Using an external electric field, one can modulate the bandgap of Bernal stacked bilayer graphene by breaking A-~B symmetry. We analyze strain effects on the bilayer graphene using the extended Huckel theory and find that reduced interlayer distance results in higher bandgap modulation, as expected. Furthermore, above about 2.5 angstrom interlayer distance, the bandgap is direct, follows a convex relation to electric field and saturates to a value determined by the interlayer distance. However, below about 2.5 angstrom, the bandgap is indirect, the trend becomes concave and a threshold electric field is observed, which also depends on the stacking distance.
We develop two types of graphene devices based on nanoelectromechanical systems (NEMS), that allows transport measurement in the presence of in situ strain modulation. Different mobility and conductance responses to strain were observed for single layer and bilayer samples. These types of devices can be extended to other 2D membranes such as MoS2, providing transport, optical or other measurements with in situ strain.
Using the first principles calculations, we show that mechanically tunable electronic energy gap is realizable in bilayer graphene if different homogeneous strains are applied to the two layers. It is shown that the size of energy gap can be simply controlled by adjusting the strength and direction of these strains. We also show that the effect originates from the occurrence of strain-induced pseudo-scalar potentials in graphene. When homogeneous strains with different strengths are applied to each layer of bilayer graphene, transverse electric fields across the two layers can be generated wit…
For controlling the critical electric fields of the topological phase transition in single bilayer Bi(111), we investigated topological phases in a strained system through first-principles calculations. We found a quadratic band touching semimetallic state at tensile strain $ε=0.5$%. Around this strain, the topological phase can be switched to a trivial insulator by an infinitesimal electric field. The positions at which Dirac cones appear in the electric-field-induced topological phase transition changed for the strain $ε>0.5$% and $ε<0.5$%. Our results indicate that this topological phase tr…
A monolayer of CrI$_3$ is a two-dimensional crystal that in its equilibrium configuration is a ferromagnetic semiconductor, however, two coupled layers can be ferromagnetic or antiferromagnetic depending on the stacking. We study the magnetic phase diagram upon the strain of the antiferromagnetically coupled bilayer with C2/m symmetry. We found that strain may be an efficient tool to tune the magnetic phase of the structure. A tensile strain stabilizes the antiferromagnetic phase, while a compressive strain turns the system ferromagnetic. We understood that behavior by looking at the relative …
We use micro-Raman and photoluminescence (PL) spectroscopy at 300K to investigate the influence of uniaxial tensile strain on the vibrational and optoelectronic properties of monolayer and bilayer MoS2 on a flexible substrate. The initially degenerate E^1_{2g} Raman mode is split into a doublet as a direct consequence of the strain applied to MoS2 through Van der Waals coupling at the sample-substrate interface. We observe a strong shift of the direct band gap of 48meV/(% of strain) for the monolayer and 46meV/% for the bilayer, whose indirect gap shifts by 86meV/%. We find a strong decrease o…
Here we study the evolution of local electronic properties of a twisted graphene bilayer induced by a strain and a high curvature. The strain and curvature strongly affect the local band structures of the twisted graphene bilayer; the energy difference of the two low-energy van Hove singularities decreases with increasing the lattice deformations and the states condensed into well-defined pseudo-Landau levels, which mimic the quantization of massive Dirac fermions in a magnetic field of about 100 T, along a graphene wrinkle. The joint effect of strain and out-of-plane distortion in the graphen…
Detection of local strain at the nanometer scale with high sensitivity remains challenging. Here we report near-field infrared nano-imaging of local strains in bilayer graphene through probing strain-induced shifts of phonon frequency. As a non-polar crystal, intrinsic bilayer graphene possesses little infrared response at its transverse optical (TO) phonon frequency. The reported optical detection of local strain is enabled by applying a vertical electrical field that breaks the symmetry of the two graphene layers and introduces finite electrical dipole moment to graphene phonon. The activate…
In this work, the electrical properties of bilayer Antimonene with different stacking orders are studied. Density functional theory with van der Waals (vdW) correction is used to investigate the electrical performances. Two configurations demonstrate considerable bandgaps, whereas, the bandgaps are close to zero for other structures. The in-plane biaxial strain is applied to modify the electrical properties. The bandgap reaches a maximum at a specific strain level and then closes at more enormous compressive and tensile strains. The energy of three valleys ($Γ$, Q, and K) in the conduction ban…
In two-dimensional (2D) twisted bilayers, the van der Waals (vdW) interlayer interaction introduces atomic-scale reconstruction at interface by locally rotating lattice to form strain-field vortex networks in their moiré superlattice. However, direct imaging the tiny local lattice rotation of the strain-field vortex requires extremely high spatial resolution and is an outstanding challenge in experiment. Here, a topmost small-period graphene moiré pattern is introduced to magnify sub-Angstrom distortions of the lattice and tiny local lattice rotation in underlying twisted bilayer graphene (TBG…
Using full-potential density functional calculations within local density approximation (LDA), we predict that mechanically tunable band-gap and quasi-particle-effective-mass are realizable in graphene/hexagonal-BN hetero-bilayer (C/h-BN HBL) by application of in-plane homogeneous biaxial strain. While providing one of the possible reasons for the experimentally observed gap-less pristine-graphene-like electronic properties of C/h-BN HBL, which theoretically has a narrow band-gap, we suggest a schematic experiment for verification of our results which may find applications in nano-electromecha…
Van der Waals heteroepitaxy allows deterministic control over lattice mismatch or azimuthal orientation between atomic layers to produce long wavelength superlattices. The resulting electronic phases depend critically on the superlattice periodicity as well as localized structural deformations that introduce disorder and strain. Here, we introduce Bragg interferometry, based on four-dimensional scanning transmission electron microscopy, to capture atomic displacement fields in twisted bilayer graphene with twist angles < 2°. Nanoscale spatial fluctuations in twist angle and uniaxial heterostra…
With exceptional electrical and mechanical properties and at the same time air-stability, layered MoSi2N4 has recently draw great attention. However, band structure engineering via strain and electric field, which is vital for practical applications, has not yet been explored. In this work, we show that the biaxial strain and external electric field are effective ways for the band gap engineering of bilayer MoSi$_2$N$_4$ and WSi$_2$N$_4$. It is found that strain can lead to indirect band gap to direct band gap transition. On the other hand, electric field can result in semiconductor to metal t…
Twist bilayer graphenes with magical angle have nearly flat band, which become strongly correlated electron systems. Herein, we propose another system based on strained bilayer graphene that have flat band at the intrinsic Fermi level. The top and bottom layers are uniaxially stretched along different directions. When the strength and directions of the strain satisfy certain condition, the periodical lattices of the two layers are commensurate to each other. The regions with AA, AB and BA stacking arrange in a triangular lattice. With magical strain, the bands around the intrinsic Fermi level …
In this work, the structural, electrical, and optical properties of bilayer SiX (X= N, P, As, and Sb) are studied using density functional theory (DFT). Five different stacking orders are considered for every compound and their structural properties are presented. The band structure of these materials demonstrates that they are indirect semiconductors. The out-of-plane strain has been applied to tune the bandgap and its electrical properties. The bandgap increases with tensile strain, whereas, compressive strain leads to semiconductor-to-metal transition. The sensitivity of the bandgap to the …
Topological properties of electronic states in multivalley two-dimensional materials, such as mono- and bilayer graphene, or thin films of rhombohedral graphite, give rise to various unusual magneto-transport regimes. Here, we investigate the tunability of the topological magnetic moment (related to the Berry curvature) of electronic states in bilayer graphene using strain and vertical bias. We show how one can controllably vary the valley $g$-factor of the band-edge electrons, $g_v^*$, across the range $10 < |g_v^*| < 200$, and we discuss the manifestations of the topological magnetic moment …
In this letter we use graphene bubbles to study the Raman spectrum of graphene under biaxial (e.g. isotropic) strain. Our Gruneisen parameters are in excellent agreement with the theoretical values. Discrepancy in the previously reported values is attributed to the interaction of graphene with the substrate. Bilayer balloons (intentionally pressurized membranes) have been used to avoid the effect of the substrate and to study the dependence of strain on the inter-layer interactions.
Due to low dimensionality, the controlled stacking of the graphene films and their electronic properties are susceptible to environmental changes including strain. The strain-induced modification of the electronic properties such as the emergence and modulation of bandgaps crucially depends on the stacking of the graphene films. However, to date, only the impact of strain on electronic properties of Bernal and AA-stacked bilayer graphene has been extensively investigated in theoretical studies. Exploiting density functional theory and tight-binding calculation, we investigate the impacts of in…
Mo$X_2$ ($X$=S or Se) is a semiconductor family with two-dimensional structure. And a recent calculation predicted the superconductivity in electron doped MoS$_2$ monolayer. In this work, the electronic structure and lattice dynamics of Mo$X_2$ bilayers with monolayer Na intercalated, have been calculated. According to the electron-phonon interaction, it is predicted that these bilayers can be transformed from indirect-gap semiconductors to a superconductors by Na intercalation. More interestingly, the biaxial tensile strain can significantly enhance the superconducting temperature up to $\sim…
We show that topology of the low-energy band structure in bilayer graphene critically depends on mechanical deformations of the crystal which may easily develop in suspended graphene flakes. We describe the Lifshitz transition that takes place in strained bilayers upon splitting the parabollic bands at intermediate energies into several Dirac cones at the energy scale of few meV. Then, we show how this affects the electron Landau level spectra and the quantum Hall effect.
Very recently, twisted graphene bilayer (TGB) around the first magic angle 1.1° has attracted much attention for the realization of exotic quantum states, such as correlated insulator behavior and unconventional superconductivity. Here we elaborately studied a series of TGBs around the first magic angle engineered by heterostrain, where each layer is strained independently. Our experiment indicated that a moderate heterostrain enables the structural evolution from the small-angle TGB ( ~ 1.5°) to the strained magic-angle TGB (θ ~ 1.1°), exhibiting the characteristic low-energy flat bands. The …
We report the influence of uniaxial tensile mechanical strain in the range 0-2.2% on the phonon spectra and bandstructures of monolayer and bilayer molybdenum disulfide (MoS2) two-dimensional crystals. First, we employ Raman spectroscopy to observe phonon softening with increased strain, breaking the degeneracy in the E' Raman mode of MoS2, and extract a Grüneisen parameter of ~1.06. Second, using photoluminescence spectroscopy we measure a decrease in the optical band gap of MoS2 that is roughly linear with strain, ~45 meV% strain for monolayer MoS2 and ~120 meV% strain for bilayer MoS2. Thir…
Electronic properties of bilayer graphene are distinct from both the conventional two dimensional electron gas and monolayer graphene due to its particular chiral properties and excitation charge carrier dispersions. We study the effect of strain on the electronic structure, the edge-states and charge transport of bilayer graphene nanoribbon at zero-temperature. We demonstrate a valley polarized quantum Hall effect in biased bilayer graphene when the system is subjected to a perpendicular magnetic field. In this system a topological phase transition from a quantum valley Hall to a valley polar…
Intrinsic bilayer graphene is a gapless semimetal. Under the application of a bias field it becomes a semiconductor with a direct band gap that is proportional to the applied field. Under a layer-asymmetric strain (where the upper layer undergoes compression and lower layer tension or visa-versa) we find that the band gap of a biased bilayer graphene ribbon becomes indirect and, for higher strains, becomes negative returning the material its original semimetal state. As a result, the conductivity of the ribbon increases and can be almost an order of magnitude larger that of the intrinsic unbia…
The recent emergence of strain gradient engineering directly affects the nanomechanics, optoelectronics and thermal transport fields in 2D materials. More specifically, large suspended graphene under very high stress represents the quintessence for nanomechanical mass detection through unique molecular reactions. Different techniques have been used to induce strain in 2D materials, for instance by applying tip indentation, pressure or substrate bending on a graphene membrane. Nevertheless, an efficient way to control the strain of a structure is to engineer the system geometry as shown in ever…
Recent experiments have measured local uniaxial strain fields in twisted bilayer graphene (TBG). Our calculations found that the finite Berry curvature generated by breaking the sublattice symmetry and the band proximity between narrow bands in these TBG induces a giant Berry dipole of order 10\,nm or larger. The large Berry dipole leads to transverse topological non-linear charge currents which dominates over the linear bulk valley current at experimentally accessible crossover in-plane electric field of $\sim 0.1 {\rm mV} / μ\rm{m}$. This anomalous Hall effect, due to Berry dipole, is strong…
We study the electronic and topological properties of fully relaxed twisted bilayer (TBG) and double bilayer (TDBG) graphene under perpendicular pressure. An approach has been proposed to obtain the equilibrium in-plane structural deformation and out-of-plane corrugation in moiré superlattices under pressure. We find that the in-plane relaxation becomes much stronger under higher pressure, while the corrugation height in each layer is maintained. The comparison between band structures of relaxed and rigid structures demonstrates that not only the gaps on the electron and hole sides ($Δ_e$ and …
We develop a theory for describing frictional drag in bilayer systems with in-plane periodic potential modulations, and use it to investigate the drag between bilayer systems in which one of the layers is modulated in one direction. At low temperatures, as the density of carriers in the modulated layer is changed, we show that the transresistivity component in the direction of modulation can change its sign. We also give a physical explanation for this behavior.
We show how the excitonic features of biaxial MoS2 flakes are very sensitive to biaxial strain. We find a lower bound for the gauge factors of the A exciton and B exciton of (-41 +- 2) meV/% and (-45 +- 2) meV/% respectively, which are larger than those found for single-layer MoS2. Interestingly, the interlayer exciton feature also shifts upon biaxial strain but with a gauge factor that is systematically larger than that found for the A exciton, (-48 +- 4) meV/%. We attribute this larger gauge factor for the interlayer exciton to the strain tunable van der Waals interaction due to the Poisson …
We review the effect of uniaxial strain on the low-energy electronic dispersion and Landau level structure of bilayer graphene. Based on the tight-binding approach, we derive a strain-induced term in the low-energy Hamiltonian and show how strain affects the low-energy electronic band structure. Depending on the magnitude and direction of applied strain, we identify three regimes of qualitatively different electronic dispersions. We also show that in a weak magnetic field, sufficient strain results in the filling factor ff=+-4 being the most stable in the quantum Hall effect measurement, inste…
We study the electronic properties of commensurate faulted bilayer graphene by diagonalizing the one-particle Hamiltonian of the bilayer system in a complete basis of Bloch states of the individual graphene layers. Our novel approach is very general and can be easily extended to any commensurate graphene-based heterostructure. Here, we consider three cases: i) twisted bilayer graphene, ii) bilayer graphene where triaxial stress is applied to one layer, and iii) bilayer graphene where uniaxial stress is applied to one layer. We show that the resulting superstructures can be divided into distinc…
The superposition of flexoelectronic doping and topological phonons give rise to topological electronic magnetism of phonon in an inhomogeneously strained Si in the bilayer structure with metal. In case of ferromagnetic metal and Si bilayer structure, the flexoelectronic doping will also give rise to larger spin current, which will lead to large spin to charge conversion due to topological electronic magnetism of phonon. By applying a temperature difference to ferromagnetic metal/Si bilayer structure under an applied strain gradient, a large thermoelectric response can be generated. In this ex…
We study the Landau quantization of the electronic spectrum for graphene bilayers that are rotationally faulted to produce periodic superlattices. Commensurate twisted bilayers exist in two families distinguished by their sublattice exchange parity. We show that these two families exhibit distinct Landau quantized spectra distinguished both by the interlayer coupling of their zero modes and by an amplitude modulation of their spectra at energies above their low energy interlayer coherence scales. These modulations can provide a powerful experimental probe of the magnitude of a weak coherence s…
The electronic wavefunctions in moiré materials are highly sensitive to the details of the local atomic configuration enabling Bloch band geometry and topology to be controlled by stacking and strain. Here we predict that large injection currents (under circular polarized irradiation) can develop in strained twisted bilayer graphene (TBG) heterostructures with broken sublattice symmetry; such bulk photovoltaic currents flow even in the absence of a p-n junction and can be controlled by the helicity of incident light. As we argue, large injection current rates proceed from strong and highly pea…
Spin-to-heat current conversion effects have been investigated in bilayer films consisting of a paramagnetic metal (PM; Pt, W, or Ta) and a ferromagnetic metal (FM; CoFeB or permalloy). When a charge current is applied to the PM/FM bilayer film, a spin current is generated across the PM/FM interface owing to the spin Hall effect in PM. The spin current was found to exhibit cooling and heating features depending on the sign of the spin Hall angle of PM, where the spin-current-induced contribution is estimated by subtracting the contribution of the anomalous Ettingshausen effect in FM monolayer …
We report a first-principles study on the elastic, vibrational, and electronic properties of recently synthesized phosphorene. By calculating Grüneisen parameters, we evaluate the frequency shift of Raman/infrared active modes via symmetric biaxial strain. We also study an inducing semiconductor-metal transition, the gap size, and effective mass of carriers in various strain configurations. Furthermore, we unfold the emergence of a peculiar Dirac-shaped dispersion for specific strain conditions, including the zigzag-oriented tensile strain. The observed linear energy spectrum has distinct velo…
Using full-potential density functional theory (DFT) calculations, we found a small asymmetry in the Fermi velocity of electrons and holes in graphene. These Fermi velocity values and their average were found to decrease with increasing in-plane homogeneous biaxial strain; the variation in Fermi velocity is quadratic in strain. The results, which can be verified by Landau level spectroscopy and quantum capacitance measurements of bi-axially strained graphene, promise potential applications in graphene based straintronics and flexible electronics.
By means of atomistic tight-binding calculations, we investigate the effects of uniaxial strain on the electronic bandstructure of twisted graphene bilayer. We find that the bandstructure is dramatically deformed and the degeneracy of the bands is broken by strain. As a conseqence, the number of Dirac cones can double and the van Hove singularity points are separated in energy. The dependence of these effects on the strength of strain, its applied direction and the twist angle is carefully clarified. As an important result, we demonstrate that the position of van Hove singularities can be modu…
Graphene/MoS2 heterostructures are formed by combining the nanosheets of graphene and monolayer MoS2. The electronic features of both constituent monolayers are rather well-preserved in the resultant heterostructure due to the weak van der Waals interaction between the layers. However, the proximity of MoS2 induces strong spin orbit coupling effect of strength ~1 meV in graphene, which is nearly three orders of magnitude larger than the intrinsic spin orbit coupling of pristine graphene. This opens a bandgap in graphene and further causes anticrossings of the spin-nondegenerate bands near the …
We theoretically investigate silicon doped bilayer graphene, Si-BLG, with different stoichiometry of Si-BLG structures. The dangling bonds of C-Si atoms are found at low concentration ratio of Si atoms inducing sp$^3$-hybridization of buckled pattern in the structure. The Si-BLG with dangling bonds revel strong mechanical response at low strain of a uniaxial load, and the fracture strain is seen at low strain ratio. The sp$^3$-hybridization forms a small bandgap which induces an intermediate thermal and optical response of the system. In contrast, at higher Si concentration ratio, the Young mo…
Moiré superlattices in twistronic heterostructures are a powerful tool for materials engineering. In marginally twisted (small misalignment angle, $θ$) bilayers of nearly lattice-matched two-dimensional (2D) crystals moiré patterns take the form of domains of commensurate stacking, separated by a network of domain walls (NoDW) with strain hot spots at the NoDW nodes. Here, we show that, for type-II transition metal dichalcogenide bilayers MoX$_2$/WX$_2$ (X=S, Se), the hydrostatic strain component in these hot spots creates quantum dots for electrons and holes. We investigate the electron/hole …
The analytical two-chain Frenkel-Kontorova model is used to describe domain wall networks in bilayer graphene upon biaxial stretching of one of the layers. We show that the commensurate-incommensurate phase transition leading to formation of a regular triangular domain wall network at the relative biaxial elongation of $3.0\cdot 10^{-3}$ is followed by the transition to another incommensurate phase with a striped network at the elongation of $3.7\cdot 10^{-3}$. The reentrant transition to the phase with a triangular domain wall network is predicted for the elongation $\sim10^{-2}$.
We report on first-principles total-energy and phonon calculations that clarify structural stability and electronic properties of freestanding bilayer silicene. By extensive structural exploration, we reach all the stable structures reported before and find four new dynamically stable structures, including the structure with the largest cohesive energy. We find that atomic protrusion from the layer is the principal relaxation pattern which stabilizes bilayer silicene and determines the lateral periodicity. The hybrid-functional calculation shows that the most stable bilayer silicene is a semic…
The structural and electronic properties of graphene leads its charge carriers to behave like relativistic particles, which is described by a Dirac-like Hamiltonian. Since graphene is a monolayer of carbon atoms, the strain due to elastic deformations will give rise to so-called `pseudomagnetic fields (PMF)' in graphene sheet, and that has been realized experimentally in strained graphene sample. Here we propose a realistic strained graphene bilayer (SGB) device to detect the pseudo-magnetoexcitons (PME) in the absence of external magnetic field. The carriers in each graphene layer suffer diff…
