Strain engineering is a powerful tool for tuning the electronic, magnetic, and topological properties of two-dimensional (2D) materials and thin films - particularly at high values of strain (>3%) where many electronic, magnetic, and structural transitions have been predicted. However, most approaches to tuning strain in 2D materials are limited below 1.5%, with poor repeatability when cycling strain and low strain transfer when cooling to cryogenic temperatures. Here, we report a high-yield sample preparation and device strain platform that overcomes these limitations, enabling precise, reversible strain tuning up to the intrinsic strain-to-failure of the materials tested herein. In addition, we show that this platform can be used to controllably design uniform linear strain gradients across of 10's of $μ$m, providing a novel route to systematically investigate flexoelectric and flexomagnetic phenomena. Using CrSBr as a model system, we demonstrate uniform uniaxial strain, up to ~4%, with negligible slippage and linear strain gradients of up to 0.06%/$μ$m. We further show that our strain approach is applicable to a broad class of 2D materials, validating its performance for three different phases of transition metal dichalcogenides: 2H-MoTe$_2$, 1T$^\prime$-MoTe$_2$ and T$_\mathrm{d}$-WTe$_2$. In T$_\mathrm{d}$-WTe$_2$, verified by theoretical calculations, we show a continuous redshift of the A$_1^3$ mode, up to a record-breaking ~5.5% strain, with a clear separation of the A$_1^3$ and A$_1^2$ modes starting at 2% strain.
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…
Uniaxial and biaxial strain approaches are usually implemented to switch the ferroelastic states, which play a key role in the application of the ferroics and shape memory materials. In this work, by using the first-principles calculations, we found not only uniaxial strain, but also shear strain can induce a novel ferroelastic switching, in which the van der Waals (vdW) layered direction rotates with the ferroelastic transition in layered bulk PdSe2. The shear strain induces ferroelastic switching with three times amplitude smaller than uniaxial strain. The novel three-states ferroelastic swi…
We theoretically investigate the effect of <100> uniaxial strain on a Ge-on-Si laser using deformation potentials. We predict a sudden and dramatic ~200x threshold reduction upon applying sufficient uniaxial tensile strain to the Ge gain medium. This anomalous reduction is accompanied by an abrupt jump in the emission wavelength and is explained by how the light-hole band raises relative to the heavy-hole band due to uniaxial strain. Approximately 3.2% uniaxial strain is required to achieve this anomalous threshold reduction for 1x1019 cm-3 n-type doping, and a complex interaction between unia…
Terahertz Raman spectroscopy was performed on high-mobility organic single-crystal semiconductors, by which the phonon energy at the Gamma point was qualified as a function of external uniaxial strain. The observation of peak shifts in Raman modes under uniaxial strain revealed that application of an external strain can effectively tune the intermolecular vibration that particularly correlates electron-phonon coupling. Terahertz Raman spectroscopy conducted in conjunction with molecular dynamics simulation provides an in-depth understanding of the recently discovered very large strain effect o…
We investigate the influence of uniaxial strain on site occupancy of hydrogen vanadium, using density functional theory. The site occupancy is found to be strongly influenced by the strain state of the lattice. The results provide the conceptual framework of the atomistic description of the observed hysteresis in the alpha to beta phase transition in bulk, as well as the preferred octahedral occupancy of hydrogen in strained V layers.
Graphene was deposited on a transparent and flexible substrate and tensile strain up to ~0.8% was loaded by stretching the substrate in one direction. Raman spectra of strained graphene show significant redshifts of 2D and G band (-27.8 cm^-1 and -14.2 cm^-1per 1% strain, respectively), because of the elongation of the carbon-carbon bonds. This indicates that uniaxial strain has been successfully applied on graphene. We also proposed that by applying uniaxial strain on graphene, tunable bandgap at K point can be realized. First principle calculations predicted a bandgap opening of ~300 meV for…
Characterization of strain in two-dimensional (2D) crystals is important for understanding their properties and performance. Using first-principles calculations, we study the effects of uniaxial strain on the Raman-active modes in monolayer MoS$_2$. We show that the in-plane $E'$ mode at 384 cm$^{-1}$ and the out-of-plane $A_1'$ mode at 403 cm$^{-1}$ can serve as fingerprints for the uniaxial strain in this 2D material. Specifically, under a uniaxial strain, the doubly degenerate $E'$ mode splits into two non-degenerate modes: one is $E_{\parallel}'$ mode in which atoms vibrate in parallel to …
In this Letter, we investigate the strain-induced band-gap modulation of both armchair and zigzag graphane nanoribbons based on the first-principles calculations. Within the elastic range, the band gap changes linearly with the uniaxial strain, where the band-gap of graphane nanoribbonsis more sensitive to compressive than tensile deformation. The band-gap deformation mainly originates from the shift of valence band edge of graphane nanoribbons under stain. Our results imply the great potential of graphane nanoribbons in the pressure sensor and optical electronics applications.
Molecular dynamics simulations are performed to investigate the buckling of single-layer MoS2 under uniaxial compression. The strain rate is found to play an important role on the critical buckling strain, where higher strain rate leads to larger critical strain. The critical strain is almost temperature-independent for T<50 K, and it increases with increasing temperature for T>50 K owning to the thermal vibration assisted healing mechanism on the buckling deformation. The length-dependence of the critical strain from our simulations is in good agreement with the prediction of the Euler buckli…
Antiferromagnetic thin films typically exhibit a multi-domain state, and control of the antiferromagnetic Néel vector is challenging as antiferromagnetic materials are robust to magnetic perturbations. By relying on anisotropic in-plane strain engineering of epitaxial thin films of the prototypical antiferromagnetic material LaFeO3, uniaxial Néel vector control is demonstrated. Orthorhombic (011)- and (101)-oriented DyScO3, GdScO3 and NdGaO3 substrates are used to engineer different anisotropic in-plane strain states. The anisotropic in-plane strain stabilises structurally monodomain monoclini…
We performed first - principles relativistic full-potential linearized augmented plane wave calculations for strained tetragonal ferromagnetic La(Ba)MnO$_3$ with an assumed experimental structure of thin strained tetragonal La$_{0.67}$Ca$_{0.33}$MnO$_3$ (LCMO) films grown on SrTiO$_3$[001] and LaAlO$_3$[001] substrates. The calculated uniaxial magnetic anisotropy energy (MAE) values, are in good quantitative agreement with experiment for LCMO films on SrTiO$_3$ substrate. We also analyze the applicability of linear magnetoelastic theory for describing the stain dependence of MAE, and estimate …
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 behavior of PbTiO$_3$ under uniaxial strains and stresses is investigated from first-principles calculations within density functional theory. We show that irrespectively of the uniaxial mechanical constraint applied, the system keeps a purely ferroelectric ground-state, with the polarization aligned either along the constraint direction ($FE_z$ phase) or along one of the pseudo-cubic axis perpendicular to it ($FE_x$ phase). This contrasts with the cases of isotropic or biaxial mechanical constraints for which novel phases combining ferroelectic and antiferrodistortive motions have been pr…
We present a computational study of the magnetic anisotropy energy for a given concentration of the Mn ions in the GaAs host, in the framework of the density functional theory. We focus on the influence of a different kind of strains on the uniaxial magnetic anisotropy constants $K_1$ and $K_2$, which reflect the magnetic anisotropy energy out- and in- (001) plane, respectively. We have shown that the general trends for the applied biaxial strain on anisotropy constants are consistent with the experimental data. We have predicted the critical strains, for which the magnetization vector changes…
In the present work, a method for the study of the structural deformations of two dimensional planar structures under uniaxial strain is presented. The method is based on molecular mechanics using the original stick and spiral model and a modified one which includes second nearest neighbor interactions for bond stretching. As we show, the method allows an accurate prediction of the structural deformations of any two dimensional planar structure as a function of strain, along any strain direction in the elastic regime, if structural deformations are known along specific strain directions, which…
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%), …
Using first-principles calculations we determine the role of compressive and tensile uniaxial and equibiaxial strain on the structural, electronic and magnetic properties of V$_2$O$_3$. We find that compressive strain increases the energy cost to transition from the high-temperature paramagnetic metallic phase to the low-temperature antiferromagnetic insulating phase. This shift in the energy difference can be explained by changes in the V-V bond lengths that are antiferromagnetically aligned in the low temperature structure. The insights that we have obtained provide a microscopic explanation…
Charge transport in Rubrene single crystals under uniaxial mechanical strain is systematically investigated in the crystal's two in-plane transport directions both under tensile and compressive strain applied parallel or perpendicular to the current direction. The density of trap states remains unchanged. The field-effect mobility as a benchmark figures for intermolecular transport is found to increase with compressive strain and vice versa with a magnitude of -1.5 cm2/Vs per percent of strain independently of tranport direction. A very remarkable result is the mobility change when the crystal…
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…
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}$14 GPa for loading along [001], [011], and [111] directions). However, the pressure interval of mixed phase for [011] loading is much shorter than loading along other o…
Electronic Phase Transformations and Energy Gap Variations in Uniaxial and Biaxial Strained Monolayer VS$_2$ TMDs: A Comprehensive DFT and Beyond-DFT Study
Electronic structures of wurtzite GaAs nanowires in the [0001] direction were studied using first-principles calculations. It was found that the band gap of GaAs nanowires experience a direct-to-indirect transition when the diameter of the nanowires is smaller than ~28 Å. For those thin GaAs nanowires with an indirect band gap, it was found that the gap can be tuned to be direct if a moderate external uniaxial strain is applied. Both tensile and compressive strain can trigger the indirect-to-direct gap transition. The critical strains for the gap-transition are determined by the energy crossov…
We report on a systematic study of the stress transferred from an electromechanical piezo-stack into GaAs wafers under a wide variety of experimental conditions. We show that the strains in the semiconductor lattice, which were monitored in situ by means of X-ray diffraction, are strongly dependent on both the wafer thickness and on the selection of the glue which is used to bond the wafer to the piezoelectric actuator. We have identified an optimal set of parameters that reproducibly transfers the largest distortions at room temperature. We have studied strains produced not only by the freque…
Uniaxial tensile properties of hexagonal boron nitride nanoribbons and dependence of these properties on temperature, strain rate, and the inclusion of vacancy defects have been explored with molecular dynamics simulations using Tersoff potential. The ultimate tensile strength of pristine hexagonal boron nitride nanoribbon of 26 nm x 5 nm with armchair chirality is found to be 100.5 GPa. The ultimate tensile strength and strain have been found decreasing with increasing the temperature while an opposite trend has been observed for increasing the strain rate. Furthermore, the vacancy defects re…
The effects of uniaxial strain on the structural, orbital, optical, and magnetic properties of LaMnO_3 are calculated using a general elastic energy expression, along with a tight-binding parameterization of the band theory. Tensile uniaxial strain of the order of 2 % (i.e., of the order of magnitude of those induced in thin films by lattice mismatch with substrates) is found to lead to changes in the magnetic ground state, leading to dramatic changes in the band structure and optical conductivity spectrum. The magnetostriction effect associated with the Neel transition of bulk(unstrained) LaM…
The identification of the crystalline axis of anisotropic black phosphorus (BP) is key for the study of its physical properties and for its optical and electronic applications. Herein, we show that by applying an in-plane uniaxial strain and measuring the changes of Raman shifts, the crystalline axis of BP can be reliably determined. The strain effects on Raman shifts are angle-dependent, which can be expressed as a combination of Raman responses under zigzag and armchair strains. Different from previous polarized optical spectroscopic means, the proposed method does not rely on the laser pola…
Non-collinear spin order that breaks space inversion symmetry and allows efficient electric-field control of magnetism makes BiFeO$_3$ a promising candidate for applications in low-power spintronic devices. Epitaxial strain effects have been intensively studied and exhibit significant modulation of the magnetic order in BiFeO$_3$, but tuning its spin structure with continuously varied uniaxial strain is still lacking up to date. Here, we apply \emph{in situ} uniaxial strain to a freestanding BiFeO$_3$ film and use scanning NV microscope to image the nanoscale magnetic order in real-space. The …
Among the interfacial transport modulations to the LaAlO3/SrTiO3 (LAO/STO) heterostructure, mechanical strain has been proven to be an effective approach by growing the LAO/STO films on different substrates with varying lattice mismatches to STO. However, this lattice-mismatch-induced strain effect is static and biaxial, hindering the study of the strain effect in a dynamic way. In this work we realize dynamic and uniaxial strain to the LAO/STO oxide heterostructure at low temperature, through mechanical coupling from a magnetostrictive template. This anisotropic strain results in symmetry bre…
Decoupling the effects of geometry and nature of strain in LaMnO$_3$: Interplay of dynamic correlations and uniaxial strain driving magnetic phase transitions
Strain manipulation of the magnetic domains, such as the stripe domains and skyrmions, has attracted considerable attention because of its potential applications for magnetic logic and memory devices. Here, utilizing phase-field modeling, we demonstrate the deterministic modulation of the orientation and the configuration of the stripe domains and skyrmions by using a uniaxial strain. The reorientation of the stripe domains can be caused by a suitable strain, and the direction of the reorientated domains is determined by the direction of the applied uniaxial strain and the type of domain walls…
Structural strain severely impacts material properties such as the linear and non-linear optical response. Moreover, strain plays a key role, e.g., in the physics of ferroelectrics and in particular of their domain walls. $μ$-Raman spectroscopy is a well-suited technique for the investigation of such strain effects, as it allows to measure the lattice dynamics locally. However, quantifying and reconstructing strain fields from Raman maps requires knowledge on the strain dependence of phonon frequencies. In this work, we have analyzed both theoretically and experimentally the phonon frequencies…
The effect of uniaxial strain on electronic structure and magnetism in LaMnO$_3$ is studied from a model Hamiltonian that illustrates the competition between the Jahn-Teller, super exchange, and double exchange interactions. We retain in our model the three main octahedral distortions ($Q_1, Q_2$, and $Q_3$), which couple to the Mn $(e_g)$ electrons. Our results show the ground state to be a type A antiferromagnetic (AFM) insulating state for the unstrained case, consistent with experiments. With tensile strain (stretching along the c axis), the ground state changes into a ferromagnetic and ev…
Uniaxial tensile tests are performed on a polymethyl methacrylate (PMMA) grade over a range of temperatures near the glass transition and over two decades of strain rate. Deformation maps are constructed for Young's modulus, flow strength, and failure strain as a function of temperature for selected strain rates. The glassy, glass transition and rubbery regimes are identified, and constitutive relations are calibrated for the modulus and flow strength within each regime.
Graphene is the two-dimensional building block for carbon allotropes of every other dimensionality. Since its experimental discovery, graphene continues to attract enormous interest, in particular as a new kind of matter, in which electron transport is governed by a Dirac-like wave equation, and as a model system for studying electronic and phonon properties of other, more complex, graphitic materials[1-4]. Here, we uncover the constitutive relation of graphene and probe new physics of its optical phonons, by studying its Raman spectrum as a function of uniaxial strain. We find that the doubly…
Strain engineering provides an effective way of tailoring the electronic and optoelectronic properties of semiconductor nanomaterials and nanodevices, giving rise to novel functionalities. Here, we present direct experimental evidence of strain-induced modifications of hole mobility in individual GaAs nanowires, using in situ transmission electron microscopy (TEM). The conductivity of the nanowires varied with applied uniaxial tensile stress, showing an initial decrease of ~5-20% up to a stress of 1~ 2 GPa, subsequently increasing up to the elastic limit of the nanowires. This is attributed to…
The electronic structure of Pb$_{1-x}$Sn$_{x}$Te is studied by using the relativistic Korringa-Kohn-Rostoker Green function method in the framework of density functional theory. For all concentrations $x$, Pb$_{1-x}$Sn$_{x}$Te is a direct semiconductor with a narrow band gap. In contrast to pure lead telluride, tin telluride shows an inverted band characteristic close to the Fermi energy. It will be shown that this particular property can be tuned, first, by alloying PbTe and SnTe and, second, by applying hydrostatic pressure or uniaxial strain. Furthermore, the magnitude of strain needed to s…
