Controlling energy gap of bilayer graphene by strain

Manipulating 2D Materials through Strain Engineering

This review explores the growing interest in 2D layered materials, such as graphene, h-BN, transition metal dichalcogenides (TMDs), and black phosphorus (BP), with a specific focus on recent advances in strain engineering. Both experimental and theoretical results are delved into, highlighting the potential of strain to modulate physical properties, thereby enhancing device performance. Various strain engineering methods are summarized, and the impact of strain on the electrical, optical, magnetic, thermal, and valleytronic properties of 2D materials is thoroughly examined. Finally, the review concludes by addressing potential applications and challenges in utilizing strain engineering for functional devices, offering valuable insights for further research and applications in optoelectronics, thermionics, and spintronics.

Nanocarbon-based sensors for the structural health monitoring of smart biocomposites

Structural health monitoring (SHM) is a critical aspect of ensuring the safety and durability of smart biocomposite materials used as multifunctional materials. Smart biocomposites are composed of renewable or biodegradable materials and have emerged as eco-friendly alternatives of traditional non-biodegradable glass fiber-based composite materials. Although biocomposites exhibit fascinating properties and many desirable traits, real-time and early stage SHM is the most challenging issue to enable their long-term use. Smart biocomposites are integrated with sensors for in situ identification of the progress of damage and composite failure. The sensitivity of such smart biocomposites is a key functionality, which can be tuned by the introduction of an appropriate filler. In particular, nanocarbons hold promising potential to be incorporated in SHM applications of biocomposites. This review focused on the potential applications of nanocarbons in SHM of biocomposites. The aspects related to fabrication techniques and working mechanism of sensors are comprehensively discussed. Furthermore, their unique mechanical and electrical properties and sustainable nature ensure seamless integration into biocomposites, allowing for real-time monitoring without compromising the material's properties. These sensors offer multi-parameter sensing capabilities, such as strain, pressure, humidity, temperature, and chemical exposure, allowing a comprehensive assessment of biocomposite health. Additionally, their durability and longevity in harsh conditions, along with wireless connectivity options, provide cost-effective and sustainable SHM solutions. As research in this field advances, ongoing efforts seek to enhance the sensitivity and selectivity of these sensors, optimizing their performance for real-world applications. This review highlights the significant advances, ongoing efforts to enhance the sensitivity and selectivity, and performance optimization of nanocarbon-based sensors along with their working mechanism in the field of SHM for smart biocomposites. The key challenges and future research perspectives facing the conversion of nanocarbons to smart biocomposites are also displayed.

Capping layer enabled controlled fragmentation of two-dimensional materials by cold drawing

Cold drawing, a well-established processing technique in the polymer industry, was recently revisited and discovered as an efficient material structuring method to create ordered patterns in composites consisting of both cold-drawable polymers and brittle target materials. Such a high-yield and low-cost manufacturing technique enables the large-scale fabrication of micro-ribbon structures for a wide range of functional materials, including two-dimensional (2D) layered materials. Compared to the abundant phenomenological results from experiments, however, the underlying mechanisms of this technique are not fully explored. Here, supported by experimental investigation, finite element calculations, and theoretical modeling, we systematically study the effect of a capping layer on the controlled fragmentation of 2D materials deposited on polymer substrates during the cold drawing. The capping layer is found to prevent the premature fracture of the 2D thin films during elastic deformation of the substrate, when a specific requirement proposed by the theoretical model is satisfied. Controlled fragmentation is enabled in the necking stage due to the protective effect of the capping layer, which also influences the size of the resulting fragments. Flexible and stretchable electrodes based on 2D material ribbons are fabricated to demonstrate the effectiveness of the proposed roadmap. This study gives an accurate understanding of interactions between 2D materials, polymer substrates, and capping layers during cold drawing, and offers guidance for potential applications such as flexible electronics.

One-Dimensional Moiré Physics and Chemistry in Heterostrained Bilayer Graphene

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

Strain-induced stacking transition in bilayer graphene

Strain, both naturally occurring and deliberately engineered, can have a considerable effect on the structural and electronic properties of 2D and layered materials. Uniaxial or biaxial heterostrain modifies the stacking arrangement of bilayer graphene (BLG) which subsequently influences the electronic structure of the bilayer. Here, we use density functional theory (DFT) calculations to investigate the interplay between an external applied heterostrain and the resulting stacking in BLG. We determine how a strain applied to one layer is transferred to a second, 'free' layer and at what critical strain the ground-state AB-stacking is disrupted. To overcome limitations introduced by periodic boundary conditions, we consider an approximate system consisting of an infinite graphene sheet and an armchair graphene nanoribbon. We find that above a critical strain of∼1%, it is energetically favourable for the free layer to be unstrained, indicating a transition between uniform AB-stacking and non-uniform mixed stacking. This is in agreement with a simple model estimate based on the individual energy contributions of strain and stacking effects. Our findings suggest that small levels of strain provide a platform to reversibly engineer stacking order and Moiré features in bilayers, providing a viable alternative to twistronics to engineer topological and exotic physical phenomena in such systems.

Defects Produced during Wet Transfer Affect the Electrical Properties of Graphene

Graphene has been widely used due to its excellent electrical, mechanical and chemical properties. Defects produced during its transfer process will seriously affect the performance of graphene devices. In this paper, single-layer graphene was transferred onto glass and silicon dioxide (SiO2) substrates by wet transfer technology, and the square resistances thereof were tested. Due to the different binding forces of the transferred graphene surfaces, there may have been pollutants present. PMMA residues, graphene laminations and other defects that occurred in the wet transfer process were analyzed by X-ray photoelectron spectroscopy and Raman spectroscopy. These defects influenced the square resistance of the produced graphene films, and of these defects, PMMA residue was the most influential; square resistance increased with increasing PMMA residue.

The Performance of Graphene-Enhanced THz Grating: Impact of the Gold Layer Imperfectness

We report the performance of a graphene-enhanced THz grating fabricated by depositing a gold layer on the femtosecond micromachined SiO₂ substrate. The morphology of the gold plated patterned substrate was studied by scanning electron microscopy (SEM) and atomic force microscopy (AFM), while the quality of the chemical vapor deposition (CVD) graphene was evaluated by Raman spectroscopy. The electromagnetic (EM) response of the metasurface comprising the graphene sheet and the gold plated substrate was studied by THz time domain spectroscopy in the 100 GHz–1 THz frequency range. We employed the finite elements method (FEM) to model the metasurface EM response by adjusting the ac conductivity of the gold layer covering the patterned SiO₂ substrate to reproduce the measured transmission/reflection spectra. The results of the numerical simulation reveal the impact of the imperfectness of the gold layer on the performance of the THz metasurface. The experimental results are well described in terms of the Drude–Smith model of metal conductivity that takes into account the anisotropic scattering of the carriers in thin metal films.

Graphene as a Piezoresistive Material in Strain Sensing Applications

High accuracy measurement of mechanical strain is critical and broadly practiced in several application areas including structural health monitoring, industrial process control, manufacturing, avionics and the automotive industry, to name a few. Strain sensors, otherwise known as strain gauges, are fueled by various nanomaterials, among which graphene has attracted great interest in recent years, due to its unique electro-mechanical characteristics. Graphene shows not only exceptional physical properties but also has remarkable mechanical properties, such as piezoresistivity, which makes it a perfect candidate for strain sensing applications. In the present review, we provide an in-depth overview of the latest studies focusing on graphene and its strain sensing mechanism along with various applications. We start by providing a description of the fundamental properties, synthesis techniques and characterization methods of graphene, and then build forward to the discussion of numerous types of graphene-based strain sensors with side-by-side tabular comparison in terms of figures-of-merit, including strain range and sensitivity, otherwise referred to as the gauge factor. We demonstrate the material synthesis, device fabrication and integration challenges for researchers to achieve both wide strain range and high sensitivity in graphene-based strain sensors. Last of all, several applications of graphene-based strain sensors for different purposes are described. All in all, the evolutionary process of graphene-based strain sensors in recent years, as well as the upcoming challenges and future directions for emerging studies are highlighted.

Electrorheological Fluids of GO/Graphene-Based Nanoplates

Due to their unique anisotropic morphology and properties, graphene-based materials have received extensive attention in the field of smart materials. Recent studies show that graphene-based materials have potential application as a dispersed phase to develop high-performance electrorheological (ER) fluids, a kind of smart suspension whose viscosity and viscoelastic properties can be adjusted by external electric fields. However, pure graphene is not suitable for use as the dispersed phase of ER fluids due to the electric short circuit caused by its high electrical conductivity under electric fields. However, graphene oxide (GO) and graphene-based composites are suitable for use as the dispersed phase of ER fluids and show significantly enhanced property. In this review, we look critically at the latest developments of ER fluids based on GO and graphene-based composites, including their preparation, electrically tunable ER property, and dispersed stability. The mechanism behind enhanced ER property is discussed according to dielectric spectrum analysis. Finally, we also propose the remaining challenges and possible developments for the future outlook in this field.

Strain-inducing photochemical chlorination of graphene nanoribbons on SiC (0001)

As different low-dimensional materials are sought to be incorporated into microelectronic devices, graphene integration is dependent on the development of band gap opening strategies. Amidst the different methods currently investigated, application of strain and use of electronic quantum confinement have shown promising results. In the present work, epitaxial graphene nanoribbons (GNR), formed by surface graphitization of SiC (0001) on crystalline step edges, were submitted to photochemical chlorination. The incorporation of Cl into the buffer layer underlying graphene increased the compressive uniaxial strain in the ribbons. Such method is a promising tool for tuning the band gap of GNRs.

Sizable Band Gap in Epitaxial Bilayer Graphene Induced by Silicene Intercalation

Opening a band gap in bilayer graphene (BLG) is of significance for potential applications in graphene-based electronic and photonic devices. Here, we report the generation of a sizable band gap in BLG by intercalating silicene between BLG and Ru substrate. We first grow high-quality Bernal-stacked BLG on Ru(0001) and then intercalate silicene to the interface between the BLG and Ru, which is confirmed by low-energy electron diffraction and scanning tunneling microscopy. Raman spectroscopy shows that the G and 2D peaks of the intercalated BLG are restored to the freestanding-BLG features. Angle-resolved photoelectron spectroscopy measurements show that a band gap of about 0.2 eV opens in the BLG. Density functional theory calculations indicate that the large-gap opening results from a cooperative contribution of the doping and rippling/strain in the BLG. This work provides insightful understanding on the mechanism of band gap opening in BLG and enhances the potential of graphene-based device development.

Molecular dynamics simulation on the formation and development of interlayer dislocations in bilayer graphene

Molecular dynamics simulations are used to study the formation and development of interlayer dislocations in bilayer graphene (BLG) subjected to uniaxial tension. Two different BLGs are employed for the simulation: armchair (AC-BLG) and zigzag (ZZ-BLG). The atomic-level strains are calculated and the parameter 'dislocation intensity' is introduced to identify the dislocations. The interlayer dislocation is found to start at the edge and propagate to the center. For AC-BLG, the dislocations arise successively with the increase of applied strain, and all dislocations have the same width. For ZZ-BLG, the first dislocation arises alone. After that, two dislocations with different widths appear together every time. The simulated dislocation widths are in good agreement with existing experimental results. Across every dislocation, there is a transition from AB stacking to AC stacking, or vice versa. When temperature is taken into account, the dislocation boundaries become indistinct and the formation of dislocations is postponed due to the existence of dispersive small slippages. Due to the disturbance of temperature, dislocations present reciprocating movement. These findings contribute to the understanding of interlayer dislocations in two-dimensional materials, and will enable the exploration of many more strain related fundamental science problems and application challenges.

Gate-tunable high magnetoresistance in monolayer Fe3GeTe2 spin valves

Here we design a monolayer Fe₃GeTe₂ spin-valve device by attaching two ends to ferromagnetic electrodes. A high magnetoresistance of ~ 390% is obtained and significantly increased to 450 ~ 510% after the gates are introduced.

Spin-layer locked gapless states in gated bilayer graphene

Gated bilayer graphene exhibits spin-degenerate gapless states with a topological character localized at stacking domain walls. These states allow for one-dimensional currents along the domain walls. We herein demonstrate that these topologically protected currents are spin-polarized and locked in a single layer when bilayer graphene contains stacking domain walls decorated with magnetic defects. The magnetic defects, which we model as π-vacancies, perturb the topological states but also lift their spin degeneracy. One gapless state survives the perturbation of these defects, and its spin polarization is largely localized in one layer. The spin-polarized current in the topological state flows in a single layer, and this finding suggests the possibility of effectively exploiting these states in spintronic applications.

Stress- and electric-field-induced band gap tuning in hexagonal boron phosphide layers

Two-dimensional hexagonal boron phosphide presents great potential in applications of electronics and optoelectronics due to its high carrier mobility and moderate band gap. In this work, we investigate the effect of stress and electric field on the electronic properties of hexagonal boron phosphide layers based on first-principles calculations. We find that both the band gap and the carrier effective masses of hexagonal boron phosphide monolayer gradually increase with stress from compression to tension. As for hexagonal boron phosphide bilayer with two stacking orders (AB_B-P and AB_B-B) upon applied electric field, the band gap monotonously increases with the enhancement of electric field for AB_B-P bilayer, while it undergoes a band gap closing and reopening process for AB_B-B bilayer. We employ the tight-binding model to explain the mechanism of different band gap variations of two stacking orders with electric field. Moreover, we discuss the band gap variation of hexagonal boron phosphide bilayer with combined effect of stress and electric field. The investigation here presents an insight into the effective manipulation towards the electronic properties of hexagonal boron phosphide, which will further enable the broader applications of the hexagonal boron phosphide in modern electronic and optoelectronic fields.

Strain engineering of the electronic and transport properties of monolayer tellurenyne

Two-dimensional (2D) materials exhibiting quality electronic properties such as suitable band gap, giant Rashba effect and high carrier mobility are essential for promising applications in electronics and spintronics. Strain engineering has been recognized as an effective strategy to engineer the atomic and electronic properties of 2D materials. Herein, based on density functional theory, we demonstrate that the electronic properties of tellurenyne can be tuned well by using uniaxial strain. We find that tellurenyne retains the unique noncovalent bond structure and exhibits good stability under the uniaxial strain. Meanwhile, the band gap of tellurenyne can be tuned to a large scale (0.33-1.18 eV and 0.73-1.27 eV under the uniaxial strain along and perpendicular to the chain direction, respectively). Under 10% tension strain along the chain direction, the Rashba constant reaches 2.96 eV Å, belonging to giant Rashba systems. More importantly, the hole mobility of tellurenyne along the chain direction reaches 1.1 × 105 cm2 V-1 s-1 under 10% tension strain along the chain direction, which is one order of magnitude larger than that of phosphorene. Therefore, these remarkable electronic properties of tellurenyne engineered by using strain indicate its potential applications in electronics and spintronics.

Bioinspired Pretextured Reduced Graphene Oxide Patterns with Multiscale Topographies for High-Performance Mechanosensors

Highly sensitive mechanical sensing is vital for the emerging field of skin mimicry and wearable healthcare systems. To date, it remains a big challenge to fabricate mechanosensors with both high sensitivity and a wide sensing range. In nature, slit sensilla are crack-shaped sensory organs of arachnids, which are highly sensitive to tiny external mechanical stimuli. Here, inspired by the geometry of slit sensilla, a concept is developed that pretextures reduced graphene oxide (RGO) nanocoating into multiscale topographies with agminated crumples and interlaced cracks (crumpled & cracked RGO) through an efficient and scalable mechanically driven process. Both the sensitivity and the workable range can be facilely tuned by adjusting the crack density. The resulting mechanosensor exhibits a comprehensive superior performance including high sensitivity (a gauge factor of 205 to 3256), a wide and tunable sensing range (from 0-40 to 0-180%), long-term stability (over 5000 cycles), and multiple sensing functions. Based on its excellent performances, the mechanosensor can be used as a wearable electronic to in situ monitor subtle physiological signals and vigorous body actions. The rationally designed crumpled & cracked RGO provides a promising platform for artificial electronic skin and portable healthcare systems.

Asymmetric 3D Elastic-Plastic Strain-Modulated Electron Energy Structure in Monolayer Graphene by Laser Shocking

Graphene has a great potential to replace silicon in prospective semiconductor industries due to its outstanding electronic and transport properties; nonetheless, its lack of energy bandgap is a substantial limitation for practical applications. To date, straining graphene to break its lattice symmetry is perhaps the most efficient approach toward realizing bandgap tunability in graphene. However, due to the weak lattice deformation induced by uniaxial or in-plane shear strain, most strained graphene studies have yielded bandgaps <1 eV. In this work, a modulated inhomogeneous local asymmetric elastic-plastic straining is reported that utilizes GPa-level laser shocking at a high strain rate (dε/dt) ≈ 10⁶ -10⁷ s^-1 , with excellent formability, inducing tunable bandgaps in graphene of up to 2.1 eV, as determined by scanning tunneling spectroscopy. High-resolution imaging and Raman spectroscopy reveal strain-induced modifications to the atomic and electronic structure in graphene and first-principles simulations predict the measured bandgap openings. Laser shock modulation of semimetallic graphene to a semiconducting material with controllable bandgap has the potential to benefit the electronic and optoelectronic industries.

Tunable band gap of graphyne-based homo- and hetero-structures by stacking sequences, strain and electric field

A comprehensive investigation was carried out on graphyne/graphyne (Gyne/Gyne), graphyne-like BN/graphyne-like BN (BNyne/BNyne) and graphyne/graphyne-like BN (Gyne/BNyne) bilayer structures using van der Waals (vdW)-corrected density functional theory. These bilayers exhibited distinct stacking-dependent characteristics in their ground state electronic structure and also had different responses to external strain and a vertical electric field. For the Gyne/Gyne and Gyne/BNyne bilayers, the application of biaxial tensile strain led to an increase in the band gap, while the application of biaxial compressive strain in addition to uniaxial strain, either under tension or compression, induced a reduction in the band gap. However, in the case of the BNyne/BNyne bilayer, the application of biaxial tensile strain led to a decrease in the band gap, but an increase in the band gap occurred under biaxial compressive strain, which could be explained by a change in the ionic nature of the B-N bonds. Under a vertical electric field, the band gaps of the homo-bilayers (Gyne/Gyne and BNyne/BNyne) decreased and were symmetrical. However, the hetero-bilayer (Gyne/BNyne) exhibited a decreased band gap under a positive electric field, but an almost constant band gap under a negative electric field. The physical origin of the band gap variation under an electric field was unraveled using energy-band theory. Our findings pave the way for experimental research and provide valuable insight into two-dimensional vdW layered structures for use in next generation flexible nanoelectronics and optoelectronic devices.

A Review of Current Development of Graphene Mechanics

Graphene, a two-dimensional carbon in honeycomb crystal with single-atom thickness, possesses extraordinary properties and fascinating applications. Graphene mechanics is very important, as it relates to the integrity and various nanomechanical behaviors including flexing, moving, rotating, vibrating, and even twisting of graphene. The relationship between the strain and stress plays an essential role in graphene mechanics. Strain can dramatically influence the electronic and optical properties, and could be utilized to engineering those properties. Furthermore, graphene with specific kinds of defects exhibit mechanical enhancements and thus the electronic enhancements. In this short review, we focus on the current development of graphene mechanics, including tension and compression, fracture, shearing, bending, friction, and dynamics properties of graphene from both experiments and numerical simulations. We also touch graphene derivatives, including graphane, graphone, graphyne, fluorographene, and graphene oxide, which carve some fancy mechanical properties out from graphene. Our review summarizes the current achievements of graphene mechanics, and then shows the future prospects.

The organic-2D transition metal dichalcogenide heterointerface

Since the first isolation of graphene, new classes of two-dimensional (2D) materials have offered fascinating platforms for fundamental science and technology explorations at the nanometer scale. In particular, 2D transition metal dichalcogenides (TMD) such as MoS2 and WSe2 have been intensely investigated due to their unique electronic and optical properties, including tunable optical bandgaps, direct-indirect bandgap crossover, strong spin-orbit coupling, etc., for next-generation flexible nanoelectronics and nanophotonics applications. On the other hand, organics have always been excellent materials for flexible electronics. A plethora of organic molecules, including donors, acceptors, and photosensitive molecules, can be synthesized using low cost and scalable procedures. Marrying the fields of organics and 2D TMDs will bring benefits that are not present in either material alone, enabling even better, multifunctional flexible devices. Central to the realization of such devices is a fundamental understanding of the organic-2D TMD interface. Here, we review the organic-2D TMD interface from both chemical and physical perspectives. We discuss the current understanding of the interfacial interactions between the organic layers and the TMDs, as well as the energy level alignment at the interface, focusing in particular on surface charge transfer and electronic screening effects. Applications from the literature are discussed, especially in optoelectronics and p-n hetero- and homo-junctions. We conclude with an outlook on future scientific and device developments based on organic-2D TMD heterointerfaces.

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.

Controlling the layer localization of gapless states in bilayer graphene with a gate voltage

Experiments in gated bilayer graphene with stacking domain walls present topological gapless states protected by no-valley mixing. Here we research these states under gate voltages using atomistic models, which allow us to elucidate their origin. We find that the gate potential controls the layer localization of the two states, which switches non-trivially between layers depending on the applied gate voltage magnitude. We also show how these bilayer gapless states arise from bands of single-layer graphene by analyzing the formation of carbon bonds between layers. Based on this analysis we provide a model Hamiltonian with analytical solutions, which explains the layer localization as a function of the ratio between the applied potential and interlayer hopping. Our results open a route for the manipulation of gapless states in electronic devices, analogous to the proposed writing and reading memories in topological insulators.

Metallic nanoislands on graphene: A metamaterial for chemical, mechanical, optical, and biological applications

Graphene decorated with metallic nanoparticles exhibits electronic, optical, and mechanical properties that neither the graphene nor the metal possess alone. These composite films have electrical conductivity and optical properties that can be modulated by a range of physical, chemical, and biological signals. Such properties are controlled by the morphology of the nanoisland films, which can be deposited on graphene using a variety of techniques, including in situ chemical synthesis and physical vapor deposition. These techniques produce non-random (though loosely defined) morphologies, but can be combined with lithography to generate deterministic patterns. Applications of these composite films include chemical sensing and catalysis, energy storage and transport (including photoconductivity), mechanical sensing (using a highly sensitive piezroresistive effect), optical sensing (including so-called "piezoplasmonic" effects), and cellular biophysics (i.e sensing the contractions of cardiomyocytes and myoblasts).

Recent progress in van der Waals heterojunctions

Following the development of many novel two-dimensional (2D) materials, investigations of van der Waals heterojunctions (vdWHs) have attracted significant attention due to their excellent properties such as smooth heterointerface, highly gate-tunable bandgap, and ultrafast carrier transport. Benefits from the atom-scale thickness, physical and chemical properties and ease of manipulation of the heterojunctions formulated by weak vdW forces were demonstrated to indicate their outstanding potential in electronic and optoelectronic applications, including photodetection and energy harvesting, and the possibility of integrating them with the existing semiconductor technology for the next-generation electronic and sensing devices. In this review, we summarized the recent developments of vdWHs and emphasized their applications. Basically, we introduced the physical properties and some newly discovered phenomena in vdWHs. Then, we emphatically presented four classical vdWHs and some novel heterostructures formed by vdW forces. Based on their unique physical properties and structures, we highlighted the applications of vdWHs including in photodiodes, phototransistors, tunneling devices, and memory devices. Finally, we provided a conclusion on the recent advances in vdWHs and outlined our perspectives. We aim for this review to serve as a solid foundation in this field and to pave the way for future research on vdW-based materials and their heterostructures.

Coulomb Oscillations in a Gate-Controlled Few-Layer Graphene Quantum Dot

Graphene quantum dots could be an ideal host for spin qubits and thus have been extensively investigated based on graphene nanoribbons and etched nanostructures; however, edge and substrate-induced disorders severely limit device functionality. Here, we report the confinement of quantum dots in few-layer graphene with tunable barriers, defined by local strain and electrostatic gating. Transport measurements unambiguously reveal that confinement barriers are formed by inducing a band gap via the electrostatic gating together with local strain induced constriction. Numerical simulations according to the local top-gate geometry confirm the band gap opening by a perpendicular electric field. We investigate the magnetic field dependence of the energy-level spectra in these graphene quantum dots. Experimental results reveal a complex evolution of Coulomb oscillations with the magnetic field, featuring kinks at level crossings. The simulation of energy spectrum shows that the kink features and the magnetic field dependence are consistent with experimental observations, implying the hybridized nature of energy-level spectrum of these graphene quantum dots.

Tuning Surface Properties of Low Dimensional Materials via Strain Engineering

The promising and versatile applications of low dimensional materials are largely due to their surface properties, which along with their underlying electronic structures have been well studied. However, these materials may not be directly useful for applications requiring properties other than their natal ones. In recent years, strain has been shown to be an additionally useful handle to tune the physical and chemical properties of materials by changing their geometric and electronic structures. The strategies for producing strain are summarized. Then, the electronic structure of quasi-two dimensional layered non-metallic materials (e.g., graphene, MX2, BP, Ge nanosheets) under strain are discussed. Later, the strain effects on catalytic properties of metal-catalyst loaded with strain are focused on. Both experimental and computational perspectives for dealing with strained systems are covered. Finally, an outlook on engineering surface properties utilizing strain is provided.

Nonlinear electro-magneto-mechanical constitutive modelling of monolayer graphene

Using the classical theory of invariants for the specific class of graphene's symmetry, we constitutively characterize electro-magneto-mechanical interactions of graphene at continuum level. Graphene's energy depends on five arguments: the Finger strain tensor, the curvature tensor, the shift vector, the effective electric field intensity and the effective magnetic induction. The Finger strain tensor describes in- surface phenomena, the curvature tensor is responsible for the out-of-surface motions, while the shift vector is used due to the fact that graphene is a multilattice. The electric and the magnetic fields are described by the effective electric field intensity and the effective magnetic induction, respectively. An energy with the above arguments that also respects graphene's symmetries is found to have 42 invariants. Using these invariants, we evaluate all relevant measures by finding derivatives of the energy with respect to the five arguments of the energy. We also lay down the field equations that should be satisfied. These are the Maxwell equations, the momentum equation, the moment of momentum equation and the equation ruling the shift vector. Our framework is general enough to capture fully coupled processes in the finite deformation regime.

Existence of nontrivial topologically protected states at grain boundaries in bilayer graphene: signatures and electrical switching

Recent experiments [L. Ju, et al., Nature, 2015, 520, 650] confirm the existence of gapless states at domain walls created in gated bilayer graphene, when the sublattice stacking is changed from AB to BA. These states are significant because they are topologically protected, valley-polarized and give rise to conductance along the domain wall. Current theoretical models predict the appearance of such states only at domain walls, which preserve the sublattice order. Here we show that the appearance of the topologically protected states in stacking domain walls can be much more common in bilayer graphene, since they can also emerge in unexpected geometries, e.g., at grain boundaries with atomic-scale topological defects. We focus on a bilayer system in which one of the layers contains a line of octagon-double pentagon defects that mix graphene sublattices. We demonstrate that gap states are preserved even with pentagonal defects. Remarkably, unlike previous predictions, the number of gap states changes by inverting the gate polarization, yielding an asymmetric conductance along the grain boundary under gate reversal. This effect, linked to defect states, should be detectable in transport measurements and could be exploited in electrical switches.

Bandgap engineering of MoS2/MX2 (MX2 = WS2, MoSe2 and WSe2) heterobilayers subjected to biaxial strain and normal compressive strain

Among MoS₂/MX₂ heterobilayers only the MoS₂/WSe₂ system exhibits a direct bandgap, and strain can be used to tune the direct bandgap character of the MoS₂/MoSe₂ and MoS₂/WSe₂ heterobilayers.

Tuning the hydrogen evolution activity of MS2 (M = Mo or Nb) monolayers by strain engineering

Strain can tune the HER activity of monolayer MS₂ (M = Mo or Nb) in both 1H and 1T phases, among which 1T-MoS₂ and 1H-NbS₂ exhibit better strain tunability towards their HER activities since more active sites are induced.

Graphene flakes under controlled biaxial deformation

Thin membranes, such as monolayer graphene of monoatomic thickness, are bound to exhibit lateral buckling under uniaxial tensile loading that impairs its mechanical behaviour. In this work, we have developed an experimental device to subject 2D materials to controlled equibiaxial strain on supported beams that can be flexed up or down to subject the material to either compression or tension, respectively. Using strain gauges in tandem with Raman spectroscopy measurements, we monitor the G and 2D phonon properties of graphene under biaxial strain and thus extract important information about the uptake of stress under these conditions. The experimental shift over strain for the G and 2D Raman peaks were found to be in the range of 62.3 ± 5 cm^–1/%, and 148.2 ± 6 cm^–1/%, respectively, for monolayer but also bilayer graphenes. The corresponding Grüneisen parameters for the G and 2D peaks were found to be between 1.97 ± 0.15 and 2.86 ± 0.12, respectively. These values agree reasonably well with those obtained from small-strain bubble-type experiments. The results presented are also backed up by classical and ab initio molecular dynamics simulations and excellent agreement of Γ-E_2g shifts with strains and the Grüneisen parameter was observed.

Extreme sensitivity of the electric-field-induced band gap to the electronic topological transition in sliding bilayer graphene

We have investigated the effect of electronic topological transition on the electric field-induced band gap in sliding bilayer graphene by using the density functional theory calculations. The electric field-induced band gap was found to be extremely sensitive to the electronic topological transition. At the electronic topological transition induced by layer sliding, four Dirac cones in the Bernal-stacked bilayer graphene reduces to two Dirac cones with equal or unequal Dirac energies depending on the sliding direction. While the critical electric field required for the band gap opening increases with increasing lateral shift for the two Dirac cones with unequal Dirac energies, the critical field is essentially zero with or without a lateral shift for the two Dirac cones with equal Dirac energies. The critical field is determined by the Dirac energy difference and the electronic screening effect. The electronic screening effect was also found to be enhanced with increasing lateral shift, apparently indicating that the massless helical and massive chiral fermions are responsible for the perfect and imperfect electronic screening, respectively.

Graphene wrinkling induced by monodisperse nanoparticles: facile control and quantification

Controlled wrinkling of single-layer graphene (1-LG) at nanometer scale was achieved by introducing monodisperse nanoparticles (NPs), with size comparable to the strain coherence length, underneath the 1-LG. Typical fingerprint of the delaminated fraction is identified as substantial contribution to the principal Raman modes of the 1-LG (G and G'). Correlation analysis of the Raman shift of the G and G' modes clearly resolved the 1-LG in contact and delaminated from the substrate, respectively. Intensity of Raman features of the delaminated 1-LG increases linearly with the amount of the wrinkles, as determined by advanced processing of atomic force microscopy data. Our study thus offers universal approach for both fine tuning and facile quantification of the graphene topography up to ~60% of wrinkling.

Graphene Mechanics: Current Status and Perspectives

The mechanical properties of 2D materials such as monolayer graphene are of extreme importance for several potential applications. We summarize the experimental and theoretical results to date on mechanical loading of freely suspended or fully supported graphene. We assess the obtained axial properties of the material in tension and compression and comment on the methods used for deriving the various reported values. We also report on past and current efforts to define the elastic constants of graphene in a 3D representation. Current areas of research that are concerned with the effect of production method and/or the presence of defects upon the mechanical integrity of graphene are also covered. Finally, we examine extensively the work related to the effect of graphene deformation upon its electronic properties and the possibility of employing strained graphene in future electronic applications.

Strain-induced conduction gap in vertical devices made of misoriented graphene layers

We investigate the effects of uniaxial strain on the transport properties of vertical devices made of two misoriented (or twisted) graphene layers, which partially overlap each other. We find that because of the different orientations of the two graphene lattices, their Dirac points can be displaced and separated in the k-space by the effects of strain. Hence, a finite conduction gap as large as a few hundred meV can be obtained in the device with a small strain of only a few percent. The dependence of this conduction gap on the strain magnitude, strain direction, channel orientation and twist angle are clarified and presented. On this basis, the strong modulation of conductance and significant improvement of Seebeck coefficient are shown. The suggested devices therefore may be very promising for improving applications of graphene, e.g., as transistors or strain and thermal sensors.

A first-principles study on three-dimensional covalently-bonded hexagonal boron nitride nanoribbons

We studied three-dimensional honeycomb-structure boron nitride (BN) allotrope using first-principles calculations and the tight-binding method. Interconnected by sp(3)-bonding at the vertices, hexagonal BN nanoribbons construct highly-porous, covalently-bonded hexagonal BN nanoribbons (CBBNs). We investigated the structural and mechanical properties of CBBNs with various sizes, compared with those of carbon and other BN allotropes. The mechanical and thermal stabilities are also checked. Our calculations show that, despite the high porosity and low mass density, CBBNs are stable and mechanically hard materials as cubic BN. Moreover, our calculated results suggest that CBBNs can be regarded as a binary alloy of sp(2)- and sp(3)-bonded BNs following the Vegard's rule in average bond lengths and bulk moduli. Calculated band structures show that the band gap of CBBNs has similar variation upon increasing size as BN nanoribbons and is also limited by the second-neighbor interaction between the pz states of sp(2)-bonded atoms in adjacent nanoribbons.

Uniaxial strain-induced mechanical and electronic property modulation of silicene

We perform first-principles calculations of mechanical and electronic properties of silicene under uniaxial strains. Poisson's ratio and the rigidity of silicene show strong chirality dependence under large uniaxial strains. The ultimate strains of silicene with uniaxial strain are smaller than those with biaxial strain. We find that uniaxial strains induce Dirac point deviation from the high-symmetry points in the Brillouin zone and semimetal-metal transitions. Therefore, no bandgap opens under the uniaxial strain. Due to its peculiar structure and variable sp (3)/sp (2) ratio of the chemical bond, the deviation directions of Dirac points from the high-symmetry points in the Brillouin zone and variation of Fermi velocities of silicene exhibit significant difference from those of graphene. Fermi velocities show strong anisotropy with respect to the wave vector directions and change slightly before the semimetal-metal transition. We also find that the work function of silicene increases monotonously with the increasing uniaxial strains.

PACS NUMBERS

61.46.-w; 62.20.D-; 73.22.Dj.

Strain engineering of Kapitza resistance in few-layer graphene

We demonstrate through molecular dynamics simulations that the Kapitza resistance in few-layer graphene (FLG) can be controlled by applying mechanical strain. For unstrained FLG, the Kapitza resistance decreases with the increase of thickness and reaches an asymptotic value of 6 × 10(-10) m(2)K/W at a thickness about 16 nm. Uniaxial cross-plane strain is found to increase the Kapitza resistance in FLG monotonically, when the applied strain varies from compressive to tensile. Moreover, uniaxial strain couples the in-plane and out-of-plane strain/stress when the surface of FLG is buckled. We find that with a compressive cross-plane stress of 2 GPa, the Kapitza resistance is reduced by about 50%. On the other hand it is almost tripled with a tensile cross-plane stress of 1 GPa. Remarkably, compressive in-plane strain can either increase or reduce the Kapitza resistance, depending on the specific way it is applied. Our study suggests that graphene can be exploited for both heat dissipation and insulation through strain engineering.

Control over band structure and tunneling in bilayer graphene induced by velocity engineering

The band structure and transport properties of massive Dirac fermions in bilayer graphene with velocity modulation in space are investigated in the presence of a previously created band gap. It is pointed out that velocity engineering may be considered as a factor to control the band gap of symmetry-broken bilayer graphene. The band gap is direct and independent of velocity value if the velocity modulated in two layers is set up equally. Otherwise, in the case of interlayer asymmetric velocity, not only is the band gap indirect, but also the electron-hole symmetry fails. This band gap is controllable by the ratio of the velocity modulated in the upper layer to the velocity modulated in the lower layer. In more detail, the shift of momentum from the conduction band edge to the valence band edge can be engineered by the gate bias and velocity ratio. A transfer matrix method is also elaborated to calculate the four-band coherent conductance through a velocity barrier possibly subjected to a gate bias. Electronic transport depends on the ratio of velocity modulated inside the barrier to that for surrounding regions. As a result, a quantum version of total internal reflection is observed for thick enough velocity barriers. Moreover, a transport gap originating from the applied gate bias is engineered by modulating the velocities of the carriers in the upper and lower layers.

Supramolecular Assembly of DNA on Graphene Nanoribbons

Graphene's adhesive and charge delocalization properties offer the opportunity for the direct study of biological molecule in the nanoscale regime. The inherent charge on DNA base pairs and the associated phosphate backbone can be probed by non-covalent interactions with graphene, which is a useful platform for the creation of anisotropic nanopatterned biological assemblies. Here, we report the graphene nanoribbon (GNR) supported anisotropic supramolecular self-assembly of single stranded adenine (A), cytosine (C), guanine (G), thymine (T), AT, and GC 20mer oligonucleotides, as well as the unique ordering of double stranded plasmid (circular) and Herring sperm (linear) DNA. The GNRs serve as a double sided adhesive platform for attachment to the SiO2 substrate, as well as DNA oligomers and polymers. The self-assembly is attributed to donor-acceptor interactions between DNA and graphene. These findings demonstrate that the DNA-GNR assembly yields a prospective route to novel bio-relevant nanostructures.

The electronic properties of bilayer graphene

We review the electronic properties of bilayer graphene, beginning with a description of the tight-binding model of bilayer graphene and the derivation of the effective Hamiltonian describing massive chiral quasiparticles in two parabolic bands at low energies. We take into account five tight-binding parameters of the Slonczewski-Weiss-McClure model of bulk graphite plus intra- and interlayer asymmetry between atomic sites which induce band gaps in the low-energy spectrum. The Hartree model of screening and band-gap opening due to interlayer asymmetry in the presence of external gates is presented. The tight-binding model is used to describe optical and transport properties including the integer quantum Hall effect, and we also discuss orbital magnetism, phonons and the influence of strain on electronic properties. We conclude with an overview of electronic interaction effects.

First-principles study of the effects of mechanical strains on the radiation hardness of hexagonal boron nitride monolayers

We investigate the strain effect on the radiation hardness of hexagonal boron nitride (h-BN) monolayers using density functional theory calculations. Both compressive and tensile strains are studied in elastic domains along the zigzag, armchair, and biaxial directions. We observe a reduction in radiation hardness to form boron and nitrogen monovacancies under all strains. The origin of this effect is the strain-induced reduction of the energy barrier to displace an atom. An implication of our results is the vulnerability of strained nanomaterials to radiation damage.