Phonon and structural changes in deformed Bernal stacked bilayer graphene

An Atomistic Insight into Moiré Reconstruction in Twisted Bilayer Graphene beyond the Magic Angle

Twisted bilayer graphene exhibits electronic properties strongly correlated with the size and arrangement of moiré patterns. While rigid rotation of the two graphene layers results in a moiré interference pattern, local rearrangements of atoms due to interlayer van der Waals interactions result in atomic reconstruction within the moiré cells. Manipulating these patterns by controlling the twist angle and externally applied strain provides a promising route to tuning their properties. Atomic reconstruction has been extensively studied for angles close to or smaller than the magic angle (θ _m = 1.1°). However, this effect has not been explored for applied strain and is believed to be negligible for high twist angles. Using interpretive and fundamental physical measurements, we use theoretical and numerical analyses to resolve atomic reconstruction in angles above θ _m . In addition, we propose a method to identify local regions within moiré cells and track their evolution with strain for a range of representative high twist angles. Our results show that atomic reconstruction is actively present beyond the magic angle, and its contribution to the moiré cell evolution is significant. Our theoretical method to correlate local and global phonon behavior further validates the role of reconstruction at higher angles. Our findings provide a better understanding of moiré reconstruction in large twist angles and the evolution of moiré cells under the application of strain, which might be potentially crucial for twistronics-based applications.

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.

Strain Engineering of Low-Dimensional Materials for Emerging Quantum Phenomena and Functionalities

Recent discoveries of exotic physical phenomena, such as unconventional superconductivity in magic-angle twisted bilayer graphene, dissipationless Dirac fermions in topological insulators, and quantum spin liquids, have triggered tremendous interest in quantum materials. The macroscopic revelation of quantum mechanical effects in quantum materials is associated with strong electron-electron correlations in the lattice, particularly where materials have reduced dimensionality. Owing to the strong correlations and confined geometry, altering atomic spacing and crystal symmetry via strain has emerged as an effective and versatile pathway for perturbing the subtle equilibrium of quantum states. This review highlights recent advances in strain-tunable quantum phenomena and functionalities, with particular focus on low-dimensional quantum materials. Experimental strategies for strain engineering are first discussed in terms of heterogeneity and elastic reconfigurability of strain distribution. The nontrivial quantum properties of several strain-quantum coupled platforms, including 2D van der Waals materials and heterostructures, topological insulators, superconducting oxides, and metal halide perovskites, are next outlined, with current challenges and future opportunities in quantum straintronics followed. Overall, strain engineering of quantum phenomena and functionalities is a rich field for fundamental research of many-body interactions and holds substantial promise for next-generation electronics capable of ultrafast, dissipationless, and secure information processing and communications.

Possible pair-graphene structures govern the thermodynamic properties of arbitrarily stacked few-layer graphene

The thermodynamic properties of few-layer graphene arbitrarily stacked on LiNbO3 crystal were characterized by measuring the parameters of a surface acoustic wave as it passed through the graphene/LiNbO3 interface. The parameters considered included the propagation velocity, frequency, and attenuation. Mono-, bi-, tri-, tetra-, and penta-layer graphene samples were prepared by transferring individual graphene layers onto LiNbO3 crystal surfaces at room temperature. Intra-layer lattice deformation was observed in all five samples. Further inter-layer lattice deformation was confirmed in samples with odd numbers of layers. The inter-layer lattice deformation caused stick-slip friction at the graphene/LiNbO3 interface near the temperature at which the layers were stacked. The thermal expansion coefficient of the deformed few-layer graphene transitioned from positive to negative as the number of layers increased. To explain the experimental results, we proposed a few-layer graphene even-odd layer number stacking order effect. A stable pair-graphene structure formed preferentially in the few-layer graphene. In even-layer graphene, the pair-graphene structure formed directly on the LiNbO3 substrate. Contrasting phenomena were noted with odd-layer graphene. Single-layer graphene was bound to the substrate after the stable pair-graphene structure was formed. The pair-graphene structure affected the stacking order and inter-layer lattice deformation of few-layer graphene substantially.

Efficient Mechanical Stress Transfer in Multilayer Graphene with a Ladder-like Architecture

We report that few graphene flakes embedded into polymer matrices can be mechanically stretched to relatively large deformation (>1%) in an efficient way by adopting a particular ladder-like morphology consisting of consecutive mono-, bi-, tri-, and four-layer graphene units. In this type of flake architecture, all of the layers adhere to the surrounding polymer inducing similar deformation on the individual graphene layers, preventing interlayer sliding and optimizing the strain transfer efficiency. We have exploited Raman spectroscopy to quantify this effect from a mechanical standpoint. The finite element method and molecular dynamics simulations have been used to interpret the above experimental findings. The results suggest that a step pyramid-like architecture of a flake can be ideal for efficient loading of layered materials embedded into a polymer and that there are two prevailing mechanisms that govern axial stress transfer, namely, interfacial shear transfer and axial transmission through the ends. This concept can be easily applied to other two-dimensional materials and related van der Waals heterostructures fabricated either by mechanical exfoliation or chemical vapor deposition by appropriate patterning. This work opens new perspectives in numerous applications, including high volume fraction composites, flexible electronics, and straintronic devices.

Fundamental Insights into Graphene Strain Sensing

Graphene has been studied extensively for use in flexible electronics as ultrasensitive and wide-area strain sensors. Many sensors demonstrated so far rely on graphene networks, such that the spatial resolution is compromised, and they are unable to measure strain variations on a fine scale such as those resulting from substrate/interface failure. In this study, mono-/few-layer graphene are demonstrated to be good candidates for strain sensing with high spatial resolution to evaluate features <100 nm. The fundamentals of strain sensing-interaction with the target-have been discussed to shed light on the sensitivity and durability for future sensor fabrication. The proof-of-concept strain sensors have been shown to be able to monitor different states, e.g., the initiation and evolution, of crazes. The analysis also leads to the evaluation of interfacial energy and realization of high local strain in graphene that is applicable for other 2D materials for ultrasensitive strain sensing and bandgap opening applications.

Strain engineering of 2D semiconductors and graphene: from strain fields to band-structure tuning and photonic applications

Two-dimensional (2D) transition metal dichalcogenides (TMDCs) and graphene compose a new family of crystalline materials with atomic thicknesses and exotic mechanical, electronic, and optical properties. Due to their inherent exceptional mechanical flexibility and strength, these 2D materials provide an ideal platform for strain engineering, enabling versatile modulation and significant enhancement of their optical properties. For instance, recent theoretical and experimental investigations have demonstrated flexible control over their electronic states via application of external strains, such as uniaxial strain and biaxial strain. Meanwhile, many nondestructive optical measurement methods, typically including absorption, reflectance, photoluminescence, and Raman spectroscopies, can be readily exploited to quantitatively determine strain-engineered optical properties. This review begins with an introduction to the macroscopic theory of crystal elasticity and microscopic effective low-energy Hamiltonians coupled with strain fields, and then summarizes recent advances in strain-induced optical responses of 2D TMDCs and graphene, followed by the strain engineering techniques. It concludes with exciting applications associated with strained 2D materials, discussions on existing open questions, and an outlook on this intriguing emerging field.

Tunable macroscale structural superlubricity in two-layer graphene via strain engineering

Achieving structural superlubricity in graphitic samples of macroscale size is particularly challenging due to difficulties in sliding large contact areas of commensurate stacking domains. Here, we show the presence of macroscale structural superlubricity between two randomly stacked graphene layers produced by both mechanical exfoliation and chemical vapour deposition. By measuring the shifts of Raman peaks under strain we estimate the values of frictional interlayer shear stress (ILSS) in the superlubricity regime (mm scale) under ambient conditions. The random incommensurate stacking, the presence of wrinkles and the mismatch in the lattice constant between two graphene layers induced by the tensile strain differential are considered responsible for the facile shearing at the macroscale. Furthermore, molecular dynamic simulations show that the stick-slip behaviour does not hold for incommensurate chiral shearing directions for which the ILSS decreases substantially, supporting the experimental observations. Our results pave the way for overcoming several limitations in achieving macroscale superlubricity using graphene.

Liquids relax and unify strain in graphene

Solid substrates often induce non-uniform strain and doping in graphene monolayer, therefore altering the intrinsic properties of graphene, reducing its charge carrier mobilities and, consequently, the overall electrical performance. Here, we exploit confocal Raman spectroscopy to study graphene directly free-floating on the surface of water, and show that liquid supports relief the preexisting strain, have negligible doping effect and restore the uniformity of the properties throughout the graphene sheet. Such an effect originates from the structural adaptability and flexibility, lesser contamination and weaker intermolecular bonding of liquids compared to solid supports, independently of the chemical nature of the liquid. Moreover, we demonstrate that water provides a platform to study and distinguish chemical defects from substrate-induced defects, in the particular case of hydrogenated graphene. Liquid supports, thus, are advantageous over solid supports for a range of applications, particularly for monitoring changes in the graphene structure upon chemical modification.

Here, the authors report water as a superior platform to suspend graphene compared to solid substrates that induce non-uniformity and do not provide structural flexibility. They utilize confocal Raman spectroscopy to study graphene floating freely on the surface of water to show that a liquid support relieves the pre-existing strain.

Stress-transfer from polymer substrates to monolayer and few-layer graphenes

In the present study, the stress transfer mechanism in graphene-polymer systems under tension is examined experimentally using the technique of laser Raman microscopy. We discuss in detail the effect of graphene edge geometry, lateral size and thickness which need to be taken under consideration when using graphene as a protective layer. The systems examined were composed of graphene flakes with a large length (over ∼50 microns) and a thickness of one to three layers simply deposited onto PMMA substrates which were then loaded to a tension of ∼1.60% strain. The stress transfer profiles were found to be linear while the results show that large lateral sizes of over twenty microns are needed in order to provide effective reinforcement at levels of strain higher than 1%. Moreover, the stress built up has been found to be quite sensitive to both edge shape and geometry of the loaded flakes. Finally, the transfer lengths were found to increase with the increase of graphene layers. The outcomes of the present study provide crucial insight into the issue of stress transfer from polymers to graphene nano-inclusions as a function of edge geometry, lateral size and thickness in a number of applications.

The strength of mechanically-exfoliated monolayer graphene deformed on a rigid polymer substrate

The deformation and fracture behaviour of one-atom-thick mechanically exfoliated graphene has been studied in detail. Monolayer graphene flakes with different lengths, widths and shapes were successfully prepared by mechanical exfoliation and deposited onto poly(methyl methacrylate) (PMMA) beams. The fracture behaviour of the monolayer graphene was followed by deforming the PMMA beams. Through in situ Raman mapping at different strain levels, the distributions of strain over the graphene flakes were determined from the shift of the graphene Raman 2D band. The failure mechanisms of the exfoliated graphene were either by flake fracture or failure of the graphene/polymer interface. The fracture of the flakes was observed from the formation of cracks identified from the appearance of lines of zero strain in the strain contour maps. It was found that the strength of the monolayer graphene flakes decreased with increasing flake width. The strength dropped to less than ∼10 GPa for large flakes, thought to be due to the presence of defects. It is shown that a pair of topological defects in monolayer graphene will form a pseudo crack and the effect of such defects upon the strength of monolayer graphene has been modelled using molecular mechanical simulations.

Interfacial Mechanical Properties of Double-Layer Graphene with Consideration of the Effect of Stacking Mode

The mechanical performance and the effect of the stacking mode of the double-layer graphene interface are studied. Three kinds of double-layer graphene-PET composite structure specimens with different stacking methods are designed. By combining micro-Raman spectroscopy with a microtensile loading device, in situ and real-time measurements are carried out for the specimens during the uniaxial loading process. Based on mechanical analysis, a method for peak splitting of the Raman spectra of double-layer polycrystalline graphene is developed to extract the strain information for each layer of graphene. The strain distribution and shear stress distribution of graphene in each layer during the loading process are determined experimentally. The strain transfer between the two interfaces is analyzed, and the mechanical parameters of interfaces are given quantitatively, the interlayer shear stress of graphene is 0.084 MPa. Finally, double-layer graphene with different stacking modes is studied. The results show that the different lengths of the upper and lower layers of graphene lead to a stress concentration of 0.7-1 GPa at the boundary of the short layer of graphene when stacked. The stress concentration problem of double-layer graphene should be considered for the practical application in microelectrical components.

Wrinkling formation in simply-supported graphenes under tension and compression loadings

Wrinkles in supported graphenes can be formed either by uniaxial compression or uniaxial tension beyond a certain critical load depending on the mode of loading. In the first case, the wrinkling direction is normal to the compression axis whereas in tension, wrinkles of the same pattern are formed parallel to the loading direction due to Poisson's (lateral) contraction. Herein we show by direct AFM observations that in simply-supported graphenes such instabilities appear as periodic wrinkles over existing stochastic undulations caused by the underlying-substrate-roughness. The critical strain for the generation of these wrinkles in both tension and compression is less than 1% which particularly for the former is far lower than the predicted tensile strain to fracture of suspended graphene estimated at ∼30%. Based on these findings, a constitutive model that provides the critical tensile strain for induced buckling in the lateral direction is proposed that depends only on the graphene-support interaction and not on the nature of the substrate. Understanding the wrinkling failure of graphenes under strain is of paramount importance as it leads to new threshold limits beyond which the physical-mechanical properties of graphene are impaired.

Strain engineering, efficient excitonic photoluminescence, and exciton funnelling in unmodified MoS2 nanosheets

We established locally varying strain fields in unmodified MoS₂ nanosheets. The approach relies on dry release in place of multilayer MoS₂ on textured Si substrates. By this process we demonstrated intense photoluminescence, a ∼70 meV decrease of the transition energy, and exciton funneling in ∼4 nm-thick MoS₂ films.

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.

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.

Two-dimensional analysis of the double-resonant 2D Raman mode in bilayer graphene

By computing the double-resonant Raman scattering cross section completely from first principles and including the electron-electron interaction at the GW level, we unravel the dominant contributions for the double-resonant 2D mode in bilayer graphene. We show that, in contrast to previous works, the so-called inner processes are dominant and that the 2D-mode line shape is described by three dominant resonances around the K point. We show that the splitting of the transversal optical (TO) phonon branch in the Γ-K direction, as large as 12  cm(-1) in the GW approximation, is of great importance for a thorough description of the 2D-mode line shape. Finally, we present a method to extract the TO phonon splitting and the splitting of the electronic bands from experimental data.

Formation and photovoltaic performance of few-layered graphene-decorated TiO2 nanocrystals used in dye-sensitized solar cells

Few-layer graphene/TiO2 nanocrystal composites are successfully in situ synthesized at a low temperature of 400 °C using C28H16Br2 as the precursor. Raman mapping images show that the TiO2 nanocrystals are very uniformly dispersed in the composite films, and the in situ coating during the thermal decomposition process will favor the formation of a good interface combination between the few-layered graphene and the TiO2 nanocrystals. The few-layer graphene/TiO2 nanocrystal composites are used as photoanodes in dye-sensitized solar cells (DSSCs), and the conversion efficiency of 8.25% is obtained under full sun irradiation (AM 1.5), which increases by 65% compared with that of the pure TiO2 nanocrystal DSSCs (5.01%). It is found that the good interface combination between few-layered graphene and TiO2 nanocrystals may improve the electric conductivity and lifetime of photoinduced electrons in DSSCs. Moreover, some carbon atoms are doped into the crystal structure of the TiO2 nanocrystals during the thermal decomposition process, which will enhance the light absorption by narrowing the band gap and favor the improvement of the photovoltaic efficiency.

Carbon isotope labelling in graphene research

The large scale production of graphene for any potential application relies on catalytic chemical vapour deposition (CVD). Despite much effort put into the graphene CVD research, there are still many challenges to be solved, not only concerning the growth itself, but also the subsequent treatment, i.e. transfer from the catalyst to a desired substrate. The need for fast progress naturally necessitates easy-to-use, versatile and efficient characterization methods. This perspective reviews the recent advances and potential of probably the most prospective one--Raman spectroscopy in connection with carbon isotope labelling of the CVD grown graphene layers. We discuss its use for the explanation and optimization of the growth process, followed by examples of employing isotope engineering in the studies of fundamental properties of graphene, not only by Raman spectroscopy.

Vacancy inter-layer migration in multi-layered graphene

The migration of vacancies between graphene layers and carbon nanotube walls has been observed in experiments, in which it is well known that the migration of vacancies between adjacent layers is prohibited by a very large energy barrier (∼7.0 eV). This contradiction has been a major puzzle for a number of years. In the present study, by using density functional tight-binding molecular dynamic simulations and first principle calculations, we have found that interaction between vacancies or vacancy holes in neighbouring graphene layers can greatly reduce the barrier, to ∼3 eV or less, and this expedites the migration process. In addition, all the vacancies in a multi-layered graphene gather to form a single hole in one layer. Our study has revealed a new mechanism for healing the defect in graphene materials and successfully explains the experimental puzzle. Our results have important applications in the engineering of graphene materials.

Reversible loss of Bernal stacking during the deformation of few-layer graphene in nanocomposites

The deformation of nanocomposites containing graphene flakes with different numbers of layers has been investigated with the use of Raman spectroscopy. It has been found that there is a shift of the 2D band to lower wavenumber and that the rate of band shift per unit strain tends to decrease as the number of graphene layers increases. It has been demonstrated that band broadening takes place during tensile deformation for mono- and bilayer graphene but that band narrowing occurs when the number of graphene layers is more than two. It is also found that the characteristic asymmetric shape of the 2D Raman band for the graphene with three or more layers changes to a symmetrical shape above about 0.4% strain and that it reverts to an asymmetric shape on unloading. This change in Raman band shape and width has been interpreted as being due to a reversible loss of Bernal stacking in the few-layer graphene during deformation. It has been shown that the elastic strain energy released from the unloading of the inner graphene layers in the few-layer material (~0.2 meV/atom) is similar to the accepted value of the stacking fault energies of graphite and few layer graphene. It is further shown that this loss of Bernal stacking can be accommodated by the formation of arrays of partial dislocations and stacking faults on the basal plane. The effect of the reversible loss of Bernal stacking upon the electronic structure of few-layer graphene and the possibility of using it to modify the electronic structure of few-layer graphene are discussed.