hybridization of plasmons and phonons, showing coupling energies of the order 20 meV. Our findings are further supported by theoretical calculations and numerical simulations.

Electronic and optical properties of silicene nanomeshes

We have investigated the electronic and optical properties of silicene nanomeshes (SNMs) using first-principle calculations.

Inverse relationship between carrier mobility and bandgap in graphene

A frequently stated advantage of gapless graphene is its high carrier mobility. However, when a nonzero bandgap is opened, the mobility drops dramatically. The hardness to achieve high mobility and large on∕off ratio simultaneously limits the development of graphene electronics. To explore the underlying mechanism, we investigated the intrinsic mobility of armchair graphene nanoribbons (AGNRs) under phonon scattering by combining first-principles calculations and a tight-binding analysis. A linear dependence of the effective mass on bandgap was demonstrated to be responsible for the inverse mobility-gap relationship. The deformation-potential constant was found to be determined by the strain dependence of the Fermi energy and the bandgap, resulting in two mobility branches, and is essential for the high mobility of AGNRs. In addition, we showed that the transport polarity of AGNRs can be switched by applying a uniaxial strain.

Toward single-layer uniform hexagonal boron nitride-graphene patchworks with zigzag linking edges

The atomic layer of hybridized hexagonal boron nitride (h-BN) and graphene has attracted a great deal of attention after the pioneering work of P. M. Ajayan et al. on Cu foils because of their unusual electronic properties (Ci, L. J.; et al. Nat. Mater. 2010, 9, 430-435). However, many fundamental issues are still not clear, including the in-plane atomic continuity as well as the edge type at the boundary of hybridized h-BN and graphene domains. To clarify these issues, we have successfully grown a perfect single-layer h-BN-graphene (BNC) patchwork on a selected Rh(111) substrate, via a two-step patching growth approach. With the ideal sample, we convinced that at the in-plane linking interface, graphene and h-BN can be linked perfectly at an atomic scale. More importantly, we found that zigzag linking edges were preferably formed, as demonstrated by atomic-scale scanning tunneling microscopy images, which was also theoretically verified using density functional theory calculations. We believe the experimental and theoretical works are of particular importance to obtain a fundamental understanding of the BNC hybrid and to establish a deliberate structural control targeting high-performance electronic and spintronic devices.

Widely tunable carrier mobility of boron nitride-embedded graphene

The carrier transport in boron nitride-embedded graphene (BNG) is studied using density functional theory coupled with the Boltzmann transport equation. Under a phonon scattering mechanism, the intrinsic carrier mobility of BNG at room temperature is tunable from 1.7 × 10(3) to 1.1 × 10(5) cm(2) V(-1) s(-1) when the bandgap is between 0.38 and 1.39 eV. Some specific BNG materials even show ultrahigh mobility up to 6.6 × 10(6) cm(2) V(-1) s(-1) , and the transport polarity (whether it is electron or hole transport) can be tailored by the application of a uniaxial strain. The wide mobility variation of BNG is attributed to the dependence of the effective mass and the deformation potential constant on the carbon concentration and width. The results indicate that BNG can have both a large on-off ratio and high carrier mobility and is thus a promising material for electronic devices.

Universal rule on chirality-dependent bandgaps in graphene antidot lattices

Graphene with periodically patterned antidots has attracted intense research attention as it represents a facile route to open a bandgap for graphene electronics. However, not all graphene antidot lattices (GALs) can open a bandgap and a guiding rule is missing. Here, through systematic first-principles calculations, it is found that bandgaps in triangular GALs are surprisingly well defined by a chirality vector R = n a1 + ma2 connecting two neighboring antidots, where a1 and a2 are the basis vectors of graphene. The bandgap opens in the GALs with (n-m)mod3 = 0 but remains closed in those with (n-m)mod3 = ±1, reminiscent of the gap-chirality rule in carbon nanotubes. Remarkably, the gap value in GALs allows ample modulation by adjusting the length of chirality vectors, shape and size of the antidots. The gap-chirality relation in GALs stems from the chirality-dependent atomic structures of GALs as revealed by a super-atom model as well as Clar sextet analyses. This chirality-dependent bandgap is further shown to be a generic behavior in any parallelogram GAL and thus serves as an essential stepping stone for experimenters to realize graphene devices by antidot engineering.

Photo-induced free radical modification of graphene

Graphene has stimulated enormous interest due to its intriguing structure and fascinating properties. The extremely high carrier mobility, mechanical flexibility, and optical transparency as well as the versatility for band structure engineering make graphene a promising candidate for next-generation carbon-based electronic devices. Graphene chemistry, the covalent functionalization of graphene as a 2D giant molecule, offers a promising direction to controllably tailor its properties through the introduction of various chemical decorations. One of the great challenges for graphene functionalization originates from its strong chemical stability, thus highly reactive chemical species are needed as the reactants. In recent years, novel photochemical approaches have been developed to achieve efficient graphene modification and bandgap modulation, following a general concept of "Photochemical Bandgap Engineering of Graphene". In this article, such kinds of photochemical graphene engineering are demonstrated, together with a brief discussion on the future directions, challenges, and opportunities in this fascinating research area.

Influence of edge imperfections on the transport behavior of graphene nanomeshes

The electronic and transport properties of graphene nanomeshes (GNMs) were investigated using the density-functional theory and the non-equilibrium Green's function method. Our research indicates that the edge imperfections, such as edge roughness and edge doping, are of vital importance to the transport properties of GNMs. While the tunneling between the localized states caused by edge roughness would result in the metallic transport behavior of intrinsic GNMs, the experimentally observed semiconducting behavior could be explained by p-doping of GNMs with oxygen-containing groups. Furthermore, we found that the balance between the density of localized edge states and that of the edge O-doping is the key to the semiconductor behavior of GNMs. Unfortunately, the small density of edge states would lead to an ultra-low yield of semiconductor GNMs.

Bandgap opening by patterning graphene

Owing to its remarkable electronic and transport properties, graphene has great potential of replacing silicon for next-generation electronics and optoelectronics; but its zero bandgap associated with Dirac fermions prevents such applications. Among numerous attempts to create semiconducting graphene, periodic patterning using defects, passivation, doping, nanoscale perforation, etc., is particularly promising and has been realized experimentally. However, despite extensive theoretical investigations, the precise role of periodic modulations on electronic structures of graphene remains elusive. Here we employ both the tight-binding modeling and first-principles electronic structure calculations to show that the appearance of bandgap in patterned graphene has a geometric symmetry origin. Thus the analytic rule of gap-opening by patterning graphene is derived, which indicates that if a modified graphene is a semiconductor, its two corresponding carbon nanotubes, whose chiral vectors equal graphene's supercell lattice vectors, are both semimetals.