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 of the PL polarization linked to optical valley initialization for both monolayer and bilayer samples, indicating that scattering to the spin-degenerate Gamma valley plays a key role.
The optical properties of monolayer and bilayer transition metal dichalcogenide semiconductors are governed by excitons in different spin and valley configurations, providing versatile aspects for van der Waals heterostructures and devices. We present experimental and theoretical studies of exciton energy splittings in external magnetic field in neutral and charged WSe$_2$ monolayer and bilayer crystals embedded in a field effect device for active doping control. We develop theoretical methods to calculate the exciton $g$-factors from first principles and tight-binding for all possible spin-va…
The electronic property of monolayer-bilayer hybrid graphene with a zigzag interface is studied by both the Dirac equation and numerical calculation. There are two types of zigzag interface stacks. The dispersion and local density of states behave quit differently along the interface at the Fermi energy due to the different locations of the edge state. We hope our study can give some insights in the understanding of the transport and STM experiments.
Using first-principles full-potential density functional calculations, we predict that mechanically tunable band-gap is realizable in ZnS monolayer in graphene-like honeycomb structure by application of in-plane homogeneous biaxial strain. A transition point from direct-to-indirect gap-phase is predicted to exist for biaxial tensile strain lying in the interval (2.645%, 3.171%). In the two gap-phases, the band gap decreases with increasing strain and varies linearly with strain.
We report the fabrication and characterization of gate-defined hole quantum dots in monolayer and bilayer WSe$_2$. The devices were operated with gates above and below the WSe$_2$ layer to accumulate a hole gas, which for some devices was then selectively depleted to define the dot. Temperature dependence of conductance in the Coulomb blockade regime is consistent with transport through a single level, and excited state transport through the dots was observed at temperatures up to 10 K. For adjacent charge states of a bilayer WSe$_2$ dot, magnetic field dependence of excited state energies was…
Graphene hybrid planar structures consisting of two regions with different quantum Hall (QH) states exhibit unusual transport properties1-5, originating from chiral edge states equilibration at the interface of the two different regions6. Here we present a sub-nanometre-resolved scanning tunnelling microscopy (STM) and spectroscopy (STS) study of a monolayer-bilayer graphene planar junction in the QH regime. The atomically well-defined interface of such a junction allows us to spatially resolve the interface electronic properties. Around the interface, we detect Landau quantization of massless…
We report the current-driven dynamics of frustrated skyrmions in an antiferromagnetically exchange coupled bilayer system, where the bilayer skyrmion consists of two monolayer skyrmions with opposite skyrmion numbers $Q$. We show that the in-plane current-driven bilayer skyrmion moves in a straight path, while the out-of-plane current-driven bilayer skyrmion moves in a circular path. It is found that the in-plane current-driven mobility of a bilayer skyrmion is much better than the monolayer one at a large ratio of $β/α$, where $α$ and $β$ denote the damping parameter and non-adiabatic spin tr…
Graphene nanostructures exhibit an intrinsic advantage in relation to the gate delay in three-terminal devices and provide additional benefits when operate in the quantum capacitance limit. In this paper, we developed a simple model that captures the Fermi energy and temperature dependence of the quantum capacitance for monolayer and bilayer graphene devices. Quantum capacitance is calculated from the broadened density of states taking into account electron-hole puddles and possible finite lifetime of electronic states through a Gaussian broadening distribution. The obtained results are in agr…
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.
We have mapped the Dirac point in exfoliated monolayer and bilayer graphene using spatially resolved scanning tunneling spectroscopy (STS) measurements at low temperature. The Dirac point shifts in energy at different locations in graphene. However, a cross correlation with the topography shows no correlation indicating that topographic features such as ripples are not the primary source of the variation. Rather, we attribute the shift of the Dirac point to random charged impurities located near the graphene. Our findings emphasize the need to advance exfoliated graphene sample preparation to …
Generally, stacking two quantum spin Hall insulators gives rise to a trivial insulator. Here, based on first-principles electronic structure calculations, we confirm that monolayer TaIrTe$_{4}$ is a quantum spin Hall insulator and remarkably find that bilayer TaIrTe$_{4}$ is still a quantum spin Hall insulator. Theoretical analysis indicates that the covalent-like interlayer interaction in combination with the small bandgap at time-reversal invariant $Γ$ point results in new band inversion in bilayer TaIrTe$_{4}$, namely, the emergence of quantum spin Hall phase. Meanwhile, a topological phase…
In this brief report, we show the equivalence between the tight-binding descriptions of the monolayer and bilayer honeycomb lattices. With appropriate value of the third nearest neighbors coupling, the Hamiltonian for a monolayer is equivalent to the low energy effective Hamiltonian for bilayer in the presence of trigonal warping. A simple physical argument is provided to explain this correspondance.
Moiré superlattices of van der Waals heterostructures provide a powerful new way to engineer the electronic structures of two-dimensional (2D) materials. Many novel quantum phenomena have emerged in different moiré heterostructures, such as correlated insulators, superconductors, and Chern insulators in graphene systems and moiré excitons in transition metal dichalcogenide (TMDC) systems. Twisted phosphorene offers another attractive system to explore moiré physics because phosphorene features an anisotropic rectangular lattice, different from the isotropic hexagonal lattice in graphene and TM…
Vertical and lateral heterostructures of van der Waals materials provide tremendous flexibility for band structure engineering. Since electronic bands are sensitively affected by defects, strain, and interlayer coupling, the edge and heterojunction of these two-dimensional (2D) systems may exhibit novel physical properties, which can be fully revealed only by spatially resolved probes. Here, we report the spatial mapping of photoconductivity in a monolayer-bilayer WSe2 lateral heterostructure under multiple excitation lasers. As the photon energy increases, the light-induced conductivity detec…
The polarization analysis of optical transitions in monolayer and bilayer transition-metal dichalcogenides provides invaluable information on the spin and valley (pseudospin) degrees of freedom. To explain optical properties of a given monolayer transition-metal dichalcogenide, one should consider (i) the order of its spin-split conduction bands, (ii) whether intervalley scattering is prone to phonon bottleneck, (iii) and whether valley mixing by electron-hole exchange can take place. Using these principles, we present a consistent physical picture that elucidates a variety of features in the …
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…
Using first-principles calculations, we study the structural and electronic properties of the bilayer SnS/graphene, bilayer SnS/bilayer graphene (AA-stacked), bilayer SnS/bilayer graphene (AB-stacked) and monolayer SnS/graphene/monolayer SnS van der Waals (vdW) heterostructures. Electronic properties of all components of the vdW heterostructures are well preserved, which reflects the weakness of the vdW interaction. In the cases of bilayer SnS/graphene and bilayer SnS/bilayer graphene (AA-stacked), an Ohmic contact is formed which can be turned first into p-type and then into n-type Schottky c…
We report the strong dependence of resistance on uniaxial strain in monolayer WSe2 at various temperatures, where the gauge factor can reach as large as 2400. The observation of strain-dependent resistance and giant gauge factor is attributed to the emergence of nonzero Berry curvature dipole. Upon increasing strain, Berry curvature dipole can generate net orbital magnetization, which would introduce additional magnetic scattering, decreasing the mobility and thus conductivity. Our work demonstrates the strain engineering of Berry curvature and thus the transport properties, making monolayer W…
High-harmonic generation (HHG) in solids is an emerging method to probe ultrafast electron dynamics in solids at attosecond timescale. In this work, we study HHG from monolayer and bilayer graphene. Bilayer graphenes with AA and AB stacking are considered in this work. It is found that the monolayer and bilayer graphenes exhibit significantly different harmonic spectra. The difference in the spectra is attributed to the interlayer coupling between the two layers. Also, the intraband and interband contributions to the total harmonic spectrum play a significant role. Moreover, interesting polari…
Electron's tunneling through potential barrier in monolayer and bilayer graphene lattices is investigated by using full tight-binding model. Emphasis is placed on the resonance tunneling feature and inter-valley scattering probability. It is shown that normal incidence transmission probabilities for monolayer and bilayer graphene exhibit different properties. Our calculation indicates that valleytronics in graphene systems may be detected, generated and controlled by changing the structure parameters of the external electric potential.
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…
Molybdenum disulfide (MoS2) is a layered semiconductor which has become very important recently as an emerging electronic device material. Being an intrinsic semiconductor the two-dimensional MoS2 has major advantages as the channel material in field-effect transistors. In this work we determine the electronic structure of MoS2 with the highly accurate screened hybrid functional within the density functional theory (DFT) including the spin-orbit coupling. Using the DFT electronic structures as target, we have developed a single generic tight-binding (TB) model that accurately produces the elec…
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 …
Closed expressions for the Green functions of the stationary two-dimensional two-component Schrodinger equation for an electron moving in monolayer and bilayer graphene in the presence of a magnetic field are obtained in terms of the Whittaker functions.
In this work, the electrical properties of monolayer InSb in the presence of biaxial strain using density functional theory are investigated. Here, we first explore the band structure of InSb with and without spin-orbit coupling (SOC) consideration. The electron and hole effective mass modify with SOC consideration. The electron and hole effective masses lowered two and ten times, respectively. The location of valleys in conduction and valence band for various strains are explored, and the corresponding effective masses are reported. A lower effective mass is obtained for both electron and hol…
We use an atomistic approach to study the electronic properties of monolayer and bilayer black phosphorus in the vicinity of a charged defect. In particular, we combine screened defect potentials obtained from first-principles linear response theory with large-scale tight-binding simulations to calculate the wavefunctions and energies of bound acceptor and donor states. As a consequence of the anisotropic band structure, the defect states in these systems form distorted hydrogenic orbitals with a different ordering than in isotropic materials. For the monolayer, we study the dependence of the …
Multiple magnetic states, valley electronics, and topological phase transitions in two-dimensional Janus XYZH (X = Sc, Y, La, Y = Cl, Br, I, and Z = S, Se, Te): From monolayers to bilayers
We present ab initio calculations which show that the direct-band-gap, effective masses and Fermi velocities of charge carriers in ZnO monolayer (ML-ZnO) in graphene-like honeycomb structure are all tunable by application of in-plane homogeneous biaxial strain. Within our simulated strain limit of $\pm 10$%, the band gap remains direct and shows a strong non-linear variation with strain. Moreover, the average Fermi velocity of electrons in unstrained ML-ZnO is of the same order of magnitude as that in graphene. The results promise potential applications of ML-ZnO in mechatronics/straintronics …
Graphene monolayers supported on oxide substrates have been demonstrated with superior charge mobility and thermal transport for potential device applications. Morphological corrugation can strongly influence the transport properties of the supported graphene. In this paper, we theoretically analyze the morphological stability of a graphene monolayer on an oxide substrate, subject to van der Waals interactions and in-plane mismatch strains. First, we define the equilibrium separation and the interfacial adhesion energy as the two key parameters that characterize the van der Waals interaction b…
This work investigates the electronic properties of the energy spectrum of a hybrid system composed of (i) a circular quantum dot of monolayer graphene surrounded by an infinite sheet of AA-stacked bilayer graphene and (ii) a circular quantum dot of AA-stacked graphene bilayer surrounded by infinite monolayer graphene. We establish analytical findings for the related energy levels and wave functions using the continuum model and the zigzag boundary conditions at the graphene monolayer-bilayer interface. We investigate the effects of perpendicular magnetic, dot radius, and electrical fields on …
The electron transmission between monolayer and bilayer graphene is theoretically studied for zigzag and armchair boundaries within an effective-mass scheme. Due to the presence of an evanescent wave in the bilayer graphene, traveling modes are well connected to each other. The transmission through the boundary is strongly dependent on the incident angle and the dependence is opposite between the K and K' points, leading to valley polarization of transmitted wave.
Self-assembled monolayers (SAMs) of organic molecules are widely employed in surface chemistry and biology, and serve as ultra-fine lithographic resists. Due to their small thickness of only a few nanometers, the analysis of patterned monolayer surfaces using conventional methods requires thorough point-by-point scanning using complicated equipment. In the work reported herein, patterned monolayers are simply and directly observed using a bright-field optical microscope. The monolayers modify the spectral reflectivity pattern of a silica-on-silicon thin film, and introduce a contrast between b…
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…
By using first-principles calculations, we investigated the monolayer $ReS_2$ with vacancies under strain engineering, specifically focusing on its energy of formation, band gap, electron density of states, effective mass and optical properties. The calculated results disclose that S4 defect is more likely to form than other kinds of vacancies. Asymmetric deformation induced by strain makes its band structure transformation from direct band gap to indirect band gap. The analysis of the partial density of states indicates that the Re-d, Re-p and S-d orbitals are the major components of the defe…
The electronic and optoelectronic properties of two dimensional materials have been extensively explored in graphene and layered transition metal dichalcogenides (TMDs). Spintronics in these two-dimensional materials could provide novel opportunities for future electronics, for example, efficient generation of spin current, which should enable the efficient manipulation of magnetic elements. So far, the quantitative determination of charge current induced spin current and spin-orbit torques (SOTs) on the magnetic layer adjacent to two-dimensional materials is still lacking. Here, we report a l…
On the basis of tight-binding lattice model, the edge states of monolayer and bilayer graphene nanoribbons (GNRs) with different edge terminations are studied. The effects of edge-hopping modulation, spin-orbital coupling (SOC), and bias voltage on bilayer GNRs are discussed. We observe the following: (i) Some new extra edge states can be created by edge-hopping modulation for monolayer GNRs. (ii) Intralayer Rashba SOC plays a role in depressing the band energy gap $E_g$ opened by intrinsic SOC for both monolayer and bilayer GNRs. An almost linear dependent relation, i.e., $E_g\sim λ_R$, is fo…
In monolayer transition metal dichalcogenides, quantum emitters are associated with localized strain that can be deterministically applied to create designer nano-arrays of single photon sources. Despite an overwhelming empirical correlation with local strain, the nanoscale interplay between strain, excitons, defects and local crystalline structure that gives rise to these quantum emitters is poorly understood. Here, we combine room-temperature nano-optical imaging and spectroscopy of excitons in nanobubbles of localized strain in monolayer WSe2 with atomistic structural models to elucidate ho…
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 this study, we first show that the argon flow during epitaxial graphene growth is an important parameter to control the quality of the buffer and the graphene layer. Atomic force microscopy (AFM) and low-energy electron diffraction (LEED) measurements reveal that the decomposition of the SiC substrate strongly depends on the Ar mass flow rate while pressure and temperature are kept constant. Our data are interpreted by a model based on the competition of the SiC decomposition rate, controlled by the Ar flow, with a uniform graphene buffer layer formation under the equilibrium process at the…
We study theoretically effects of an anisotropic elastic strain on the exciton energy spectrum fine structure and optical selection rules in atom-thin crystals based on transition-metal dichalcogenides. The presence of strain breaks the chiral selection rules at the $\bm K$-points of the Brillouin zone and makes optical transitions linearly polarized. The orientation of the induced linear polarization is related to the main axes of the strain tensor. Elastic strain provides an additive contribution to the exciton fine structure splitting in agreement with experimental evidence obtained from un…
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…
In this work, the electrical and spin properties of monolayer MoSi2X4 (X= N, P, As, and Sb) under vertical strain are investigated. The band structures state that MoSi2N4 is an indirect semiconductor, whereas other compounds are direct semiconductors. The vertical strain has been selected to modify the electrical properties. The bandgap shows a maximum and decreases for both tensile and compressive strains. The valence band at K-point displays a large spin-splitting, whereas the conduction band has a negligible splitting. On the other hand, the second conduction band has a large spin-splitting…
The strain effects on the spin-orbit induced splitting of the valence band maximum and conduction band minimum in monolayer MoS2 and the gap in graphene are calculated using first-principles calculations. The dependence of these splittings on the various symmetry types of strain is described by means of an effective Hamiltonian based on the method of invariants and the parameters in the model are extracted by fitting to the theory. These splittings are related to acoustic phonon deformation potentials, or electron-phonon coupling matrix elements which enter the spin-dependent scattering theory…
An improved composite-boson theory of quantum Hall ferromagnets is formulated both for the monolayer and bilayer systems. In this scheme the field operator describes solely the physical degrees of freedom representing the deviation from the ground state. Skyrmions are charged excitations confined to the lowest Landau level. By evaluating the excitation energy of one skyrmion in the interlayer-coherent phase it is shown that the bilayer QH state becomes stabler as the interlayer density difference becomes larger.
Electrons behave like a classical fluid with a momentum distribution function that varies slowly in space and time when the quantum mechanical carrier-carrier scattering dominates over all other scattering processes. Recent experiments in monolayer and bilayer graphene have reported signatures of such hydrodynamic electron behavior in ultra-clean devices. In this theoretical work, starting from a microscopic treatment of electron-electron, electron-phonon and electron-impurity interactions within the Random Phase Approximation, we demonstrate that monolayer and bilayer graphene both host two d…
The tight-binding model of electrons in graphene is reviewed. We derive low-energy Hamiltonians supporting massless Dirac-like chiral fermions and massive chiral fermions in monolayer and bilayer graphene, respectively, and we describe how their chirality is manifest in the sequencing of plateaus observed in the integer quantum Hall effect. The opening of a tuneable band gap in bilayer graphene in response to a transverse electric field is described, and we explain how Hartree theory may be used to develop a simple analytical model of screening.
We use the T-matrix approximation to analyze the effect of a localized impurity on the local density of states in mono- and bilayer graphene. For monolayer graphene the Friedel oscillations generated by intranodal scattering obey an inverse-square law, while the internodal ones obey an inverse law. In the Fourier transform this translates into a filled circle of high intensity in the center of the Brillouin zone, and empty circular contours around its corners. For bilayer graphene both types of oscillations obey an inverse law.
We present an overview of the theoretical understanding of Hofstadter butterflies in monolayer and bilayer graphene. After a brief introduction on the past work in conventional semiconductor systems, we discuss the novel electronic properties of monolayer and bilayer graphene that helped to detect experimentally the fractal nature of the energy spectrum. We have discussed the theoretical background on the Moiré pattern in graphene. This pattern was crucial in determining the butterfly structure. We have also touched upon the role of electron-electron interaction in the butterfly pattern in gra…
We study the electronic spin relaxation effect in the hole-doped monolayer and bilayer transition-metal dichalcogenides in the presence of the crystal defects. We consider realistic models of the lattice vacancy and actually estimate the spin relaxation rate using the multi-orbital tight-binding model. In the monolayer, the spin-relaxation time is found to be extremely long compared to the momentum relaxation time, and this is attributed to the fact that the spin hybridization in the band structure is suppressed by the mirror reflection symmetry. The bilayer TMD has a much shorter spin relaxat…
Electronic structure of graphene monolayer-bilayer junction in a magnetic field is studied within an effective-mass approximation. The energy spectrum is characterized by interface Landau levels, i.e., the locally flat bands appearing near the boundary region, resulting in a series of characteristic peaks in the local density of states. Their energies are independent of boundary types such as zigzag or armchair. In the atomic scale, the local density of states shows a Kekulé pattern due to the valley mixing in the armchair boundary, while does not in the zigzag boundary.
The morphology and electronic structure of pentacene (Pn) deposited on Cu(111) was studied using scanning tunneling microscopy (STM) and spectroscopy (STS). Deposition of a multilayer followed by annealing to reduce coverage to a monolayer results in the formation of either of two unique phases: a 2D herringbone structure previously unobserved for any linear acene, or a 'random- tiling' structure. Coverage greater than a monolayer promotes the formation of a bilayer phase similar to that observed for Pn/Ag(111). STS shows that the electronic structure of the first layer is strongly modified du…
We calculate the Fermi energy dependence of the (time-averaged) current and shot noise in an impurity-free carbon bilayer (length $L\ll$ width $W$), and compare with known results for a monolayer. At the Dirac point of charge neutrality, the bilayer transmits as two independent monolayers in parallel: Both current and noise are resonant at twice the monolayer value, so that their ratio (the Fano factor) has the same 1/3 value as in a monolayer -- and the same value as in a diffusive metal. The range of Fermi energies around the Dirac point within which this pseudo-diffusive result holds is sma…
Anisotropic materials, with orientation-dependent properties, have attracted more and more attention due to their compelling tunable and flexible performance in electronic and optomechanical devices. So far, two-dimensional (2D) black phosphorus shows the largest known anisotropic behavior, which is highly desired for synaptic and neuromorphic devices, multifunctional directional memories, and even polarization-sensitive photodetector, whereas it is unstable at ambient conditions. Recently, 2D few-layered As2S3 with superior chemical stability was successfully exfoliated in experiments. Howeve…
