Recent Progress in Strain Engineering on Van der Waals 2D Materials: Tunable Electrical, Electrochemical, Magnetic, and Optical Properties

Strain engineering is a promising way to tune the electrical, electrochemical, magnetic, and optical properties of 2D materials, with the potential to achieve high‐performance 2D‐material‐based devices ultimately. This review discusses the experimental and theoretical results from recent advances in the strain engineering of 2D materials. Some novel methods to induce strain are summarized and then the tunable electrical and optical/optoelectronic properties of 2D materials via strain engineering are highlighted, including particularly the previously less‐discussed strain tuning of superconducting, magnetic, and electrochemical properties. Also, future perspectives of strain engineering are given for its potential applications in functional devices. The state of the survey presents the ever‐increasing advantages and popularity of strain engineering for tuning properties of 2D materials. Suggestions and insights for further research and applications in optical, electronic, and spintronic devices are provided.


Introduction
2D materials are atomically thin layers with high flexibility and strain sensitivity. [1][2][3] Phonons and electrons in 2D materials are limited in the planar dimensions, resulting in many distinct and outstanding properties compared to their 3D bulk www.advmat.de www.advancedsciencenews.com Strain engineering is an effective and promising way to manipulate the electrical, magnetic, and optical properties of 2D materials. The multiple tunable functionalities (electrical, magnetic, optical, and mechanical) and their intercouplings in 2D materials provide rich opportunities to design innovative materials or composites with broad applications in electromechanical devices and sensors, etc. Given the promising application of strain engineering of 2D materials, there have emerged increasing number of research studies and review papers on this topic.  For example, Guinea [29] reviewed strain engineering on the electronic properties of graphene. Bissett et al. [30] summarized recent advances in strain engineering using Raman spectroscopy and electrical transport and the effect of strain on the chemical function of graphene. Roldán et al. [31] discussed the progress of strain engineering to control the electronic and optical properties of semiconducting 2D crystals. Si et al. [32] examined the effect of strain in graphene on the electronic structure, Raman spectra, the electronphonon coupling, pseudo magnetic fields, and the potential applications of strain engineering in the self-assembly of foreign atoms on the surface of graphene. Deng et al. [2] introduced the structure and mechanical properties of different kinds of 2D nanomaterials, summarized the methods to induce strain, and reviewed various modified properties caused by strain engineering, followed by a discussion about future perspectives. Dai et al. [1] summarized new opportunities and challenges focusing on the interface properties. Du et al. [3] outlined the recent progress of strain engineering on the flexible optoelectronics of 2D materials and discussed the current challenges in this area. Blundo et al. [33] have comprehensively summarized strain-tuned electronic, optical, and vibrational properties of 2D crystals.
Despite the fair number of reviews already published on this topic as cited above,  we present an updated review motivated by the rapid pace of advancement in this field and a number of more recent and important new developments, ranging from new experimental methods to new or less reviewed properties (e.g., magnetic, superconducting, electrochemical) explored in strain engineering. In this review, we summarized and discussed recently reported new methods to induce strain, updated the latest developments on the modification of electrical, magnetic, and optical properties of 2D materials by strain engineering, and presented future perspectives.

Novel Methodology to Induce Strain
Different methods have been previously applied to induce or engineer strain in 2D materials, through intrinsic ripples, mechanical exfoliation, epitaxial growth, thermal expansion mismatch, strain relaxation and critical thickness in heterostructures, chemical doping and absorption, deformation of flexible substrates, substrate surface topography modification, piezoelectric substrate actuation, as well as pressurized blisters, blown-bubble, and tip indentation. The advantages and disadvantages of all these methods have been summarized by Deng et al. [2] previously. Some newly emerging or optimized approaches to induce strain in 2D materials are updated and discussed herein.

Polymer Encapsulation
One limitation in many previous methods for straining and manipulating 2D materials is weak van der Waals (vdW) interaction and severe slippage between the substrate and 2D material. Recently, Li et al. [34] developed a simple method to efficiently modulate the strain of 2D materials by polymer encapsulation (Figure 1a,b). Using a spin-coating approach, the monolayer 2D material (MoS 2 ) was encapsulated in a flexible PVA substrate (Figure 1a,b). The mechanical strain could easily be transferred with negligible decoupling or slippage because of the strong interaction between 2D material and spin-coated PVA. When the uniaxial strain was applied to monolayer MoS 2 , a modulation rate (≈136 meV per %) and a bandgap modulation (≈300 meV) were observed. The modulation rate and bandgap modulation are two times of the results previously obtained. [34] It is worth noting that this simple method is also applicable to other 2D materials, including WS 2 or WSe 2, for increased bandgap modulation. [34] However, the spin-coating encapsulation approach can only provide strong interaction primarily between one layer of 2D material and the PVA substrate. At the same time, vdW heterostructures would remain bonded by weak vdW interaction, and the interlayer transfer of strain may mainly determine the overall device strain property. [34] Therefore, this method should be further optimized to work well to introduce strain on vdW heterostructures.

Local Strain Application
Some available approaches for strain induction are not ideal because they need complicated growth steps or macroscopic mechanical stresses. Furthermore, these methods cannot manage the strain locally at individual flake level and on a large scale to many individual devices on a single chip in engineering 2D material devices. Several studies reported the application of local strains. [35,36] For example, Mikael et al. [35] demonstrated the application of the nitride stressor layer to cause triaxial compressive stress in bilayer graphene. Colangelo et al. [36] used micrometric polymeric actuators to control local deformation in graphene. Peña et al. [37] reported a new method to induce compressive and tensile strain into MoS 2 through depositing stressed thin films to encapsulate exfoliated flakes. This technique can be used to directly engineer MoS 2 strain magnitude by modifying deposited thin film stress, allowing the application of different strains on a flake-to-flake level. After depositing a tensile thin-film stressor onto MoS 2 , the stressor would contract and result in compressive strain transferred to the MoS 2 layers. Due to substrate adhesion, when MoS 2 was grown on conventional substrates such as MgO or SiO 2 , only limited strain was transferred to monolayers. [37] To avoid this limitation, Peña et al. tested stressors on vdW heterostructures composed of monolayer (1L) MoS 2 on hexagonal boron nitride (h-BN). This method allows 0.85% of strain to be applied to the monolayer MoS 2 with a corresponding bandgap change (75 meV) induced by strain. It is expected that strain could be engineered to be higher if higher stressed thin films were used. [37] This study presented a different mechanism where strain is transferred using evaporated stressed polycrystalline thin www.advmat.de www.advancedsciencenews.com films. Another advantage of this technique is that the thin film stressors are analogous to SiN x based stressors, which are implemented in industrial complementary metal-oxidesemiconductor (CMOS) processes to increase Si mobility, implying that this technique is scalable and has the potential to be used for large-scale integration of strain engineered TMDC devices. Interestingly, Di Giorgio et al. [38] exposed mechanically exfoliated MoS 2 flakes on top of a Si/SiO 2 substrate through hydrogen ion irradiation to form hydrogen-filled, micro-and nano-sized spherical membranes (spontaneously   [34] Copyright 2020, The Authors, published by Springer Nature. c) Schematic illustration of the process used to achieve spontaneous and ordered domes. d) Tapping-mode AFM topography of uncoated MoS 2 surface after proton irradiation. e) Tapping-mode AFM topography of patterned HSQ-MoS 2 surface after proton irradiation. c-e) Reproduced with permission. [38] Copyright 2020, Wiley-VCH. f) Formation of random and patterned arrays of MoS 2 domes. Reproduced with permission. [39] Copyright 2020, Wiley-VCH. g) Schematic illustration of AFM tip induced graphene nanobubbles (GNBs). h) Enclosed pattern of GNBs generated through AFM tip using the ramp mode. The tip voltages used to form GNBs located at outer, middle, and inner loops are −8, −7, and −6 V, respectively. i) Bubble display of GNBs formed by AFM tip with voltage ranging from −4 to −9 V working at the contact mode. j) Generation of programmable GNBs with the increase of tip voltage from −4 to −11 V. g-j) Reproduced under the terms of the CC-BY Creative Commons Attribution 4.0 International license (https://creativecommons.org/ licenses/by/4.0). [41] Copyright 2019, The Authors, published by Springer Nature.
www.advmat.de www.advancedsciencenews.com formed domes), which holds a significant, local biaxial strain (Figure 1c-e), reaching up to 7-8%. Similarly, Blundo et al. [39] reported a method to generate a mechanical constraint in MoS 2 monolayers, which led to significant changes in the morphology of the domes ( Figure 1f) and enabled periodic giant, nonuniform biaxial strains close to the rupture critical values (>10%). It is worth noting that the highest biaxial strain (12-13%) was achieved in monolayer graphene, which is a benchmark compare to other methods applying strain. [40] However, it should be noted that these high-level strains are not possible for all 2D materials. [33] Among 2D materials, graphene and transition metal dichalcogenides such as MoS 2 stand out to be highly strain tunable so far. Interestingly, Jia et al. [41] developed a method to generate programmable graphene nanobubbles with tunable shape and size at predefined locations using AFM and H atom desorption (Figure 1g-j). This method can be useful to induce predesigned nanobubble with precise size, shape and location as well as to investigate physical phenomena of 2D materials at high magnetic field regimes that do not exist naturally.

Using Chemical Vapor Deposition Process for Strain Engineering
It is worth noting that conventional strain engineering methods such as heating and mechanical bending cannot conserve strain because of their dependence on external action, which limits the application of 2D materials in strain-electronics. In other words, the generated strain would disappear once the external action is removed, which makes it impossible to further study strain dependent electronic properties. Chen et al. [42] proposed that strain is formed by differences in thermal expansion coefficient between 2D materials and substrates such as between MoS 2 and Si/SiO 2 . They developed an optimized method to tune strain during chemical vapor deposition by applying different sulfur removal temperatures. This modified method was experimentally validated to adjust the carrier mobility of mono layer MoS 2 devices as large as two orders of magnitude from ≈ 0.15 to ≈ 23 cm 2 V -1 s -1 . This method should be tested in other 2D materials and heterostructures. It should be noted that Tian et al. [43] reported a different process, that graphene can induce surface reconstruction of Cu which should be generated by partial dislocations in Cu caused by the strain induced by the mechanically very strong graphene overlayer. More research is needed to further explore the varied mechanisms on how the strain is formed between 2D materials and substrates.

Tunable Electrical Properties of 2D Materials by Strain Engineering
Effects of strain on electrical transport of 2D materials reveal intriguing physics and future applications. [44][45][46][47][48][49][50][51] Besides several pioneering studies, [46,47] one recent example of such novel physics in strain systems is the work reported by Ho et al., [49] who demonstrated the introduction of the pseudo-magnetic field in bilayer graphene using a corrugated hBN surface to introduce strain. Low-temperature measurements of the quadratic dependence of second harmonic Hall voltage with current showed clear evidence of Berry curvature change from the strain-induced pseudo-magnetic field. The pseudo-magnetic field also caused a difference in the interlayer and intralayer coupling of the bilayer graphene, resulting in the planar Hall effect (Figure 2a). In another example for monolayer graphene, [44] the uniaxial strain of 0.21% induced scalar potential of 0.008 V, causing a shift in the Dirac point. The monolayer graphene was strained using a wedge setup and flexible polyimide substrate (Figure 2b).
Wu et al. [50] used flexible polyimide substrates to strain and demonstrate that odd layer MoS 2 can generate piezo current and voltage when strained at room temperature. The polarity of the induced voltage and current flipped if the direction of strain was rotated by 90°. A strain of 0.53% applied on a single flake resulted in a peak output of 15 mV and 20 pA and an efficiency of 5.08% in conversion of mechanical-to-electrical energy. Polyimide substrates have also been employed to strain transition-metal-dichalcogenide FETs. Shen et al. [45] demonstrated that 1.35% of strain applied on WSe 2 using such a method resulted in a bandgap shift of 100 meV. The bandgap shift was calculated from the change in flat band voltage (Figure 2c,d). Strained PtSe 2 using a similar method exhibited more than a 3% resistance change with an applied strain of 0.04%. [51] Using flexible substrate Su-8 instead of polyimide, Park et al. obtained up to 9.78% change in resistance in CVD grown bilayer MoS 2 with a strain of 0.145%. This study investigated the practical application of strain by placing the Su-8 film on the fingertip before introducing strain by bending with pen tips of varying diameters. [52] 2D materials that show phase transition from semiconducting to metallic are potentially applicable in logic transistors, integrated circuits, thermochromic windows, and topological devices. Transition metal dichalcogenides (TMDs) are 2D materials that have multiple structural and electronic phases. Zhao et al. [53] theoretically investigated the effect of strain engineering on the phase transition between 2H-and 1T′-MoTe 2 and found that the tensile strain along the armchair direction (+3.08%) or compression along with zigzag orientation (−3.40%) is required for phase transition (Figure 2e-j). Furthermore, a combined effect of strain engineering and charge doping was noted; the injected charge significantly affected the critical strain. The critical strain decreases linearly with the increase of the holedoping concentration. [53] This study presents a strategy for phase engineering in 2D materials.

Tunable Superconductivity by Strain Engineering
Strain engineering has also been demonstrated theoretically and experimentally to be able to change the superconducting transition temperature (T c ) or superconducting gap-closing temperature (T g ) of conventional and unconventional superconductors. [54][55][56][57][58][59][60][61][62][63][64][65][66] For instance, Tresca et al studied the effect of inplane strain on electronic, mechanical, and magnetic properties  [44] Copyright 2021, The Authors, published by Springer Nature. c) Multilayer WSe 2 strained on bent PET showed d) shift in flat-band voltage. c,d) Reproduced with permission. [45] Copyright 2016, American Chemical Society. e-h) Partial density of state of Mo and Te atoms in pristine MoTe 2 (e), and MoTe 2 under tensile strain ε a of 1% (f), 2% (g), and 3.57% (h). The green dashed lines indicate the moving of the p z orbitals. i) Free energies of 2H-and 1T′-MoTe 2 monolayer as a function of constant lattice a. j) Relative energy profile of the 2H-1T′ transition as a function of the reaction coordination for MoTe 2 with critical compression ε b . e-j) Reproduced with permission. [53] Copyright 2021, Elsevier. www.advmat.de www.advancedsciencenews.com of monolayer FeSe and FeTe on SrTiO 3 substrate, using the first-principles density functional theory. [55] This study predicted that both FeSe and FeTe monolayer are mechanically flexible to hold large strains up to 30% and a superconducting transition is expected if FeTe monolayer can be strained higher than 9%. [55] Ge et al. reported that a small tensile strain increased T c of 2D electride MgONa to 6.15 K using the similar theory. [56] Moreover, Celebonovic et al. performed the ab initio study about the effects of biaxial strain on two superconducting materials including doped graphene and isostructural MgB 2 monolayer. [57] The results showed that biaxial strain caused phonon to soften, affected the total interaction of electrons and phonons, and led to an increase in T c in both materials. [57] Experimentally, when tensile strain was applied in single-layer FeSe on Nb-doped BaTiO 3 , a T g up to 75 K was obtained, which is a record high pairing temperature for both monolayer-thick films and Fe-based superconductor. [54] Lin et al studied the structural and superconducting properties of FeSe 0.3 Te 0.7 thin films at different thickness growing on piezoelectric PMN-PT substrates, [58] where strain can be introduced during growth but also controlled by electric field (post-growth). The results showed that biaxial tensile strain exists in the thin films and the strain relaxed with the increase of film thickness. [58] When the film thickness is larger than 200 nm, the strain was fully relaxed (Figure 3a-d). [58] This study also indicated that electric field increased the T c of the thin film, which is caused by the reduced tensile strain. [58] In a follow up study, Mei et al. developed a two-step growth method to obtain high quality FeSe 0.5 Te 0.5 thin films on PMN-PT substrate and this high quality heterostructure enabled to achieve a remarkable tuning in T c induced by electric field at 20 nm FeSe 0.5 Te 0.5 thin film. [59] Strain has also been reported to be able to control superconductivity in few-layer NbSe 2 system when grown on insulating substrates (Figure 3e) [60] These studies demonstrated that superconductivity and change in T c can be realized through strain engineering in 2D superconductors.
While this review mainly focuses on 2D materials, it is of interest to mention that there are also many examples demonstrating that strain could affect the electronic properties of bulk superconductors. Under a uniaxial strain (≈0.6%), T c of Sr 2 RuO 4 enhanced from 1.5 kelvin (K) to 3.4 K. [61] Ivashko et al. [62] have showed that strain engineering can be useful to affect the T c of Mott-insulating La 2 CuO 4 . Diamond, which could turn into a superconductor with a T c ≈ 4 K, with the increase of compression-shear strain, its T c was predicted to be able to reach 12.4 K. [63] Also, the T c of zirconium nitride (ZrN) was predicted to increase from 10.0 to 17.1 K under tensile strains. [64] The potential of strain engineering on enhancing superconductivity and ferroelectric quantum criticality has also been recently revealed through plastic deformation of SrTiO 3 . [65] These examples again demonstrated that there is a great potential of strain engineering for the manipulation of superconducting transition temperature. Epitaxial strain has been shown to be able to change a normal metal to a superconductor by growing RuO 2 thin films on (110)-oriented TiO 2 substrates. [66] This strategy for regulating superconductivity is rationally designed by comparing the density functional theory calculations and results of angle-resolved photoemission spectroscopy experiments, [66] showing promise to generate novel transition-metal superconductors.

Tunable Electrochemical Properties of 2D Materials by Strain Engineering
Strain engineering of 2D multilayered heterostructures shows great potential for tuning electrochemical properties (including ionic conduction). [67,68] By interface strain engineering of a 2D multilayered VOPO 4 -graphene heterostructure, Xiong et al. reported a novel type of zero-strain cathode for reversible intercalation of beyond-Li + ions (K + , Na + , Zn 2+ , Al 3+ ) (Figure 4). [69] When applying the 2D multilayered heterostructures as cathodes, high-performance K + -ion batteries with a stable reversible capacity of 160 mA h g -1 and a high energy density of ≈570 W h kg -1 were obtained ( Figure 4). [69] This study demonstrated that straining engineering of 2D materials is useful for high-energy storage applications beyond lithium-ion batteries. Strain engineering has been demonstrated to be useful in promoting the catalytic performance of TMDS and noble metal nanosheets as well. Zhang et al. (2022) [70] recently developed an in situ self-vulcanization method to induce biaxial strain to MoS 2 nanoshells through a form of a single-crystalline Ni 3 S 2 @ MoS 2 core-shell heterostructures with controllable layer numbers (1-5 layers). They found that an electrode with bilayer MoS 2 nanoshells exhibits an outstanding hydrogen evolution reaction (HER) activity. [70] Based on both systematical electrochemical analysis and DFT calculations, it is found that the degree of biaxial strain, MoS 2 layer numbers, and the induced sulfur vacancies contribute to the increased catalytic activity. [70] This study is useful for preparing biaxially strained TMDs electrodes with tunable layer numbers for improving electrocatalytic performance. In a broader context of thin films, we noted that Wu et al. (2022) [71] reported a simple strategy to induce the planar strain in ultrathin noble metal nanosheets by creating amorphous-crystalline phase boundaries which could expose the active strained interfaces. These boundaries induced ≈4% of surface tensile strain in the nanosheets. The strained Ir nanosheets (denoted as AC-Ir NSs) showed about 4.5-fold higher intrinsic HER activity than the benchmark commercial Pt/C catalyst. [71] The underlying mechanism as calculations by density functional theory indicated that the d-band states and hydrogen adsorption performance of the strained Ir nanosheets are optimized by the introduced tensile strain, which thereby enhanced catalysis. [71] Subsequently, this in-plane strain engineering approach has been demonstrated to extendable to other noble metal nanosheets including those of Ru and Rh, [71] suggesting this is a general method with the ability to manipulate the spatial distribution of in-plane strain to improve the hydrogen evolution performance in various ultrathin noble metal nanosheets. It would be interesting to explore and extend such studies in 2D materials, including for other types of catalysis such as oxygen evolution reaction. All these examples revealed the great potential of strain engineering in tuning and improving the electrochemical activities and electrocatalytic performance of 2D materials.

Tunable Magnetic Properties of 2D Materials by Strain Engineering
In the past several years, besides theoretical and computational studies, a plethora of experimental investigations have www.advmat.de www.advancedsciencenews.com shown that strain engineering is an effective way to tune the magnetic properties of 2D materials. [24,48, For example, changing the sign of spin-spin exchange interactions in materials with magnetic order can switch between ferromagnetic (FM) and antiferromagnetic (AFM) phases, allowing novel types of magnetoresistive devices. It has been recently reported that atomically thin vdW magnets provide a new system to modify magnetic properties in electrical or nanomechanical ways. Although a switch from AFM to FM states has been reported in the A-type antiferromagnet CrI 3 at zero magnetic fields, [81,88] the phase transition is nonreversible. Moreover, magnetic phase transitions under strain in vdW magnets, though very little experimentally explored, was predicted in multiple studies. [53,84,91,92] Phase transitions have been experimentally demonstrated in thin membranes of 2D antiferromagnetic FePS 3 , NiPS 3 and MnPS 3, which can be probed by nanomechanical resonators. [86] This study further revealed that the observed strong relationship between antiferromagnetic order and mechanical motion in ultrathin membranes of 2D materials was mediated by the specific heat, and the Néel   [58] Copyright 2015, The Authors, published by Springer Nature. e) Reproduced with permission. [60] Copyright 2020, American Chemical Society.  4 nanoflakes, and VOPO 4 -graphene, and K + ions' zero-strain intercalation. a) Different restacking and interlayer lengths for bulk VOPO 4 ·2H 2 O, VOPO 4 nanoflakes, and VOPO 4 -graphene. b) Profiles of charge/discharge and in situ X-ray diffraction (XRD) patterns of VOPO 4 -graphene. c) Enlarged in situ XRD patterns of VOPO 4 -graphene from 11° to 15°. d) VOPO 4 -graphene's interlayer distance. e) Profiles of charge/discharge and in situ XRD patterns of VOPO 4 nanoflakes as cathodes for potassium-ion batteries. f) Enlarged in situ XRD patterns of VOPO 4 nanoflakes. g) VOPO 4 nanoflakes' interlayer distance. h) Ex situ V 2p X-ray photoelectron spectroscopy of VOPO 4 -graphene in different states including initial, discharged, and charged status. i) Proposed mechanism of reversible intercalation of K + ions for VOPO 4 -graphene based 2D multilayered heterostructure. a-i) Reproduced under the terms of the CC-BY Creative Commons Attribution 4.0 International license (https://creativecommons.org/ licenses/by/4.0). [69] Copyright 2020, The Authors, published by Springer Nature. www.advmat.de www.advancedsciencenews.com temperature of FePS 3 highly depend on electrostatically induced strain ( Figure 5). [86] This technique is especially useful for the characterization phase transitions of ultrathin membranes and expected to be applicable to 2D ferromagnets, thin 2D complex oxide sheets, organic antiferromagnets and other van der Waals materials.
Interestingly, a reversible strain-induced magnetic phase transition has been recently achieved in a vdW magnet. Cenker et al. [74] reported that the magnetic properties of the A-type layered antiferromagnetic semiconductor CrSBr could be modified by the application of a continuous, in situ uniaxial tensile strain, which reached several percent at cryogenic temperatures. To apply considerable strain on thin vdW flakes, the authors cleaved a silicon substrate to generate a microscopic gap that can suspend a sample. The authors used this newly designed platform to achieve a reversible magnetic phase transition between AFM to FM states induced by strain at zero magnetic fields. Furthermore, this study reported that strain resulted in significant changes in the spin-canting process under an applied out-of-plane magnetic field, demonstrating that strain can control both the saturating field and spin-canting process. These results provide new opportunities to control magnetism and other electronic states in 2D materials and heterostructures by strain engineering, opening potential applications such as strain-actuated magnetoresistive switches, strain tuning of second-harmonic generation through control of magnetic-stateinduced inversion symmetry breaking, and strain-controlled magnetic tunnel junctions that operate without an applied magnetic field. The authors think that the strain systems employed in this study should be further applicable in other 2D materials and heterostructures to control their electronic, structural, optical, and magnetic properties, which remain to be fully demonstrated in the future.
In another study, the magnetic properties of vdW ferromagnet Cr 2 Ge 2 Te 6 and its heterostructures Cr 2 Ge 2 Te 6 /NiO, including hysteresis loops and Curie temperature (T C ) of Cr 2 Ge 2 Te 6 , have been systemically investigated. [80] The results showed that Cr 2 Ge 2 Te 6 /NiO exhibited enhanced magnetic perpendicular anisotropy and T C . The maximum T C was about 120 K, which is onefold higher than in Cr 2 Ge 2 Te 6 only. [80] Moreover, it was found that the T C was increased in Cr 2 Ge 2 Te 6 /NiO with the Cr 2 Ge 2 Te 6 thickness ranging from 5 to 200 nm. [80] The enhanced magnetic anisotropy and T C were attributed to strain in Cr 2 Ge 2 Te 6 induced by interfacing with NiO. These results demonstrated that the utilization of heterostructure and interface with other materials helps control the magnetic properties of 2D materials.
Another recent theoretical study by Hu et al. [78] investigated the effect of strain on the magnetic properties of Fe 3 GeTe 2 (FGT) monolayers. It demonstrated that ferromagnetism can be enhanced to a large extent by tensile strain in FGT monolayers. In FGT monolayers, ferromagnetism can be improved mainly due to the competing effects of direct exchange and superexchange interactions. The average magnetic moment of the iron atoms increases monotonically with increasing biaxial strain from −5% to 5% in the FGT monolayer (Figure 6).
For conventional materials, growing thin films on substrates with various lattice mismatches is a common way to induce lattice strain. [98] For example, perovskite manganites, a class of materials with interesting magnetic properties and colossal magnetoresistance (CMR, where the resistivity decreases significantly in magnetic fields), have received extensive attention in this context due to their potential application in multifunctional devices and the complicated physical mechanism underlying the influence of strain on their electronic and magnetic properties. Heteroepitaxial composites of manganite/ferroelectric (FE) have emerged recently as one platform to study and harness such tunable properties. [99,100] Piezoelectric substrates such as Pb(Mg 1/3 Nb 2/3 ) and O 3 -PbTiO 3 (PMN-PT) have also been used to introduce strain in heterostructures involving the manganites. [101,102] Also, the ferroelectric ceramic material BaTiO 3 superlattices have been shown to induce strain when integrated into silicon and affect the magnetism of LaMnO 3 with the change of BaTiO 3 thickness. [98] In principle, such piezoelectric substrates should offer a promising method for electrically straining and tuning magnetic properties of 2D magnets, offering a platform to elucidate and explore the rich interplay between electric, magnetic, and lattice degrees of freedom in such artificial "multiferroic" heterostructures.
The Ruddlesden-Popper series of ruthenates Sr n+1 Ru n O 3n+1 , which can be considered a layered material, show excellent magnetic and electronic properties. Their ferromagnetic tendencies are generally strengthened by increasing the number n of RuO 2 sheets per unit cell. [103] The single-layer n = 1 compound Sr 2 RuO 4 has been extensively investigated for its unconventional superconductivity and magnetism. [104][105][106][107][108] In contrast, the ferromagnetic metal SrRuO 3 (SRO) has promising physical properties, including vertical hysteretic shift, magnetocrystalline anisotropy, exchange bias, and anomalous Hall effect for potential utilization in magnetic tunnel junctions and spin valves. [87,102] SRO films' lattice degree of freedom has been considered to offer a significant way to change their physical properties through external fields. For instance, lattice strain-mediated electric-field regulation of magnetic and electrical properties was achieved when an in-plane compressive strain was imposed on SRO films epitaxially grown on PMN-PT single crystals through the piezoelectric response. [109,110]

Strain Tuning of Optical Emission
The first single-photon emitters (SPEs) in 2D materials were discovered 6 years ago. [111][112][113] Local strain has been applied to induce such quantum emitters in TMDC and hexagonal boron nitride (h-BN). [114] For example, So et al. [115] have used local strain to induce electrically driven deterministic SPEs in a vdW heterostructure including graphene, h-BN, and WSe 2 . Parto et al. [116] reported a method to create site-controlled SPEs in atomically thin WSe 2 using simultaneous and independent strain engineering with nanoscale stressors and defect engineering through electron-beam irradiation. Emitters showed biexciton cascaded emission, and the highest purity of singlephoton reached over 95%, and the highest working temperature reached up to 150 K (Figure 7). [116] www.advmat.de www.advancedsciencenews.com Furthermore, Mukherjee et al. [117] reported the observation of electric field tuned SPEs at positions where strain is induced using WSe 2 , hBN, and few-layer graphene on a nanopillar array. They found that the emission energies were increased (blueshift) in those strain-induced emitters, in contrast to previous studies, which showed reduction in energy of randomly occurring quantum emitters in WSe 2 [117] It is noted that the trap potential of volume and depth still vary broadly among the various nanopillar sites on the same array. Hence, further experiments are needed to explore the exact physical origin of the   [86] Copyright 2020, The Authors, published by Springer Nature.

www.advmat.de www.advancedsciencenews.com
Adv. Mater. 2023, 35,2205714 sign and magnitude of the volume of different traps. In another study, Xu et al. [118] reported radiation-and lithography-free method to deterministically activate hBN SPEs using atomic force microscopy nanoindentation; the maximum yield of SPEs reached 36% for an indent size of 400 nm. This method used hBN flakes on flat silicon dioxide-silicon substrates (Si/SiO 2 ), which has the potential to be easily applied to on-chip photonic devices. [118] While the exact nature of such indentation-induced SPEs remain to be better understood, the author suggested that the creation of structural edges and highly strained hBN local areas near the indents may both play roles for the high SPE yield achieved. [118] These studies present new ways to generate deterministic SPEs, which are helpful for the practical application of integrated quantum light sources. Also, biaxial strain has been applied through strain transfer from a PMN-PT substrate to quantum emitters consisting of few-layer graphene, h-BN, and a monolayer WSe 2 flake. [119] With the change of biaxial strain on these emitters, the authors noted that the emission axis rotated by about 40°, and a maximum energy change up to 10 meV. [119] Significant progress has been made in this area, and SPE metrics, including purity, brightness, and indistinguishability, have increased during the past several years. On the other hand, future directions should include a better understanding of the trap volumes, depths, widths, and stabilities of SPEs, as well as more detailed mechanisms on how optical properties of 2D materials could be regulated by strain or defect engineering to achieve reversible, positional-deterministic and stable SPEs for their application for solid-state quantum light sources.

Strain Tuning of Photoconduction and Photocurrent
Recent work showed that 2D indium chalcogenides such as α-In 2 Se 3 and InS 2 are great candidates for next-generation optoelectronic-related devices. Still, traditional 2D indium chalcogenide devices on SiO 2 substrates' performance are limited by the substrate's detrimental effect, which significantly restricts charge transport. While an internal electric field could alleviate the situation, interface defects are inevitably introduced using conventional stacking technology. Yang et al. [120] developed a universal and simple structure for generating highly sensitive photodetectors and optimized this structure through a combination of strain and interface engineering. A SiO 2 window was generated to afford a "suspended" α-In 2 Se 3 channel, which effectively decreased the detrimental effects of the substrate. Moreover, this method induced local strain in the suspended α-In 2 Se 3 , regulating the band structure and causing an intramolecular type-II alignment. [120] Subsequently, the interfacial charge transfer was optimized, and the photodetection performance was improved. The device showed excellent photosensitivity with a responsivity of 1672 A W −1 , an on/ off ratio of 263, a detectivity of 7.5 × 10 13 Jones, and a relatively quick response rate with 12 ms for both decay and rise. [120] The broad application potential of the proposed approach has been tested, and results showed that this method could be extended to InSe devices to improve their photodetection capability. This study provides another strategy to improve the development of high-performance photodetectors based on 2D materials; whether it applies to other 2D material-based photodetectors beyond the ones studied is to be determined. In addition, Figure 6. a) Strain dependence of the distance and the bonding length (Fe1-Fe2 distance, d Fe1Fe2 ; Fe3Te bond length, d Fe3Te ; Fe1-Te bond length, d Fe1Te ; Fe3−Ge bond length, d Fe3Ge ). b) Electron transfer of Fe, Ge, and Te atoms in the FGT monolayer. c,d) PDOS of Fe1 atom (c) and Fe3 atom (d) in the FGT monolayer under −5%, 0%, and 5% biaxial strain, respectively. The blue and red solid lines indicate spin-up and spin-down channels, respectively. a-d) Reproduced with permission. [78] Copyright 2020, American Chemical Society.

www.advmat.de www.advancedsciencenews.com
Adv. Mater. 2023, 35, 2205714 strain engineering has been reported to regulate photoresponse of a 2D α-In 2 Se 3 /WSe 2 vdW heterostructure and 2D hybrid perovskite ferroelectric single-crystalline thin-films. [121,122] For instance, with the introduction of 0.433% of tensile strain, the photocurrent of the photodetector (α-In 2 Se 3 /WSe 2 vdW heterostructure) increased around 18-folds. Moreover, excellent photodetectivity and responsivity was achieved in the photodetectors. [121] Because of the noncentrosymmetric structure of III-VI compound α-In 2 Se 3 , the strain-caused piezopotential affects the band slope close to the P-N junction interface, which thereby enhanced the separation efficiency and transfer characteristics of photogenerated electron-hole pairs through piezophototronic effect. [121] These results suggest the potential of artificial heterostructures and straining in controlling optical properties.
Strain-induced electric fields have been shown to enhance the performance of phototransistor in thin HfS 2 device. [123] The strain was introduced by the formation of HfO 2 using focused laser spots on the device. The induced strain was compressive at HfO 2 /HfS 2 interface and tensile away from the interface. In the indirect 2D semiconductor HfS 2 , the tensile strain caused charge to funnel away from the oxidized spots. Photoresponsivity of the device was enhanced up to 350% at low power by such a strain profile (Figure 8). This study suggests a potential approach to design low-power consumption multifunctional electronic and optical devices based on strain engineering.
The co-effects of the light and electric field on lattice distortion and physical properties of SRO/PMN-PT epitaxial heterostructures were recently tested. [124] Results showed a strong correlation between the electric field and light, as indicated by the tunable resistance and photoresistance effects by light illumination and the electric field, respectively, which was mediated Figure 7. a,b) Defect and strain-engineered WSe 2 single-photon emitters (SPE). c-h) Site-controlled quantum emitter array through the defect and strain engineering, i-k) electrically driven SPE formed by AFM indentation, and l-n) splitting of fine structure from the single-photon emission. a) Changes in the spatial bandgap caused by strain (dashed gray line means the dark excitonic band; the solid blue lines represent valence band and bright band, respectively). b) Overview of 1L-WSe 2 strained on a SiO 2 nanopillar (seen in yellow and W atoms displayed in blue). Neutral excitons shown as e-h pairs, generated within the excitation laser spot, indicated by th red dashed line, funnel to strain regions with low potential. There is also a dark-exciton band from WSe 2 at energies lower than the bright exciton, which is optically prohibited by the transition selection of WSe 2 . The darkexciton can be strain-tuned to a defect-level becoming intervalley defect excitons when there is a defect (on the top of irradiated nanopillar represented by a blue dash) and at strained regions. c) Overview of the prepared structure and the sample's optical dark-field image. A stack of h-BN/WSe 2 /h-BN was transferred to the SiO 2 nanopillar array. Because of exciton funneling, bright emission was noted from the pillar top. Then, the top of pillars was irradiated (arrows indicating e − arrows) to generate structural defects. d) PL spectra showing unstrained WSe 2 defect-bound excitons for different irradiation intensity ranging from N 1 = 10 5 electrons µm −1 to N 2 = 10 6 electrons µm −1 . e) PL map of irradiated and strained sites integrated spectrally for wavelengths over 775 nm, indicating the bright emission related to SPEs. Some places held more than one emitter and reached saturation incident count. Because of the localized nature of the emitters, the maps are similar to the Gaussian spots of excitation laser; f) PL spectrum (1 µW excitation power) taken from various sites indicating the sharp emission lines (75 µeV average linewidths) related to SPEs. Note: many strong emission lines are present in pairs, suggesting that exciton-biexciton pairs formed. g,h) Histograms of the number of quantum emitters tested per site through irradiating with e-beam intensity of 10 5 and 10 6 electrons µm −2, respectively. i) Overview of the vertical heterostructure including top graphene/WSe 2 /h-BN/bottom graphene on the polymer substrate, with the emission site indented by an AFM tip. j) Overview of the strained heterostructure bands after applied external bias. E B , E D , E V , and E Defect are excitonic bright band, dark excitonic band, valence band, and defect state of WSe 2 , respectively. On the right panel, the dashed red and solid lines represent the changes in spatial bandgap resulting from strain. The strain-localized dark exciton was mixed with a defect state, leading to the generation of a localized defect exciton; k) fabrication process; l) electroluminescence (EL) spectrum with high resolution measured at a selected indentation site. A separation of ≈400 µeV and a linewidth of 755 µeV exists in observed fine structure splitting. m) Normalized EL intensities of the higher (red) and lower (black) energy peaks that indicated by corresponding color arrows in (l), as a role of the angle of polarization. The fitted curves are shown by the lines. The polarization degrees and angles are 0.965° and 148° (red) and 0.946° and 56° (black), respectively; n) EL spectrum of (l) as a role of angle of polarization. a-h) Reproduced under the terms of the CC-BY Creative Commons Attribution 4.0 International license (https://creativecommons.org/licenses/by/4.0). [116] Copyright 2021, The Authors, published by Springer Nature. by strain-driven lattice-orbital coupling. [124] This study suggests a potential approach to design low-power consumption multifunctional electronic and optical devices based on complex oxide heterostructures through strain engineering that may be applicable to various oxide or nonoxide 2D materials.
Du et al. [3] summarized recent progress of strain engineering on the flexible optoelectronics of 2D materials, they commented that a universal method to evaluate flexible optoelectronics of 2D materials among various devices is missing. Finally, six parameters including response time, cutoff wavelength, linear dynamic range, specific detectivity, photoresponsivity, and external quantum efficiency for easy comparison of the performance amongst different devices for further development and success of this area were summarized.

Tuning of Photovoltaics
Strain engineering has also been shown to be an effective strategy to enhance photovoltaics in 2D materials as well as other materials such as halide perovskites theoretically and experimentally. [125][126][127][128][129][130][131][132] Bastonero et al. (2022) [126] proposed a new single-layer heterostructure PdS 2 /PtS 2 based on ab initio many-body perturbation theory. It is calculated that this heterostructure shows excellent light absorbance, yielding up to 50% in the visible spectrum and reaching a short-circuit current of 7.2 mA cm −2 after solar irradiation. [126] Also, based on firstprinciples calculations, a 2D α-As/α-AsP vdW heterostructure was shown to be useful for photovoltaic applications under an in-plane strain ranging from −6% to 6% [130] and the photocurrent of the designed bifunctional GeC/SnSSe heterostructure based on first-principles and quantum transport calculations increased by 40% under a 4% tensile strain. [132] Experimentally, the flexo-photovoltaic effect (bulk photovoltaic effect induced by a strain gradient) was demonstrated in an archetypal 2D material, MoS 2 , through a strain-gradient engineering method based on structural inhomogeneity and phase transition of MoS 2 /VO 2 . [133] The bulk photovoltaic coefficient in MoS 2 was found to be orders of magnitude larger than most non-centrosymmetric materials. [133] The relationship between a strain gradient and the flexo-photovoltaic effect in lowdimensional materials shows great potential to explore novel optoelectronic phenomena in strain-gradient-engineered materials for their application in photovoltaics. In another study, with 0.433% strain at 782 µW cm -2 intensity of illumination, the photocurrent of the prepared 2D α-In 2 Se 3 /WSe 2 achieved up to −164 nA, which is 304-folds higher than the I dark examined under nonstrain condition. [121] These studies suggest the great potential of strain engineering in improving photovoltaics toward better photoresponse of devices.

Conclusion and Perspectives
We have reviewed the recent progress in the strain engineering of 2D materials including several newly developed methods  for inducing strain and highlighting the ability of strain engineering to change the electrical, magnetic, and optical properties of 2D materials. Although the potential application of straining engineering on 2D materials in optical, electronic, and spintronic devices is promising, much more research is still needed in several aspects to further improve their electrical, magnetic, optical properties and their strain tuning. First, methods to induce strain should be further developed and optimized for generating position predictable, constant, repeatable, more significant, and periodic strains. Second, heterostructures show promising and attractive electrical, magnetic, and optical properties. Strain transfer between different layers of heterostructures should be explored with greater scrutiny. To add to that, the interaction and quality of interface between 2D materials and their substrates should be studied more, and the condition for the integration between them should be investigated to a greater degree for better tunable properties. Third, whether some newly developed methods for introducing strain and changing electrical, magnetic, and optical properties demonstrated in a small number of 2D materials are also applicable in other 2D materials remain to be tested. Given that different properties that each 2D material may possess, the methods may need to be adjusted accordingly. Fourth, piezoelectric substrates should provide a promising approach for electrically straining and tuning a variety of 2D materials. One example is using then to turn the magnetic properties of 2D magnets, offering a platform to elucidate and explore the rich interplay between electric, magnetic, and lattice degrees of freedom in such artificial "multiferroic" heterostructures. Fifth, it is worth noting that superconducting and magnetic 2D materials are still underexplored in strain tuning, but motivated by previous studies on strain or pressure effects on superconductors and magnetic materials in general, there should be many opportunities to study the effects of strain on them. Six, regarding the application of strain engineering to optical properties of 2D materials, a better understanding is needed of the trap volumes, depths, widths, and stabilities of SPEs, as well as more detailed mechanisms on how optical properties of 2D materials could be controlled by strain or defect engineering, to achieve reversible, positional-controllable, and stable SPEs for their application for solid-state quantum light sources.
In addition, more work is needed in theoretical research for modeling and predicting the effect and conditions of strain engineering on electrical, magnetic, and optical properties on 2D materials, and a stronger coupling between theory and experimental efforts to better understand the microscopic physical mechanisms at material and device levels and to validate the proposed theoretical model experimentally whenever feasible. Generally, the underlying mechanisms for strain engineering of 2D materials on the influence of device performance of course depend on what specific types of devices. [33,134] For example, for electronic devices such as transistors, the mechanisms for straining tuning of device performance such as transconductance (gate-tunability, on/off ratio) are based on strain tuning of band structure (such as bandgap) and other microscopic electronic transport characteristic (such as carrier mobility). For spintronic devices (involving 2D magnets), strain tuning of device performance can occur via strain tuning of magnetic exchange and anisotropy energies which in turn affects critical field and temperatures for magnetic switching and phase transitions. For photonic devices involving excitons and quantum emitters, the strain tuning can occur due to strain effects to localize excitons and enhance optical transition strength as well as modulating optical band gap (transition energy), etc. Moreover, the emerging AI techniques could be introduced and combined with the theoretical and computational research to generate more universal, effective, and accurate model to with predicting power to better understand and control electrical, magnetic, and optical properties of 2D materials through strain engineering and guide the choice and design of materials and device structures and experimental tests. With a better understanding of all the directions mentioned above, it is expected that the application of straining engineering in optical, electronic, and spintronic devices will be advanced further in the near future.