Biaxial Strain Research Articles

Biaxial and Uniaxial Strain Effect on Structural and Electronic Properties of Anatase TiO<sub>2</sub>: A First-Principle Calculation

The effect of biaxial and uniaxial strains on the electronic structure of anatase is studied using Density Functional Theory (DFT) calculation with ultrasoft pseudopotential and a generalized gradient approximation (GGA) Perdew-Burke Ernzerhof (PBE) exchange-correlation. The lattice constant is optimized using the Birch-Murnaghan equation of states (BM-EOS) to get an optimized geometric structure of anatase TiO2. We apply biaxial and uniaxial strains to this optimized structure up to 16% and find that the applied strains change the band gap energy compared to a pure anatase with a different band gap energy up to 1.61 eV for biaxial strain and 0.35 eV for uniaxial strain. The biaxial strains increase gap energies except at +16% tensile strain, decreasing the gap energy to 0.04 eV. Uniaxial strains tend to increase as the strains increase except at-12 and-16%; their gap energy differences are 0.08 and 0.20 eV, respectively, smaller than that of the zero strain. The results also show that the applied 16% tensile strain significantly lengthens the atomic bonds; thus, we conclude that the maximum strain applied to anatase TiO2 is 16%.

Strain engineering for optimized hydrogen storage: Enhancing ionic conductivity and achieving near-room-temperature desorption in Mg₂NiH₄

This study investigates strain engineering to optimize hydrogen storage in Mg₂NiH₄, with a focus on enhancing ionic conductivity and approaching room-temperature desorption. Using density functional theory (DFT), we analysed the effects of uniaxial and biaxial tensile and compressive strains on the structural, mechanical, diffusion kinetics, and electronic properties of Mg₂NiH₄. The activation energy for hydrogen diffusion was found to range from 0.38 to 0.45 eV under different strain conditions. The application of strain significantly influences ionic conductivity, with uniaxial strain resulting in values between 1.18 and 25.5 S/m, and biaxial strain yielding values from 12.3 to 18.3 S/m. Mechanical analysis shows that Mg₂NiH₄ exhibits brittle behaviour across all strain conditions. Additionally, electronic structure analysis indicates that the material maintains its metallic properties under both uniaxial and biaxial strain. Although the study did not achieve room-temperature desorption, it demonstrated significant progress, with desorption occurring at approximately 500 K. These results demonstrate that strain engineering can significantly improve ionic conductivity and facilitate hydrogen desorption closer to practical room temperature, providing valuable insights for optimizing Mg₂NiH₄ for practical hydrogen storage applications.

Strain-tunable electronic and magnetic properties of two-dimensional CrSBr material

Abstract Two-dimensional (2D) materials, particularly those with intrinsic magnetism, hold promise for next-generation spintronic devices due to their unique electronic and magnetic properties. This study investigates the impact of in-plane uniaxial and biaxial strain on the properties of monolayer CrSBr using density functional theory (DFT) and Monte Carlo (MC) simulations. We demonstrate that strain engineering can effectively modulate the electronic band structure and Curie temperature (Tc) of the CrSBr monolayer. Under uniaxial strains, transitions from indirect to direct bandgaps are observed, enhancing semiconductor characteristics. Importantly, compressive strain along the y-direction significantly increases Tc, potentially approaching room temperature. These findings highlight the role of strain manipulation in tailoring the functionality of 2D magnetic materials, crucial for advancing spintronics and nanoelectronic applications.

Theoretical insights into the ultrahigh piezoelectric performance of (BiFeO3)n/(BaTiO3)n (n = 1–5) superlattices

Perovskite structures have attracted extensive attention in microelectromechanical systems and nanoelectromechanical systems devices due to the high piezoelectric response and the low dielectric constant. The piezoelectric and dielectric properties of the tetragonal BiFeO3/BaTiO3 superlattices grown along the c-axis direction are investigated using density functional theory (DFT) and density functional perturbation theory. The calculated results demonstrate that the (BiFeO3)n/(BaTiO3)n (n = 1–5) superlattices exhibit a profoundly increased piezoelectric response compared to their bulk structures. The (BiFeO3)2/(BaTiO3)2 possesses the highest piezoelectric d33 of 697 pC/N among known lead-free perovskite systems. Furthermore, the (BiFeO3)2/(BaTiO3)2 superlattice possesses a low dielectric ɛ33, and its d33 at 2% tensile strain is 16 times larger than that of an unstrained equilibrium structure. This demonstrates that biaxial tensile strain significantly enhances the piezoelectric response. Combining the special quasirandom structure method with DFT, the structures of a 0.5BiFeO3–0.5BaTiO3 solid solution are predicted, and its calculated d33 is 58 pC/N, which is much smaller than that of a (BiFeO3)2/(BaTiO3)2 superlattice. The results suggest that the (BiFeO3)2/(BaTiO3)2 superlattice might be a potential candidate for nonvolatile random access memory, transducers and actuators, and nanoscale electronic devices.

Two-dimensional BiSbTeX2 (X = S, Se, Te) and their Janus monolayers as efficient thermoelectric materials.

Today, there is a huge need for highly efficient and sustainable energy resources to tackle environmental degradation and energy crisis. We have analyzed the electronic, mechanical and thermoelectric (TE) characteristics of two-dimensional (2D) BiSbTeX2 (X = S, Se and Te) and Janus BiSbTeXY (X/Y = S, Se and Te) monolayers by implementing first principles simulations. These monolayers' dynamic stability and thermal stability have been demonstrated through phonon dispersion spectra and ab initio molecular dynamics (AIMD) simulations, respectively. The band structure of these monolayers can be tuned by applying uniaxial and biaxial strains. The investigated lattice thermal conductivity (κl) for these monolayers lies between 0.23 and 0.37 W m-1 K-1 at 300 K. For a more precise calculation of the scattering rate, we implemented electron-phonon coupling (EPC) and spin-orbit coupling effects to calculate the transport properties. For p(n)-type carriers, the power factor of these monolayers is predicted to be as high as 2.08 × 10-3 W m-1 K-2 and (0.47 × 10-3 W m-1 K-2) at 300 K. The higher thermoelectric figure of merit (ZT) of p-type carriers at 300 K is obtained because of their very low value of κl and high power factor. Our theoretical investigation predicts that these monolayers can be potential candidates for fabricating highly efficient thermoelectric power generators.

Multiferroic properties and the layer-stacking quantum anomalous Hall effect in two-dimensional RuOHX (X = F, Cl, Br)

Exploring the physics coupled with layer degrees of freedom in materials has become a hot topic in quantum layertronics. We propose a robust second-order topological insulator monolayer RuOHX (X = F, Cl, and Br), a two-dimensional ferromagnetic semiconductor with large valley polarization, capable of undergoing topological phase transition induced by strain effect. In the bilayer RuOHX, we achieve layer-polarized anomalous Hall effect through interlayer sliding, originating from layer-stacking Berry curvature. Moreover, it can be controlled and reversed by the direction of ferroelectric polarization. Under appropriate biaxial strain, the bilayer RuOHX exhibits quantum layer spin Hall effect in which the helical edge states are manifested as spin-chirality-locking, due to the degeneracy of layer-polarized quantum anomalous Hall effect. Our work explores the potential application via layer-stacking topological properties for future quantum device applications.

Assessment of Thermoelectric Properties of Bi2Se3: Insights from Hybrid Functional Studies, Strain Engineering, and Machine Learning Methodology

AbstractThermoelectric properties in topological insulator Bi2Se3 are explored with multifaceted strategies, i.e., hybrid functional with strain and artificial intelligence methodology. The assessment with the experimental band gap values recognizes the limitations of conventional functional and the effectiveness of screened hybrid functionals. A thorough investigation into the impact of biaxial and uniaxial strain on thermoelectric parameters uncovers distinctive behaviors in n‐type and p‐type Bi2Se3, providing insights into optimal strain conditions for improved performance. Furthermore, the studies on the role of topologically non‐trivial surface states (TNSS) in thermoelectric properties reveal that TNSS significantly dominate electronic transport. Dual scattering time approximation elucidates the segregation of thermoelectric transport contributions from bulk and surface states, highlighting the importance of controlling the relaxation time ratio for enhanced thermoelectric performance. Additionally, the prediction of thermoelectric properties using Random Forest and Neural Networks models showcase impressive agreement with density functional theory predictions across varying temperatures, offering a powerful tool for understanding complex temperature‐dependent trends in thermoelectric properties. In summary, this interdisciplinary study presents a unique approach to advancing the understanding and optimization of thermoelectric properties in Bi2Se3. It provides a comprehensive framework for tailoring material behavior for diverse thermoelectric applications.

Van der Waals ZnO/HfSn2N4 Heterojunction with Exceptional Photoresponse for Photodetectors.

Two-dimensional van der Waals heterojunctions represent a promising avenue for a spectrum of optoelectronic endeavors. Nonetheless, their deployment has been somewhat constrained by the suboptimal efficiency of the photocurrent generated. In this article, a ZnO/HfSn2N4 heterojunction is proposed to achieve high photoresponse efficiency. First-principles calculations are utilized to confirm that this heterojunction possesses thermal stability with a direct bandgap (1.36 eV). It exhibits a high light absorption coefficient and high carrier mobility (2.51 × 103 cm2 V-1 s-1), and biaxial strain has a significant effect on the modulation of the band structure. As the tensile strain increases, the bandgap changes nonlinearly, transitioning from a type-II to a type-I heterojunction. When compressive strain increases, the bandgap decreases. Quantum transport simulations are employed to calculate the density of states and transmission spectrum of the ZnO/HfSn2N4 model, verifying its excellent photoresponse (a photocurrent peak reaching 4.93 a02/photon and an extinction ratio peak of 75.1). It shows that the ZnO/HfSn2N4 heterojunction is a potentially efficient photodetector.

Computational screening of Group VⅢ@C5N4 single-atom electrocatalysts for overall water splitting

Single-atom catalysts (SACs) have great potential for hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) since their high atomic utilization and strong metal–support interactions. Herein, we develop TM@C5N4 (TM = Fe, Co, Ni, Ru, Rh, Pd, Os, Ir and Pt) catalysts via embedding Group VⅢ TM in holey C5N4 substrate and further evaluate their electrocatalytic activity using density functional theory (DFT) calculations. Systematical studies indicate that Fe@C5N4, Pd@C5N4 and Ir@C5N4 catalysts all exhibit excellent HER performance, which mainly because of their small ΔGH* values of 0.101 eV, -0.114 eV and 0.070 eV, respectively. In parallel, Rh@C5N4 and Ir@C5N4 possess high OER activity along with low overpotential of 0.50 V, which is superior to the commercial IrO2 catalyst (0.56 V). Obviously, Ir@C5N4 could be utilized as bifunctional electrocatalysts both HER and OER in water splitting. Furthermore, we analyze their correlative catalytic mechanisms using the molecular orbitals. Besides, biaxial strain modulation could effectively regulate the catalytic activity of HER and OER. Particularly, 2 % biaxial tensile strain could bring Ir@C5N4 superb HER/OER catalytic performance. Finally, we anticipate that this strain engineering would provide a new perspective for developing high-performance SACs for water splitting.

Ultrasoft Conducting Polymer Hydrogels with Large Biaxial Strain and Conformal Adhesion for Sensitive Flexible Sensors

Ultrasoft Conducting Polymer Hydrogels with Large Biaxial Strain and Conformal Adhesion for Sensitive Flexible Sensors

Design of biphenylene-derived tunable dirac materials

The exploration of carbon allotropes has unveiled a series of two-dimensional (2D) materials with unique electronic and mechanical properties, yet the need for stable structures with tailored electronic properties persists. In this study, we introduce a new class of 2D carbon allotropes derived from the biphenylene network (BPN), incorporating acetylenic linkages to tune their structural and electronic characteristics. Through density functional theory calculations, we identified ten novel BPN-derived structures that exhibit both energetic and dynamic stability, confirmed by cohesive energy and phonon spectrum analyses. Among them, BPN-02 and BPN-04 are metallic, featuring critically-tilted type-III Dirac cones under ∼5 % biaxial strain, while BPN-22 is a semiconductor with a band gap of 0.95 eV and exhibits highly anisotropic carrier mobility. Additionally, these structures demonstrate significant anisotropy in their elastic properties, further distinguishing them from other 2D carbon materials like graphene. Our findings suggest that these novel BPN-based structures have strong potential for next-generation electronic and optoelectronic applications, providing new avenues for the design and synthesis of advanced carbon materials.

Strain and External Electric Field Engineering of S-Terminated MXene on Selective and Sensitive Detection of N-Containing Compound Gases: A Computational Study.

Gas sensors are used for monitoring hazardous gases and vapors. With the emergence of S-terminated MXene synthesis, herein, we explore the sensing ability of Ti3C2S2 toward N-containing gases, including NH3, NO, NO2, trimethylamine (TMA), and nicotine (NT), using first-principles calculations and a statistical thermodynamic model. We find that Ti3C2S2 exhibits high selectivity to TMA, NO, and NT with moderate adsorption energies of -0.610, -0.490, and -0.476 eV, respectively, minimizing environmental noise from ambient gases. The electronic structure of Ti3C2S2 subtly alters upon adsorption of TMA, NO, and NT, facilitating detectable signals in the sensing device. However, the adsorption of NO2 and NH3 is less pronounced due to weak physisorption (<0.3 eV). Employing engineering strategies including biaxial strain and an external electric field greatly enhances the selectivity and sensitivity of NO2 (NH3) detection by boosting adsorption strength up to -0.351 eV with ε = 5% (-0.370 eV with |E⃗| = 0.6 V/ Å). In addition, the moderate adsorption energies of the gases result in a suitable recovery time in the range of milliseconds, leading to high reusability of the sensing device. The estimated adsorption densities suggest potential coverage of these N-containing molecules even at low concentrations and room temperature. Computational analysis of the sensing capability of Ti3C2S2 using the nonequilibrium Green's function method indicates that it is a promising gas-sensing material. In addition, mechanical modifications, electric field adjustments, and gate voltage alterations could be used to obtain effective sensing materials for N-containing gas detection.

Fully spin-polarized two dimensional polar semi-metallic phase in Eu substituted GdI2 monolayer

Abstract The coexistence of seemingly mutually exclusive properties such as ferromagnetism, ferroelectricity and metallicity in atomically thin materials is the requirement of the hour in electronics as the Moore’s law faces an impending end. Only a few 2D multiferroic materials have been predicted/realized so far. The polar metals with simultaneous presence of polarity and conductivity are also equally rare. Here, we predict, based on first-principles calculations that an Eu-substituted rare-earth halide GdI2 monolayer showcases ferromagnetism, ferroelasticity while being polar and a fully spin-polarized semi-metal at the same time. The ferroelasticity and polarity are shown to be coupled making it possible to switch the polar direction using external mechanical stress. Further, it is observed that an application of biaxial tensile strain of 5% causes the spin easy-axis to shift from out-of-plane to in-plane direction. Thus, spin easy axis gets coupled with the direction of polarization in the strained monolayer making the switching of magnetization also possible using external strain. Simultaneous coexistence and coupling of the ferroic orders in a metallic 2D material makes the Eu substituted GdI2 monolayer an incredibly rare material for nano-electronics and spintronics applications.

Stacking-dependent structural and electronic properties of trilayer γ-graphyne: An approach for new 2D carbon allotropes.

Vertical stacks of two-dimensional (2D) materials with interlayer van der Waals (vdW) force have provided a versatile approach for creating hybrid materials and modulating various properties. In this work, the structural and electronic properties of trilayer γ-graphyne, involving different stacking patterns, have been investigated through first-principles approaches. The result indicates that a metal-to-semiconducting transition can be triggered simply by switching the stacking order of trilayer γ-graphyne. More interestingly, in addition to typical vdW homostructures, new 2D carbon allotropes with novel carbon networks can be achieved on the basis of trilayer γ-graphyne, arising from the absence of intralayer acetylene linkages during the structural relaxation. One of the new 2D carbon allotropes possesses an intrinsic semiconducting nature with a wide bandgap of 1.827 eV, coupled with superior structural stability beyond single-layer γ-graphyne. Moreover, the biaxial strain effect on the new 2D carbon allotrope, as well as the trilayer vdW stacks, has also been revealed in this work. Correspondingly, the in-plane tensile strain is demonstrated to further enlarge the electronic bandgaps in these carbon sheets. Therefore, the results of this work imply the great potential of few-layer graphyne in future carbon-based nanoelectronic devices, and simultaneously provide a new approach for developing and synthesizing novel 2D carbon allotropes via the vertical stacking of graphyne with inherent acetylene linkages.

Strain Engineering of ScYCCl2 MXene Monolayer and Intercalation of Metal-ions on MXene Surface: A DFT Study

The present work theoretically examines the influence of bi-axial strain on functionalized ScYCCl2 monolayer. The indirect to direct band gap transition on tensile conditions and the phase transition from semiconductor to metal on compressive strain have been studied. The analysis of extreme conditions of 10% compressive and 10% tensile strain through phonon and AIMD simulations underscore the kinetic and thermal stability, respectively of the monolayer under strain. These findings assure the possibility of experimental synthesis of the ScYCCl2 monolayer. After metallization, ScYCCl2 MXene is used as an anode of metal-ion (−Na, −K, −Li, −Mg) batteries as it has high theoretical storage capacity and low open circuit voltage. Work function engineering and the strain-dependent optical behavior of the ScYCCl2 monolayer have been examined. The work function of the ScYCCl2 monolayer has been raised under compressive strain and decreased under tensile strain. The Crystal Orbital Hamiltonian Population has been simulated under tensile and compressive strain to check the bond- strengths. Hence, the ScYCCl2 monolayer has the capability to alter its characteristics under strain. The improved optical characteristics recommend its applications in low-dimensional photonic devices and metallization after compressive strain recommends its energy storage applications in metal-ion batteries.

Robust topological insulating property in C2X-functionalized III-V monolayers

Two-dimensional topological insulators (TIs) show great potential applications in low-power quantum computing and spintronics due to the spin-polarized gapless edge states. However, the small bandgap limits their room-temperature applications. Based on first-principles calculations, a series of C2X (X = H, F, Cl, Br and I) functionalized III-V monolayers are investigated. The nontrivial bandgaps of GaBi-(C2X)2, InBi-(C2X)2, TlBi-(C2X)2and TlSb-(C2X)2are found to between 0.223 and 0.807 eV. For GaBi-(C2X)2and InBi-(C2X)2, the topological insulating properties originate from thes-px,yband inversion induced by the spin-orbital coupling (SOC) effect. While for TlBi-(C2X)2and TlSb-(C2X)2, the topological insulating properties are attributed to the SOC effect-induced band splitting. The robust topological characteristics are further confirmed by topological invariantsZ2and the test under biaxial strain. Finally, two ideal substrates are predicted to promote the applications of these TIs. These findings indicate that GaBi-(C2X)2, InBi-(C2X)2, TlBi-(C2X)2and TlSb-(C2X)2monolayers are good candidates for the fabrication of spintronic devices.

High Temperature Phonon-Mediated Superconductivity with T c above 100 K in monolayer Na(BC)2 and K(BC)2

Abstract Two-dimensional (2D) materials have demonstrated promising prospects owing to their distinctive electronic properties and exceptional mechanical properties. Among them, 2D superconductors with T c above the boiling point of liquid nitrogen (77 K) will exhibit tremendous applicable value in the future. Here, we design two 2D superconductors Na(BC)2 and K(BC)2 with MgB2-like structure, which are theoretically predicted to host T c as high as 99 and 102 K, respectively. The origin of such high T c is ascribed to the presence of two σ-bonding bands and van Hove singularity at the Fermi level. Furthermore, the T c of Na(BC)2 is boosted up to 153 K with a biaxial strain of 5%, which set a new record among 2D superconductors. The predictions of Na(BC)2 and K(BC)2 open the door to explore 2D high temperature superconductors and provide a potential future for developing new applications in 2D materials.

Microstructure characterization and formability assessment of electron beam welded Nb-10Hf-1Ti (wt.%) refractory alloy sheets

Formability study on welded blanks of Nb-based refractory alloy C-103 (Nb-10Hf-1Ti (wt.%)) has tremendous potential for utilizing smaller sheets for realization of large-size divergent portions of upper-stage liquid engine nozzle of satellite launch vehicles and thrusters of attitude orbital control systems. In this work, vacuum-annealed monolithic C-103 sheets were electron beam welded successfully to obtain defect-free welds and detailed microstructural and mechanical characterizations were investigated. Columnar epitaxial grains were found in fusion zone (FZ) instead of equiaxed grains in base metal (BM). Detailed SEM and HRTEM analyses revealed spherical shape of nano-sized HfO2 precipitates with monoclinic crystal structure in the C-103 sheet. Further, microhardness across the weld cross-section indicated that the FZ had a uniform and maximum hardness of ∼195 HV0.5 due to formation of finer nano-sized HfO2 precipitates with higher number density, followed by a lowering of hardness in a narrow heat-affected zone. A marginal reduction in tensile strength of ∼6% with a considerable decrease in ductility of ∼29% was noticed for the welded sample. However, fracture occurred in the BM region, indicating good weld integrity. Furthermore, formability of the welded blanks was evaluated in terms of limiting dome height (LDH), forming limit diagram, and deep drawn cup depth. The effect of the presence of WZ on the formability of the C-103 sheet was estimated under uniaxial, plane strain, and biaxial tensile strain paths for the first time, and the results were compared with the monolithic sample. It was noted that the failure limit of the welded specimens decreased compared to that of the monolithic sample, resulting in a lower LDH of approximately 69% and 62% when deformed along plane strain and biaxial tensile strain paths, respectively. However, a marginal variation in LDH was observed for the uniaxial strain path. Also, the welded blank had more resistance to material flow into the die cavity due to the harder weld region, resulting in a reduction of deep drawn cup depth by 52% than that of the monolithic blank. The overall results concluded that the presence of the WZ significantly affected the formability of the C-103 sheet, especially in plane strain and biaxial strain paths. However, the fracture was never found to be propagating along the weld line, indicating the ability of the weld to sustain large plastic strains. This study provides insightful information on the formability of electron beam welded C-103 sheets for the successful fabrication of space components.

Band gap correction via GGA[formula omitted]mBJ function and strained modulated physical properties of 2D-like DyOBr oxybromide

Two-dimensional (2D) oxyhalides offer unique and fascinating properties due to long-range magnetic ordering in a low dimensional limit. These have potential applications in spintronics and low-dimensional data storage devices. Herein, we demonstrate the biaxial ([110]) strain impact on the electronic and magnetic properties of thermodynamically stable 2D like DyOBr oxybromide based on the first-principles calculations including Hubbard parameter (U) and U+mBJ (modified-Becke-Johnson) methods as well as spin–orbit coupling (SOC) effects. Our calculations predict that an unstrained system exhibits an anti-ferromagnetic (AFM) insulating state with a direct wide energy band gap (Eg) of 5.404 eV within GGA+U+mBJ scheme and the estimated Neel temperature (TN) using the Ising model is 13 K, which is in excellent agreement with the experimentally observed values of 5.41 eV and 9.5 K, respectively. Moreover, it is revealed that Dy ions displayed a large partial spin magnetic moment (ms) of 4.969 μB/f.u. (per formula unit) with S = 2.5 as they lie in ＋ 3 state having the electronic configuration of [fx(x2−3y2)+fy(3x2−y2)]↑2↓1, [fxz2+fyz2]↑2↓1, [fz(x2−y2)]↑1↓0, [fxyz]↑1↓0, and [fz3]↑1↓0. Interestingly, the system displays a large magnetic anisotropy energy of 4.31 meV/atom with a magnetic easy axis of [100] (a-axis), which enhances its utilization in magnetic memory devices. Further, it is established that the AFM insulating behavior of the structure remains robust against biaxial ([110]) strain for the considered range of ±5%. However, a well-ordered shift in conduction band edge (CBE) position to higher and lower energy values is predicted for compressive and tensile strains, respectively. Strikingly, it is found that the TN increases to 265% for ＋5% strain.

Substrate Interference and Strain in the Second-Harmonic Generation from MoSe2 Monolayers.

Nonlinear optical materials of atomic thickness, such as non-centrosymmetric 2H transition metal dichalcogenide monolayers, have a second-order nonlinear susceptibility (χ(2)) whose intensity can be tuned by strain. However, whether χ(2) is enhanced or reduced by tensile strain is a subject of conflicting reports. Here, we grow high-quality MoSe2 monolayers under controlled biaxial strain created by two different substrates and study their linear and nonlinear optical responses with a combination of experimental and theoretical approaches. Up to a 15-fold overall enhancement in second-harmonic generation (SHG) intensity is observed from MoSe2 monolayers grown on SiO2 when compared to its value on a Si3N4 substrate. By considering an interference contribution from different dielectrics and their thicknesses, a factor of 2 enhancement of χ(2) was attributed to the biaxial strain: substrate interference and strain are independent handles to engineer the SHG strength of non-centrosymmetric 2D materials.