The effect of a uniaxial strain on the optical spin orientation of a cubic semiconductor is investigated by calculating the valence wavefunctions, the optical oscillator strengths and the initial electron spin polarization for near resonant light excitation from heavy and light valence levels. A strain orientation along the [001], [111] or [-110] crystal direction and a circularly-polarized light excitation parallel or perpendicular to the strain are considered. For all these cases, the total conduction electron spin polarization has a universal character since i) the oscillator strengths do not depend on the magnitude of the strain but only on its sign. ii) Although the oscillator strengths strongly depend on the configuration, the conduction electron spin polarization generated by optical transitions from both the heavy and light valence levels induced by sigma + light excitation is in all cases equal to -0.5 as predicted by the simple atomic model. iii) The spin polarization generated by light excitation from heavy and light valence levels does not depend on the deformation tensor and on the valence deformation potential, except for a strain along [-110].
The photocurrent properties of freely suspended single-walled carbon nanotubes (CNTs) are investigated as a function of uniaxial strain. We observe that at low strain, the photocurrent signal of the CNTs increases for increasing strain, while for large strain, the signal decreases, respectively. We interpret the non-monotonous behavior by a superposition of the influence of the uniaxial strain on the resistivity of the CNTs and the effects caused by Schottky contacts between the CNTs and the metal contacts.
The interplay of strain engineering and photon-assisted tunneling of electrons in graphene is considered for giving rise to atypical transport phenomena. The combination of uniaxial strain and a time-periodic potential barrier helps to control the particle transmission for a wide range of tunable parameters. With the use of the tight-biding approach, the elasticity theory, and the Floquet scattering, we found an angular shift of the maximum transmission in the sidebands for uniaxial strains breaking the mirror symmetry with respect to the normal incidence, which is called anomalous Floquet tun…
We present photoluminescence (PL) spectroscopy measurements of single-layer MoSe2 as a function of uniform uniaxial strain. A simple clamping and bending method is described that allows for application of uniaxial strain to layered, 2D materials with strains up to 1.1% without slippage. Using this technique, we find that the electronic band gap of single layer MoSe2 can be reversibly tuned by -27 +- 2 meV per percent of strain. This is in agreement with our density-functional theory calculations, which estimate a modulation of -32 meV per percent of strain, taking into account the role of defo…
We present first-principles calculations of electronic properties of graphene under uniaxial and isotropic strains, respectively. The semi-metallic nature is shown to persist up to a very large uniaxial strain of 30% except a very narrow strain range where a tiny energy gap opens. As the uniaxial strain increases along a certain direction, the Fermi velocity parallel to it decreases quickly and vanishes eventually, whereas the Fermi velocity perpendicular to it increases by as much as 25%. Thus, the low energy properties with small uniaxial strains can be described by the generalized Weyl's eq…
We study the effect of uniaxial strain on the electronic band structure of gapped graphene. We consider two types of gapped graphene, one which breaks the symmetry between the two triangular sublattices (staggered model), and another which alternates the bonds on the honeycomb lattice (Kekulé model). In the staggered model, the effect of strains below a critical value is only a shift of the band gap location. In the Kekulé model, as strain is increased, band gap location is initially pinned to a corner of the Brillouin zone while its width diminishes, and after gap closure the location of the …
We exploit the concept of strain-induced band structure engineering in graphene through the calculation of its electronic properties under uniaxial, shear, and combined uniaxial-shear deformations. We show that by combining shear deformations to uniaxial strains it is possible modulate the graphene energy gap value from zero up to $0.9$ eV. Interestingly enough, the use of a shear component allows for a gap opening at moderate absolute deformation, safely smaller than the graphene failure strain.
Strain engineering has arisen as a powerful technique to tune the electronic and optical properties of two-dimensional semiconductors like molybdenum disulfide (MoS2). Although several theoretical works predicted that biaxial strain would be more effective than uniaxial strain to tune the band structure of MoS2, a direct experimental verification is still missing in the literature. Here we implemented a simple experimental setup that allows to apply biaxial strain through the bending of a cruciform polymer substrate. We used the setup to study the effect of biaxial strain on the differential r…
We analyze the effect of tensional strain in the electronic structure of graphene. In the absence of electron-electron interactions, within linear elasticity theory, and a tight-binding approach, we observe that strain can generate a bulk spectral gap. However this gap is critical, requiring threshold deformations in excess of 20%, and only along preferred directions with respect to the underlying lattice. The gapless Dirac spectrum is robust for small and moderate deformations, and the gap appears as a consequence of the merging of the two inequivalent Dirac points, only under considerable de…
An exact mapping of the tight-binding Hamiltonian for a graphene's nanoribbon under any armchair uniaxial strain into an effective one-dimensional system is presented. As an application, for a periodic modulation we have found a gap opening at the Fermi level and a complex fractal spectrum, akin to the Hofstadter butterfly resulting from the Harper model. The latter can be explained by the commensurability or incommensurability nature of the resulting effective potential. When compared with the zig-zag uniaxial periodic strain, the spectrum shows much bigger gaps, although in general the state…
We study the effect of uniaxial strain on the band structure of ZrSe$_3$, a semiconducting material with a marked in-plane structural anisotropy. By using a modified 3-point bending test apparatus, thin ZrSe$_3$ flakes were subjected to uniaxial strain along different crystalline orientations monitoring the effect of strain on their optical properties through micro-reflectance spectroscopy. The obtained spectra showed excitonic features that blueshift upon uniaxial tension. This shift is strongly dependent on the direction along which the strain is being applied. When the flakes are strained a…
We study the dependence on the strength and orientation of applied uniaxial strain of the Drude weight in the conductivity of graphene. We find a nonmonotonic dependence on strain, which may be related to the proximity to several strain-induced electronic topological transitions. Given the relation between the Drude weight and the long-wavelength plasmon frequency, such a strain dependence can be evidenced by infrared spectroscopy measurements.
The effect of the uniaxial strain on the current-voltage characteristic of a typical armchair graphene-nanoribbon-hBN heterostructure device is simulated numerically by employing the nearest-neighbor tight-binding model and the non-equilibrium Green's function formalism. Simulations clearly reveal the following notable dependencies: (i) the strain invariably reduces the current; (ii) the strain applied in the armchair direction markedly widens the main peak of the current over a larger region of the bias voltage compared with the unstrained state; (iii) the current decreases faster when the st…
Uniaxial strain is known to modify significantly the electronic properties of graphene, a carbon single layer of atomic width. Here, we study the effect of applied strain on the composite excitations arising from the coupling of charge carriers and plasmons in graphene, i.e. the plasmarons. Specifically, we predict that the plasmaron energy dispersion, which has been recently observed experimentally in unstrained graphene, is shifted and broadened by applied uniaxial strain. Thus, strain constitutes an additional parameter which may be useful to tune graphene properties in plasmaronic devices.
We evaluate the optical reflectivity for a uniaxially strained graphene single layer between a SiO2 substrate and air. A tight binding model for the band dispersion of graphene is employed. As a function of the strain modulus and direction, graphene may traverse one of several electronic topological transitions, characterized by a change of topology of its Fermi line. This results in features in the conductivity within the optical range, which might be observable experimentally.
The spin and valley polarizations and plasmonics in Van der Waals heterostructures of strained graphene monolayer on 2D transition metal dichalcogenide (GrTMD) substrate are reported in this communication. The substrate induced interactions (SII) involve sub-lattice-resolved, and enhanced intrinsic spin-orbit couplings, the extrinsic Rashba spin-orbit coupling (RSOC), and the orbital gap related to the transfer of the electronic charge from graphene to the substrate. Furthermore, magnetic impurity atoms are deposited to the graphene surface and the corresponding exchange field is included in t…
We investigate the effect of an applied uniaxial strain on the ferromagnetic instability due to long- range Coulomb interaction between Dirac fermions in graphene. In case of undeformed graphene the ferromagnetic exchange instability occurs at sufficiently strong interaction within the Hartree- Fock approximation. In this work we show that using the same theoretical framework but with an additional applied uniaxial strain, the transition can occur for much weaker interaction, within the range in suspended graphene. We also study the consequence of strain on the formation of localized magnetic …
The Landauer-Büttiker conductivity of arbitrary uniaxial spatially dependent strain in an armchair graphene nanoribbon is studied. Due to the uniaxial character of the strain, the corresponding transfer matrix can be reduced to a product of $2\times2$ matrices. Then the conductivity and the Fano factor can be calculated from this product. As an example of the technique, sinusoidal space dependent strain fields are studied using two different strain wavelengths. For the bigger wavelength the conductivity is reduced when compared with the unstrained case, although both conductivities are almost …
The strain engineering technique allows us to alter the electronic properties of graphene in various ways. Within the continuum approximation, the influences of strain result in the appearance of a pseudo-gauge field and modulated Fermi velocity. In this study, we investigate theoretically the effect of linear uniaxial tensile strain and/or stress, which makes the Fermi velocity anisotropic, on a magnetized graphene sheet in the presence of an applied electrostatic voltage. More specifically, we analyze the consequences of the anisotropic nature of the Fermi velocity on the structure Landau le…
Recent advances in strain engineering at the nanoscale have shown the feasibility to modulate the properties of graphene. Although the electron-phonon (e-ph) coupling and Kohn anomalies in graphene define the phonon branches contributing to the resonance Raman scattering, and is relevant to the electronic and thermal transport as a scattering source, the evolution of the e-ph coupling as a function of strain has been less studied. In this work, the Kohn anomalies and the e-ph coupling in uniaxially strained graphene along armchair (AC) and zigzag (ZZ) directions were studied by means of densit…
Strain modulated electronic properties of Si/Ge core-shell nanowires along [110] direction were reported based on first principles density-functional theory calculations. Particularly, the energy dispersion relationship of the conduction/valence band was explored in detail. At the Γ point, the energy levels of both bands are significantly altered by applied uniaxial strain, which results in an evident change of band gap. In contrast, for the K vectors far away from Γ, the variation of the conduction/valence band with strain is much reduced. In addition, with a sufficient tensile strain (~1%), …
We investigate, based on the tight-binding model and in the linear deformation regime, the strain dependence of the electronic band structure of phosphorene, exposed to a uniaxial strain in one of its principle directions, the normal, the armchair and the zigzag directions. We show that the electronic band structure of strained phosphorene, for experimentally accessible carrier densities and uniaxial strains, is well described by a strain-dependent decoupled electron-hole Hamiltonian. Then, employing the decoupled Hamiltonian, we consider the strain dependence of the charged-impurity-limited c…
We derive the frequency shifts and the broadening of $Γ$ point longitudinal optical (LO) and transverse optical (TO) phonon modes, due to electron-phonon interaction, in graphene under uniaxial strain as a function of the electron density and the disorder amount. We show that, in the absence of a shear strain component, such interaction gives rise to a lifting of the degeneracy of the LO and TO modes which contributes to the splitting of the G Raman band. The anisotropy of the electronic spectrum, induced by the strain, results in a polarization dependence of the LO and TO modes. This dependen…
We study uniaxially strained graphene under the influence of non-uniform magnetic fields perpendicular to the material sample with a coordinate independent strain tensor. For that purpose, we solve the Dirac equation with anisotropic Fermi velocity and explore the conditions upon which such an equation possesses a supersymmetric structure in the quantum mechanical sense through examples. Working in a Laudau-like gauge, wave functions and energy eigenvalues are found analytically in terms of the magnetic field intensity, the anisotropy scales and other relevant parameters that shape the magneti…
Electronic screening renormalizes the linear bands of graphene and in the vicinity of the Dirac point, creates a diamond shaped structure in the quasiparticle spectral density. This is a result of electron-plasmon scattering processes which produce a finite momentum feature referred to as the `plasmaron ring'. In this work we explore the effects of uniaxial strain on these spectral features with the aim of understanding how strain modifies correlations. We derive and calculate the spectral density to the G$_0$W-RPA level which allows us to identify the dispersive behaviour of the diamond geome…
We theoretically investigate the manipulation of the quantum anomalous Hall effect (QAHE) in graphene by means of the uniaxial strain. The values of Chern number and Hall conductance demonstrate that the strained graphene in presence of Rashba spin-orbit coupling and exchange field, for vanishing intrinsic spin-orbit coupling, possesses non-trivial topological phase which is robust against the direction and modulus of the strain. Besides, we also find that the interplay between Rashba and intrinsic spin-orbit couplings results in a topological phase transition in the strained graphene. Remarka…
This paper reports on magnetometry and magnetoresistance measurements of MnSi epilayers performed in out-of-plane magnetic fields. We present a theoretical analysis of the chiral modulations that arise in confined cubic helimagnets where the uniaxial anisotropy axis and magnetic field are both out-of-plane. In contrast to in-plane field measurements (Wilson et al., Phys. Rev. B 86, 144420 (2012)), the hard-axis uniaxial anisotropy in MnSi/Si(111) increases the energy of (111)-oriented skyrmions and in-plane helicoids relative to the cone phase, and makes the cone phase the only stable magnetic…
We study the effects of an applied in-plane uniaxial strain on the plasmon dispersions of monolayer, bilayer and double-layer phosphorene structures in the long-wavelength limit within the linear elasticity theory. In the low energy limit, these effects can be modeled through the change in the curvature of the anisotropic energy band along the armchair and zigzag directions. We derive analytical relations for the plasmon modes under uniaxial strain and show that the direction of the applied strain is important. Moreover, we observe that along the armchair direction, the changes of the plasmon …
We report on a strain-induced and temperature dependent uniaxial anisotropy in V$_{2}$O$_{3}$/Ni hybrid thin films, manifested through the interfacial strain and sample microstructure, and its consequences on the angular dependent magnetization reversal. X-ray diffraction and reciprocal space maps identify the in-plane crystalline axes of the V$_{2}$O$_{3}$; atomic force and scanning electron microscopy reveal oriented rips in the film microstructure. Quasi-static magnetometry and dynamic ferromagnetic resonance measurements identify a uniaxial magnetic easy axis along the rips. Comparison wit…
Strain can induce a topological phase transition in bismuth dichalcogenides. We present the phase diagram for 3D topological insulators Bi$_2$Te$_3$, Sb$_2$Te$_3$, Bi$_2$Se$_3$ and Sb$_2$Se$_3$ with uniaxial and biaxal strain, which show metallic and insulating phases, both topologically trivial and non-trivial. In particular, uniaxial tension can drive Sb$_2$Te$_3$ into a topologically trivial insulating phase. Thus, we propose a Sb$_2$Te$_3$/Bi$_2$Te$_3$ heterojunction in which a topological interface state arises in the common gap of this topological insulator-normal insulator heterojunctio…
The main goal of our study was investigation of the influence of the deformations (sufficiently large for the establishing the non-zero gap) on electrotransport properties of impure graphene. To achieve this purpose, we implemented the simulation package that allows to perform numerical calculation of the conductivity and mobility of graphene samples subjected to two types of the uniaxial strain: along zigzag and armchair edges. All numerical calculations are performed within the Kubo-Greenwood methodology along with a tight-binding model. Transport properties are studied in case of a presence…
Molecular dynamics simulations are performed to investigate the structural phase transition in body-centered cubic (bcc) single crystal iron under high strain rate loading. We study the nucleation and growth of the hexagonal-close-packed (hcp) and face-centered-cubic (fcc) phases, and their crystal orientation dependence. Results reveal that the transition pressures are less dependent on the crystal orientations ($\mathtt{\sim}$14 GPa for loading along [001], [011], and [111] directions). However, the pressure interval of mixed phase for [011] loading is much shorter than loading along other o…
Graphene is a mechanically robust 2D material promising for flexible optoelectronic applications. However, its electromagnetic properties under strain are experimentally poorly understood. Here we present the far-infrared transmission spectra of large-area chemical-vapor deposited monolayer graphene on a polyethylene terephthalate substrate subjected to uniaxial strain. The effective strain value is calibrated using the Raman spectroscopy and corrected for a relaxation of wrinkles and folds seen directly by atomic-force microscopy. We find that while the Drude weight and the Fermi level remain…
Based on atomistic simulations, the nonlinear elastic properties of monolayer graphene nanoribbons under quasistatic uniaxial tension are predicted, emphasizing the effect of edge structures (armchair and zigzag, without and with hydrogen passivation). The results of atomistic simulations are interpreted within a theoretical framework of thermodynamics, which enables determination of the nonlinear functions for the strain-dependent edge energy and the hydrogen adsorption energy, for both zigzag and armchair edges. Due to the edge effects, the initial Young's modulus of graphene nanoribbons und…
Graphene membranes act as highly sensitive transducers in nanoelectromechanical devices due to their ultimate thinness. Previously, the piezoresistive effect has been experimentally verified in graphene using uniaxial strain in graphene. Here we report experimental and theoretical data on the uni- and biaxial piezoresistive properties of suspended graphene membranes applied to piezoresistive pressure sensors. A detailed model that utilizes a linearized Boltzman transport equation describes accurately the charge carrier density and mobility in strained graphene, and hence the gauge factor. The …
We study the fine structure of the phonon G peak in the inelastic light scattering spectra of strained graphene in the presence of a quantizing magnetic field. We show that under the conditions of the magnetophonon resonance (MPR), the spectral line shape in Raman spectra of the Γ-point longitudinal optic-transverse optical phonon undergoes multiple splitting and acquires a strong dependence on the polarization of the incoming and detected light. Interference of strain and MPR leads to the modification of the anticrossing branches, introducing the variation of the light polarization preference…
A double peak structure in the magneto-phonon resonance (MPR) spectrum of uniaxial strained graphene, under crossed electric and magnetic fields, is predicted. We focus on the $Γ$ point optical phonon modes coupled to the inter-Landau level transitions $0 \leftrightarrows \pm 1$ where MPR is expected to be more pronounced at high magnetic field. We derive the frequency shifts and the broadenings of the longitudinal (LO) and transverse (TO) optical phonon modes taking into account the effect of the strain modified electronic spectrum on the electron-phonon coupling. We show that the MPR lines a…
A simple model which combines tight-binding (TB) approximation with parameters derived from first principle calculations is developed for studying the influence of edge passivation and uniaxial strain on electron effective mass of armchair graphene nanoribbons (AGNRs). We show that these effects can be described within the same model Hamiltonian by simply modifying the model parameters i.e., the hopping integrals and onsite energies. Our model reveals a linear dependence of effective mass on band gap for H-passivated AGNRs for small band gaps. For large band gap, the effective mass dependence …
In cubic noncentrosymmetric ferromagnets uniaxial distortions suppress the helical states and stabilize Skyrmion lattices in a broad range of thermodynamical parameters. Using a phenomenological theory for modulated and localized states in chiral magnets, the equilibrium parameters of the Skyrmion and helical states are derived as functions of the applied magnetic field and induced uniaxial anisotropy. These results show that due to a combined effect of induced uniaxial anisotropy and an applied magnetic field Skyrmion lattices can be formed as thermodynamically stable states in large interval…
Intrinsic and Rashba spin-orbit interactions in strained graphene is studied within the tight-binding (TB) approach. Dependence of Slater-Koster (SK) parameters of graphene on strain are extracted by fitting the \emph{ab initio} band structure to the TB results. A generalized low-energy effective Hamiltonian in the presence of spin-orbit couplings is proposed for strained graphene subjected to an external perpendicular electric field. Dependence of the modified Rashba strength and other parameters of effective Hamiltonian on the strain and electric field are calculated. In order to analyze the…
One of the unique properties of graphene is its extremely high mechanical strength. Several studies have shown that the mechanical failure of graphene sheet under a tensile strain is due to the enhancement of the Kohn anomaly of the zone boundary transverse optical phonon modes. In this work, we derive an analytical expression of the Kohn anomaly parameter $α_{\vec{K}}$ of these phonons in graphene deformed by a uniaxial strain along the armchair direction. We show that, the tilt of Dirac cones, induced by the strain, contributes to the enhancement of the Kohn anomaly under a tensile deformati…
The vibrational and electronic properties of 2-dimensinal (2D) materials can be efficiently tuned by external strain due to their good stretchability. Resonant Raman spectroscopy is a versatile tool to study the physics of phonons, electrons and their interactions simultaneously, which is particularly useful for the investigation of strain effect on 2D materials. Here, for the first time, we report the resonant Raman study of strained few-layer InSe (γ-phase). Under ~ 1% of uniaxial tensile strain, one order of magnitude enhancement of Raman intensity for longitudinal optical (LO) phonon is ob…
InSe, a member of the layered materials family, is a superior electronic and optical material which retains a direct bandgap feature from the bulk to atomically thin few-layers and high electronic mobility down to a single layer limit. We, for the first time, exploit strain to drastically modify the bandgap of two-dimensional (2D) InSe nanoflakes. We demonstrated that we could decrease the bandgap of a few-layer InSe flake by 160 meV through applying an in-plane uniaxial tensile strain to 1.06% and increase the bandgap by 79 meV through applying an in-plane uniaxial compressive strain to 0.62%…
Due to the strong quantum confinement effect, few-layer γ-InSe exhibits a layer-dependent bandgap, spanning the visible and near infrared regions, and thus recently draws tremendous attention. As a two-dimensional material, the mechanical flexibility provides an additional tuning knob for the electronic structure. Here, for the first time, we engineer the band structures of few-layer and bulk-like InSe by uniaxial tensile strain, and observe salient shift of photoluminescence (PL) peaks. The shift rate of the optical gap is approximately 90-100 meV per 1% strain for 4- to 8-layer samples, whic…
We explore the electronic structure and topological phase diagram of heterostructures formed of graphene and ternary bismuth tellurohalide layers. We show that mechanical strain inherently present in fabricated samples could induce a topological phase transition in single-sided heterostructures, turning the sample into a novel experimental realisation of a time reversal invariant topological insulator. We construct an effective tight binding description for low energy excitations and fit the model's parameters to ab initio band structures. We propose a simple approach for predicting phase boun…
The current-voltage (I-V) characteristics of armchair graphene nanoribbons under a local uniaxial tension are investigated by using first principles quantum transport calculations. It is shown that for a given value of bias-voltage, the resulting current depends strongly on the applied tension. The observed trends are explained by means of changes in the band gaps of the nanoribbons due to the applied uniaxial tension. In the course of plastic deformation, the irreversible structural changes and derivation of carbon monatomic chains from graphene pieces can be monitored by two-probe transport …
Stacking graphene sheets forms graphite. Two in-plane vibrational modes of graphite, E1u and E2g(2), are derived from graphene E2g mode, the shifts of which under compression are all considered as results of in-plane bond shortening. Values of Gruneisen parameter have been reported to quantify such relation. However, the reason why the shift rates of these three modes with pressure differ is unclear. In this work, we introduce a new parameter to quantify the contribution of out-of-plane strain to the in-plane vibrational frequencies, suggesting that the compression of π-electrons plays a non-…
Non-equilibrium spin-polarized transport properties of antiferromagnetic stanene nanoribbons are theoretically studied under the combining effect of a normal electric field and linearly polarized irradiation based on the tight-binding model at room temperature. Due to the existence of spin-orbit coupling in stanene lattice, applying normal electric field leads to splitting of band degeneracy of spin-resolved energy levels in conduction and valence bands. Furthermore, unequivalent absorption of the polarized photons at two valleys which is attributed to an antiferromagnetic exchange field resul…
