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Based on the k·p model, at a small constant energy surface, the Rashba spin splitting has a linear relationship with momentum k, while Hexagonal warping effect and a nonzero spin projection component Sz arise at a larger constant energy surface due to nonlinear k3 terms.

Valleytronics has been widely investigated for providing new degrees of freedom to future information coding and processing. Here, it is proposed that valley polarization can be achieved by electric field induced magnetic anisotropy (MA) transformation. Through the first-principle calculations, our idea is illustrated by a concrete example of $\mathrm{VSi_2P_4}$ monolayer. The increasing electric field can induce a transition of MA from in-plane to out-of-plane by changing magnetic anisotropy energy (MAE) from negative to positive value, which is mainly due to increasing magnetocrystalline anisotropy (MCA) energy. The out-of-plane magnetization is in favour of spontaneous valley polarization in $\mathrm{VSi_2P_4}$. Within considered electric field range, $\mathrm{VSi_2P_4}$ is always ferromagnetic (FM) ground state. In a certain range of electric field, the coexistence of semiconductor and out-of-plane magnetization makes $\mathrm{VSi_2P_4}$ become a true ferrovalley (FV) material. The anomalous valley Hall effect (AVHE) can be observed under in-plane and out-of-plane electrical field in $\mathrm{VSi_2P_4}$. Our works pave the way to design the ferrovalley material by electric field., Comment: 6 pages, 6 figures. arXiv admin note: text overlap with arXiv:2207.13420

The valley degrees of freedom of carriers in crystals is useful to process information and perform logic operations, and it is a key factor for valley application to realize the valley polarization. Here, we propose a model that the valley polarization transition at different valley points (-K and K points) is produced by biaxial strain. By the first-principle calculations, we illustrate our idea with a concrete example of Janus $\mathrm{GdClF}$ monolayer. The predicted $\mathrm{GdClF}$ monolayer is dynamically, mechanically and thermally stable, and is a ferromagnetic (FM) semiconductor with perpendicular magnetic anisotropy (PMA), valence band maximum (VBM) at valley points and high Curie temperature ($T_C$). Due to its intrinsic ferromagnetism and spin orbital coupling (SOC), a spontaneous valley polarization will be induced, but the valley splitting is only -3.1 meV, which provides an opportunity to achieve valley polarization transition at different valley points by strain. In considered strain range ($a/a_0$: 0.94$\sim$1.06), the strained GdClF monolayer has always energy bandgap, strong FM coupling and PMA. The compressive strain is in favour of -K valley polarization, while the tensile strain makes for K valley polarization. The corresponding valley splitting at 0.96 and 1.04 strain are -44.5 meV and 29.4 meV, which are higher than the thermal energy of room temperature (25 meV). Due to special Janus structure, both in-plane and out-of-plane piezoelectric polarizations can be observed. It is found that the direction of in-plane piezoelectric polarizations can be overturned by strain, and the $d_{11}$ at 0.96 and 1.04 strain are -1.37 pm/V and 2.05 pm/V. Our works pave the way to design the ferrovalley material as multifunctional valleytronics and piezoelectric devices by strain., Comment: 9 pages, 10 figures. arXiv admin note: text overlap with arXiv:2109.13534

The large gap is due to correlation-enhanced spin-orbit coupling (SOC) effect of Fe atoms, which equates with artificially increasing the strength of SOC without electronic correlation.

HfS2/SMoSe, HfS2/SeMoS, ZrS2/SMoSe, and ZrS2/SeMoS heterostructures are promising overall water-splitting photocatalysts.

In this work, different doping strategies are adopted to improve the photocatalytic activity of KTaO3 (KT) by hybrid functional theory. The La and W monodoped KTs are n-type semiconductors and the photocatalytic performance of Ti, Mo, Cr, N, La–Bi, La–Cr, W–N, Cr–N, Cr–Ti doped KTs are limited by either wide bandgaps or the appeared local unoccupied impurity states. The Bi, C monodoped and La–C, Mo–N, Mo–Ti, W–Ti codoped KTs possess suitable bandgaps of 2.12, 2.06, 1.39, 2.66, 2.66, and 2.61 eV for absorbing visible light without the introduction of localized unoccupied states. The band edge alignments suggest that Mo–N and W–Ti codoped KTs possess the ability for spontaneous overall water-splitting, Bi and Mo–Ti doped KTs can only spontaneously produce oxygen, and C doped KTs only spontaneously generate hydrogen. While La–C doped KT is thermodynamically unfeasible to generating both hydrogen and oxygen. Thus, Mo–N and W–Ti codoped KTs are promising photocatalysts for overall water-splitting, and Bi, C, and Mo–Ti doped KTs are considered for Z-scheme photocatalysis.

Coexistence of intrinsic ferromagnetism and piezoelectricity, namely piezoelectric ferromagnetism (PFM), is crucial to advance multifunctional spintronic technologies. In this work, we demonstrate that Janus monolayer YBrI is a PFM, which is dynamically, mechanically and thermally stable. Electronic correlation effects on physical properties of YBrI are investigated by using generalized gradient approximation plus $U$ (GGA+$U$) approach. For out-of-plane magnetic anisotropy, YBrI is a ferrovalley (FV) material, and the valley splitting is larger than 82 meV in considered $U$ range. The anomalous valley Hall effect (AVHE) can be achieved under an in-plane electric field. However, for in-plane magnetic anisotropy, YBrI is a common ferromagnetic (FM) semiconductor. When considering intrinsic magnetic anisotropy, the easy axis of YBrI is always in-plane with magnetic anisotropy energy (MAE) from 0.309 meV to 0.237 meV ($U$=0.0 eV to 3.0 eV). However, the magnetization can be adjusted from the in-plane to off-plane direction by external magnetic field, and then lead to the occurrence of valley polarization. Moreover, missing centrosymmetry along with mirror symmetry breaking results in both in-plane and out-of-plane piezoelectricity in YBrI monolayer. At a typical $U$=2.0 eV, the $d_{11}$ is predicted to be -5.61 pm/V, which is higher than or compared with ones of other two-dimensional (2D) known materials. The electronic and piezoelectric properties of YBrI can be effectively tuned by applying a biaxial strain. For example, tensile strain can enhance valley splitting and $d_{11}$ (absolute value). The predicted Curie temperature of YBrI is higher than those of experimentally synthesized 2D ferromagnetic materials $\mathrm{CrI_3}$ and $\mathrm{Cr_2Ge_2Te_6}$., 10 pages, 12 figures

Direct Z-scheme water-splitting is a promising route to enhancing the photocatalytic performance due to the effective separation of photogenerated carriers while simultaneously preserving the strong oxidation activity of holes and reduction activity of electrons. In this work, the MoSSe/XY

Strong structural asymmetry is actively explored in two-dimensional (2D) materials, because it can give rise to many interesting physical properties. Motivated by the recent synthesis of monolayer $\mathrm{Si_2Te_2}$, we explore a family of 2D materials, termed as the Janus Si dichalcogenides (JSD), which parallel the Janus transition metal dichalcogenides and exhibit even stronger inversion asymmetry. Using first-principles calculations, we demonstrate excellent stability of these materials. We show that their strong structural asymmetry leads to pronounced intrinsic polar field, sizable spin splitting due to spin-orbit coupling, and large piezoelectric response. The spin splitting involves an out-of-plane component, which is beyond the linear Rashba model. The piezoelectric tensor has large value in both in-plane $d_{11}$ coefficient and out-of-plane $d_{31}$ coefficient, making the monolayer JSDs distinct among the existing 2D piezoelectrics. In addition, we find interesting strain-induced phase transitions in these materials. Particularly, there are multiple valleys in the conduction band that compete for the conduction band minimum, which will lead to notable changes in optical and transport properties under strain. Our work reveals a new family of Si based 2D materials, which could find promising applications in spintronic and piezoelectric devices., 8 pages, 8 figures

Two-dimensional (2D) ferromagnets have been a fascinating subject of research, and magnetic anisotropy (MA) is indispensable for stabilizing the 2D magnetic order. Here, we investigate magnetic anisotropy energy (MAE), magnetic and electronic properties ofVSi2P4by using the generalized gradient approximation plus

Two-dimensional (2D) ferromagnets have been a fascinating subject of research, and magnetic anisotropy (MA) is indispensable for stabilizing the 2D magnetic order. Here, we investigate magnetic anisotropy energy (MAE), magnetic and electronic properties of $\mathrm{VSi_2P_4}$ by using the generalized gradient approximation plus $U$ (GGA+$U$) approach. For large $U$, the magnetic shape anisotropy (MSA) energy has a more pronounced contribution to the MAE, which can overcome the magnetocrystalline anisotropy (MCA) energy to evince an easy-plane. For fixed out-of-plane MA, monolayer $\mathrm{VSi_2P_4}$ undergoes ferrovalley (FV), half-valley-metal (HVM), valley-polarized quantum anomalous Hall insulator (VQAHI), HVM and FV states with increasing $U$. However, for assumptive in-plane MA, there is no special quantum anomalous Hall (QAH) state and spontaneous valley polarization within considered $U$ range. According to the MAE and electronic structure with fixed out-of-plane or in-plane MA, the intrinsic phase diagram shows common magnetic semiconductor (CMS), FV and VQAHI in monolayer $\mathrm{VSi_2P_4}$. At representative $U$$=$3 eV widely used in references, $\mathrm{VSi_2P_4}$ can be regarded as a 2D-$XY$ magnet, not Ising-like 2D long-range order magnets predicted in previous works with only considering MCA energy. Our findings shed light on importance of MSA in determining magnetic and electronic properties of monolayer $\mathrm{VSi_2P_4}$., 7 pages,7 figures. arXiv admin note: text overlap with arXiv:2205.07012

The combination of piezoelectricity with nontrivial topological insulating phase in two-dimensional (2D) systems, namely piezoelectric quantum spin Hall insulator (PQSHI), is intriguing for exploring novel topological states toward the development of high-speed and dissipationless electronic devices. In this work, we predict a PQSHI Janus monolayer VCClBr constructed from $\mathrm{VCCl_2}$, which is dynamically, mechanically and thermally stable. In the absence of spin orbital coupling (SOC), VCClBr is a narrow gap semiconductor with gap value of 57 meV, which is different from Dirac semimetal $\mathrm{VCCl_2}$. The gap of VCClBr is due to built-in electric field caused by asymmetrical upper and lower atomic layers, which is further confirmed by external-electric-field induced gap in $\mathrm{VCCl_2}$. When including SOC, the gap of VCClBr is improved to 76 meV, which is larger than the thermal energy of room temperature (25 meV). The VCClBr is a 2D topological insulator (TI), which is confirmed by $Z_2$ topological invariant and nontrivial one-dimensional edge states. It is proved that the nontrivial topological properties of VCClBr are robust against strain (biaxial and uniaxial cases) and external electric field. Due to broken horizontal mirror symmetry, only out-of-plane piezoelectric response can be observed, when biaxial or uniaxial in-plane strain is applied. The predicted piezoelectric strain coefficients $d_{31}$ and $d_{32}$ are -0.425 pm/V and -0.219 pm/V, which are higher than or compared with ones of many 2D materials. Finally, another two Janus monolayer VCFBr and VCFCl (dynamically unstable) are constructed, and they are still PQSHIs. Moreover, their $d_{31}$ and $d_{32}$ are higher than ones of VCClBr, and the $d_{31}$ (absolute value) of VCFBr is larger than one., 10 pages, 12 figures

To easily synthesize a piezoelectric quantum anomalous Hall insulator (PQAHI), the Janus monolayer Fe2IBr (FeI0.5Br0.5) as a representative PQAHI, is generalized to monolayer FeI1-xBrx (x = 0.25 and 0.75) with α and β phases. By first-principles calculations, it is proved that monolayer FeI1-xBrx (x = 0.25 and 0.75) are dynamically, mechanically and thermally stable. They are excellent room-temperature PQAHIs with high Curie temperatures, sizable gaps and high Chern number (C = 2). Because the considered crystal structures of α and β phases possess Mx and My mirror symmetries, the topological properties of monolayer FeI1-xBrx (x = 0.25 and 0.75) are maintained. Namely, if the constructed structures have Mx and My mirror symmetries, the mixing ratio of Br and I atoms can be generalized for other proportions. It is also found that different crystal phases have important effects on the out-of-plane piezoelectric response, and the piezoelectric strain coefficient, d32, of the β phase is higher than or comparable with those of other known two-dimensional (2D) materials. To further confirm this idea, the physical and chemical properties of monolayer LiFeSe0.75S0.25 with α and β phases, as a generalization of PQAHI LiFeSe0.5S0.5, is investigated, as it has a similar electronic structure, magnetic and topological properties as LiFeSe0.5S0.5. Our work provides a practical guide to achieve PQAHIs experimentally, and the combination of piezoelectricity, topological and ferromagnetic (FM) orders makes Fe2I2-based monolayers a potential platform for multi-functional spintronics and piezoelectric electronics.

The realization of multifunctional two-dimensional (2D) materials is fundamentally intriguing, such as the combination of piezoelectricity with a topological insulating phase or ferromagnetism. In this work, a Janus monolayer SrAlGaSe4 is built from the 2D MA2Z4 family with dynamic, mechanical and thermal stabilities, which is piezoelectric due to the lack of inversion symmetry. The unstrained SrAlGaSe4 monolayer is a narrow gap normal insulator (NI) with spin orbital coupling (SOC). However, the NI to topological insulator (TI) phase transition can be induced by biaxial strain, and a piezoelectric quantum spin Hall insulator (PQSHI) can be achieved. More excitingly, the phase transformation point is only about 1.01 tensile strain, and the nontrivial band topology can hold until the considered 1.16 tensile strain. Moreover, Rashba spin splitting in the conduction bands can exist in a PQSHI due to the absence of a horizontal mirror symmetry and the presence of SOC. For monolayer SrAlGaSe4, both in-plane and very weak out-of-plane piezoelectric polarizations can be induced with the application of uniaxial strain. The calculated piezoelectric strain coefficients d11 and d31 of monolayer SrAlGaSe4 are −1.865 pm V−1 and −0.068 pm V−1 at 1.06 tensile strain as a representative TI. In fact, many PQSHIs can be realized from the 2D MA2Z4 family. To confirm that, similar to SrAlGaSe4, the coexistence of piezoelectricity and topological orders can be realized by applying strain (about 1.04 tensile strain) in the CaAlGaSe4 monolayer. This study suggests that Janus monolayer SrAlGaSe4 is a pure 2D system for a PQSHI, enabling future studies exploring the interplay between piezoelectricity and topological order, which can lead to novel applications in electronics and spintronics.

The combination of piezoelectricity with other unique properties (like the topological insulating phase and intrinsic ferromagnetism) in two-dimensional (2D) materials is worthy of much intensive study. In this work, the piezoelectric properties of 2D topological insulators InXO (X = Se and Te), derived from monolayer InX (X = Se and Te) by double-side oxygen functionalization, are studied by density functional theory (DFT). Large piezoelectric strain coefficients (e.g. d11 = −13.02 pm V−1 for InSeO and d11 = −9.64 pm V−1 for InTeO) are predicted, which are comparable and even higher than those of many other familiar 2D materials. Moreover, we propose two strategies to enhance the piezoelectric response of monolayer InXO (X = Se and Te). Firstly, biaxial strain (0.94–1.06) is applied, and the d11 (absolute value) is increased by 53%/56% for monolayer InSeO/InTeO at 1.06 strain, which is due to the increased e11 (absolute value) and reduced C11–C12. In the considered strain range, the InXO (X = Se and Te) monolayers are always 2D topological insulators, which confirms the coexistence of piezoelectricity and nontrivial band topology. Secondly, a Janus monolayer In2SeTeO2 is designed by replacing the top Se/Te atomic layer in monolayer InSeO/InTeO with Te/Se atoms, and is dynamically and mechanically stable. More excitingly, Janus monolayer In2SeTeO2 is also a 2D topological insulator with sizeable bulk gap of up to 0.158 eV, confirming the coexistence of intrinsic piezoelectricity and its topological nature. The calculated d11 is −9.9 pm V−1, which is in the middle of those of InSeO and InTeO monolayers. Finally, the carrier mobilities of monolayer InXO (X = Se and Te) are obtained, which show a rather pronounced anisotropy between electrons and holes, and are almost isotropic between the armchair and zigzag directions. Our work implies that it is possible to use the piezotronic effect to control the quantum transport process, ultimately leading to the novel device applications of monolayer InXO (X = Se and Te), and can stimulate further experimental work.

A two-dimensional (2D) material with piezoelectricity, topological and ferromagnetic (FM) properties, namely a 2D piezoelectric quantum anomalous hall insulator (PQAHI), may open new opportunities to realize novel physics and applications. Here, by first-principles calculations, a family of 2D Janus monolayer Fe2IX (X = Cl and Br) with dynamic, mechanical, and thermal stabilities is predicted to be a room-temperature PQAHI. In the absence of spin–orbit coupling (SOC), the monolayer Fe2IX (X = Cl and Br) is in a half Dirac semimetal state. When the SOC is included, these monolayers become quantum anomalous Hall (QAH) states with sizable gaps (more than 200 meV) and two chiral edge modes (Chern number C = 2). It is also found that the monolayer Fe2IX (X = Cl and Br) possesses robust QAH states against the biaxial strain. By symmetry analysis, it is found that only an out-of-plane piezoelectric response can be induced by a uniaxial strain in the basal plane. The calculated out-of-plane d31 of Fe2ICl (Fe2IBr) is 0.467 pm V−1 (0.384 pm V−1), which is higher than or comparable with those of other 2D known materials. Meanwhile, using Monte Carlo (MC) simulations, the Curie temperature TC is estimated to be 429/403 K for the monolayer Fe2ICl/Fe2IBr at the FM ground state, which is above room temperature. Finally, the interplay of electronic correlations with nontrivial band topology is studied to confirm the robustness of the QAH state. The combination of piezoelectricity, topological and FM orders makes the monolayer Fe2IX (X = Cl and Br) become a potential platform for multi-functional spintronic applications with a large gap and high TC. Our work provides the possibility to use the piezotronic effect to control QAH effects, and can stimulate further experimental works.

Two-dimensional (2D) piezoelectric ferromagnetism (PFM) is essential for the development of the next-generation multifunctional spintronic technologies. Recently, the layered van der Waals (vdW) compound MnBi2Te4 as a platform to realize the quantum anomalous Hall effect (QAHE) has attracted great interest. In this work, the Janus monolayer MnSbBiTe4 with dynamic, mechanical and thermal stabilities is constructed from a synthesized non-piezoelectric MnBi2Te4 monolayer by replacing the top Bi atomic layer with Sb atoms. The calculated results show that monolayer MnSbBiTe4 is an intrinsic ferromagnetic (FM) semiconductor with a gap value of 0.25 eV, whose easy magnetization axis is out-of-plane direction with magnetic anisotropy energy (MAE) of 158 μeV per Mn. The predicted Curie temperature TC is about 20.3 K, which is close to that of monolayer MnBi2Te4. The calculated results show that the in-plane d11 is about 5.56 pm V−1, which is higher than or comparable to those of other 2D known materials. Moreover, it is found that strain engineering can effectively tune the piezoelectric properties of Janus monolayer MnSbBiTe4. The calculated results show that tensile strain can improve the d11, which is improved to be 21.16 pm V−1 at only 1.04 strain. It is proved that the ferromagnetic order, semiconducting properties, out-of-plane easy axis and a large d11 are robust against electronic correlations. Our work provides a possible way to achieve PFM with a large d11 in well-explored vdW compound MnBi2Te4, which makes it possible to use the piezoelectric effect to tune the quantum transport process.

The combination of piezoelectricity and ferromagnetic (FM) order in a two-dimensional (2D) material, namely 2D piezoelectric ferromagnetism (PFM), may open up unprecedented opportunities for novel device applications. Here, we predict an in-plane FM semiconductor Janus monolayer NiClI with considerably large magnetic anisotropy energy (MAE) of 1.439 meV, exhibiting dynamic, mechanical and thermal stabilities. The NiClI monolayer possesses larger in-plane piezoelectricity ($d_{11}$$=$5.21 pm/V) comparable to that of $\mathrm{MoS_2}$. Furthermore, NiClI has huge out-of-plane piezoelectricity ($d_{31}$$=$1.89 pm/V), which is highly desirable for ultrathin piezoelectric device application. It is proved that huge out-of-plane piezoelectricity is robust against electronic correlation, which confirms reliability of huge $d_{31}$. Finally, being analogous to NiClI, PFM with large out-of-plane piezoelectricity can also be achieved in the Janus monolayers of NiClBr and NiBrI, with the predicted $d_{31}$ of 0.73 pm/V and 1.15 pm/V, respectively. The predicted huge out-of-plane piezoelectric response makes Janus monolayer NiClI a good platform for multifunctional semiconductor spintronic applications, which is also compatible with the bottom/top gate technologies of conventional semiconductor nanoelectronic devices., 6 pages, 4 figures

Two-dimensional (2D) materials van der Waals heterostructures (vdWHs) provides a revolutionary route towards high-performance solar energy conversion devices beyond the conventional silicon-based pn junction solar cells. Despite tremendous research progress accomplished in recent years, the searches of vdWHs with exceptional excitonic solar cell conversion efficiency and optical properties remain an open theoretical and experimental quest. Here we show that the vdWH family composed of MoSi$_2$N$_4$ and WSi$_2$N$_4$ monolayers provides a compelling material platform for developing high-performance ultrathin excitonic solar cells and photonics devices. Using first-principle calculations, we construct and classify 51 types of MoSi$_2$N$_4$ and WSi$_2$N$_4$-based [(Mo,W)Si$_2$N$_4$] vdWHs composed of various metallic, semimetallic, semiconducting, insulating and topological 2D materials. Intriguingly, MoSi$_2$N$_4$/(InSe, WSe$_2$) are identified as Type-II vdWHs with exceptional excitonic solar cell power conversion efficiency reaching well over 20%, which are competitive to state-of-art silicon solar cells. The (Mo,W)Si$_2$N$_4$ vdWH family exhibits strong optical absorption in both the visible and ultraviolet regimes. Exceedingly large peak ultraviolet absorptions over 40%, approaching the maximum absorption limit of a free-standing 2D material, can be achieved in (Mo,W)Si$_2$N$_4$/$\alpha_2$-(Mo,W)Ge$_2$P$_4$ vdWHs. Our findings unravel the enormous potential of (Mo,W)Si$_2$N$_4$ vdWHs in designing ultimately compact excitonic solar cell device technology., Comment: 30 pages, 7 figures

To easily synthesize a piezoelectric quantum anomalous Hall insulator (PQAHI), the Janus monolayer Fe

Achieving combination of spin and valley polarized states with topological insulating phase is pregnant to promote the fantastic integration of topological physics, spintronics and valleytronics. In this work, a spin-valley-coupled quantum spin Hall insulator (svc-QSHI) is predicted in Janus monolayer CSb

Two-dimensional (2D) piezoelectric ferromagnetism (PFM) is essential for the development of the next-generation multifunctional spintronic technologies. Recently, the layered van der Waals (vdW) compound MnBi

In analogy to transition-metal dichalcogenide (TMD) monolayers, which have wide applications in photoelectricity, piezoelectricity and thermoelectricity, Janus MoSSe monolayer has been successfully synthesized by substituting the top S atomic layer in MoS 2 by Se atoms. In this work, Janus monolayer ZrSSe is proposed by ab initio calculations. For the electron part, the generalized gradient approximation (GGA) plus spin-orbit coupling (SOC) is used as exchange-correlation potential, while GGA for lattice part. Calculated results show that the ZrSSe monolayer is dynamically, mechanically and thermally stable, which exhibits mechanical flexibility due to small Young’s modulus. It is found that ZrSSe monolayer is an indirect-gap semiconductor with band gap of 0.60 eV. The electronic and phonon transports of ZrSSe monolayer are investigated by semiclassical Boltzmann transport theory. In n-type doping, the ZT e between ZrSSe and ZrS 2 monolayers is almost the same due to similar outlines of conduction bands. The p-type ZT e of ZrSSe monolayer is lower than that of ZrS 2 monolayer, which is due to larger spin-orbit splitting for ZrSSe than ZrS 2 monolayer. The room-temperature sheet thermal conductance is 33.6 W K - 1 for ZrSSe monolayer, which is lower than 47.8 W K - 1 of ZrS 2 monolayer. Compared to ZrS 2 monolayer, the low sheet thermal conductance of ZrSSe monolayer is mainly due to small group velocities and short phonon lifetimes of ZA mode. Considering their ZT e and lattice thermal conductivities, the ZrSSe monolayer may have better n-type thermoelectric performance than ZrS 2 monolayer. These results can stimulate further experimental works to synthesize ZrSSe monolayer.

For two-dimensional (2D) materials, piezoelectric ferromagnetism with large out-of-plane piezoresponse is highly desirable for multifunctional ultrathin piezoelectric device application. Here, we predict that Janus monolayer CrSCl is an out-of-plane ferromagnetic semiconductor with large vertical piezoelectric response and high Curie temperature. The predicted out-of-plane piezoelectric strain coefficient d31 is −1.58 pm/V, which is higher than that of most 2D materials (compare absolute values of d31). The large out-of-plane piezoelectricity is robust against electronic correlation and biaxial strain, confirming reliability of large d31. The calculated results show that tensile strain is conducive to high Curie temperature, large magnetic anisotropy energy, and large d31. Finally, by comparing d31 of CrYX (Y = S; X = Cl, Br, I) and CrYX (Y = O; X = F, Cl, Br), we conclude that the size of d31 is positively related to electronegativity difference of X and Y atoms. Such findings can provide valuable guidelines for designing 2D piezoelectric materials with large vertical piezoelectric response.

Recently, the quantum anomalous Hall (QAH) insulators are predicted in Lithium-decorated iron-based superconductor monolayer materials (LiFeX (X=S, Se and Te)) with very high Curie temperature (\textcolor[rgb]{0.00,0.00,1.00}{PRL 125, 086401 (2020)}), which combines the topological and ferromagnetic (FM) orders. It is interesting and useful to achieve coexistence of intrinsic piezoelectricity, ferromagnetism and nontrivial band topology in single two-dimensional (2D) material, namely 2D piezoelectric quantum anomalous hall insulator (PQAHI). In this work, 2D Janus monolayer $\mathrm{Li_2Fe_2SSe}$ is predict to be a room-temperature PQAHI, which possesses dynamic, mechanical and thermal stabilities. It is predicted to be a half Dirac semimetal without spin-orbit coupling (SOC). It is found that the inclusion of SOC opens up a large nontrivial gap, which means the nontrivial bulk topology (QAH insulator), confirmed by the calculation of Berry curvature and the presence of two chiral edge states (Chern number C=2). Calculated results show that monolayer $\mathrm{Li_2Fe_2SSe}$ possesses robust QAH states against biaxial strain and electronic correlations. Compared to LiFeX, the glide mirror $G_z$ of $\mathrm{Li_2Fe_2SSe}$ disappears, which will induce only out-of-plane piezoelectric response. The calculated out-of-plane $d_{31}$ of monolayer $\mathrm{Li_2Fe_2SSe}$ is -0.238 pm/V comparable with ones of other 2D known materials. Moreover, very high Curie temperature (about 1000 K) is predicted by using Monte Carlo (MC) simulations, which means that the QAH effect can be achieved at room temperature in Janus monolayer $\mathrm{Li_2Fe_2SSe}$. Similar to monolayer $\mathrm{Li_2Fe_2SSe}$, the PQAHI can also be realized in the Janus monolayer $\mathrm{Li_2Fe_2SeTe}$., Comment: 10 pages, 14 figures. arXiv admin note: text overlap with arXiv:2105.03004

Achieving combination of spin and valley polarized states with topological insulating phase is pregnant to promote the fantastic integration of topological physics, spintronics and valleytronics. In this work, a spin-valley-coupled quantum spin Hall insulator (svc-QSHI) is predicted in Janus monolayer $\mathrm{CSb_{1.5}Bi_{1.5}}$ with dynamic, mechanical and thermal stabilities. The inequivalent valleys have opposite Berry curvature and spin moment, which can produce a spin-valley Hall effect. In the center of Brillouin zone, a Rashba-type spin splitting can be observed due to missing horizontal mirror symmetry. Moreover, monolayer $\mathrm{CSb_{1.5}Bi_{1.5}}$ shows unique Rashba-splitting edge states. Both energy band gap and spin-splitting at the valley point are larger than the thermal energy of room temperature (25 meV) with generalized gradient approximation (GGA) level, which is very important at room temperature for device applications. It is proved that the spin-valley-coupling and nontrivial quantum spin Hall (QSH) state are robust again biaxial strain. Our work may provide a new platform to achieve integration of topological physics, spintronics and valleytronics., Comment: 6 pages, 7 figures

The septuple-atomic-layer VSi2P4 with the same structure of experimentally synthesized MoSi2N4 is predicted to be a spin-gapless semiconductor (SGS) with the generalized gradient approximation (GGA). In this work, the biaxial strain is applied to tune the electronic properties of VSi2P4, and it spans a wide range of properties upon increasing the strain from a ferromagnetic metal (FMM) to SGS to a ferromagnetic semiconductor (FMS) to SGS to a ferromagnetic half-metal (FMHM). Due to broken inversion symmetry, the coexistence of ferromagnetism and piezoelectricity can be achieved in FMS VSi2P4 with the strain range of 0% to 4%. The calculated piezoelectric strain coefficients d11 for 1%, 2% and 3% strains are 4.61 pm V-1, 4.94 pm V-1 and 5.27 pm V-1, respectively, which are greater than or close to a typical value of 5 pm V-1 for bulk piezoelectric materials. Finally, similar to VSi2P4, the coexistence of piezoelectricity and ferromagnetism can be realized by strain in the VSi2N4 monolayer. Our works show that VSi2P4 in the FMS phase with intrinsic piezoelectric properties can have potential applications in spin electronic devices.

The septuple-atomic-layer $\mathrm{VSi_2P_4}$ with the same structure of experimentally synthesized $\mathrm{MoSi_2N_4}$ is predicted to be a spin-gapless semiconductor (SGS). In this work, the biaxial strain is applied to tune electronic properties of $\mathrm{VSi_2P_4}$, and it spans a wide range of properties upon the increasing strain from ferromagnetic metal (FMM) to SGS to ferromagnetic semiconductor (FMS) to SGS to ferromagnetic half-metal (FMHM). Due to broken inversion symmetry, the coexistence of ferromagnetism and piezoelectricity can be achieved in FMS $\mathrm{VSi_2P_4}$ with strain range of 0\% to 4\%. The calculated piezoelectric strain coefficients $d_{11}$ for 1\%, 2\% and 3\% strains are 4.61 pm/V, 4.94 pm/V and 5.27 pm/V, respectively, which are greater than or close to a typical value of 5 pm/V for bulk piezoelectric materials. Finally, similar to $\mathrm{VSi_2P_4}$, the coexistence of piezoelectricity and ferromagnetism can be realized by strain in the $\mathrm{VSi_2N_4}$ monolayer. Our works show that $\mathrm{VSi_2P_4}$ in FMS phase with intrinsic piezoelectric properties can have potential applications in spin electronic devices., 6 pages,7 figures

Transition Metal Dichalcogenide (TMD) monolayers have most widely studied due to their unique physical properties. Recently, Janus TMD Monolayer MoSSe with sandwiched S-Mo-Se structure has been synthesized by replacing the top S atomic layer in $\mathrm{MoS_2}$ with Se atoms. In this work, we systematically investigate the phonon transport and lattice thermal conductivity ($\kappa_L$) of MoSSe monolayer by first-principles calculations and linearized phonon Boltzmann equation within the single-mode relaxation time approximation (RTA). Calculated results show that the $\kappa_L$ of MoSSe monolayer is very lower than that of $\mathrm{MoS_2}$ monolayer, and higher than that of $\mathrm{MoSe_2}$ monolayer. The corresponding sheet thermal conductance of MoSSe monolayer is 342.50 $\mathrm{W K^{-1}}$ at room temperature. These can be understood by phonon group velocities and lifetimes. Compared with $\mathrm{MoS_2}$ monolayer, the smaller group velocities and shorter phonon lifetimes of MoSSe monolayer give rise to lower $\kappa_L$. The larger group velocities for MoSSe than $\mathrm{MoSe_2}$ monolayer is main reason of higher $\kappa_L$. The elastic properties of $\mathrm{MoS_2}$, MoSSe and $\mathrm{MoSe_2}$ monolayers are also calculated, and the order of Young's modulus is identical with that of $\kappa_L$. Calculated results show that isotope scattering leads to 5.8\% reduce of $\kappa_L$. The size effects on the $\kappa_L$ are also considered, which is usually used in the device implementation. When the characteristic length of MoSSe monolayer is about 110 nm, the $\kappa_L$ reduces to half. These results may offer perspectives on thermal management of MoSSe monolayer for applications of thermoelectrics, thermal circuits and nanoelectronics, and motivate further theoretical or experimental efforts to investigate thermal transports of Janus TMD monolayers., Comment: 7 pages, 8 figures

Janus two-dimensional (2D) materials have attracted much attention due to possessing unique properties caused by their out-of-plane asymmetry, which have been achieved in many 2D families. In this work, the Janus monolayers are predicted in new 2D $\mathrm{MA_2Z_4}$ family by means of first-principles calculations, $\mathrm{MoSi_2N_4}$ and $\mathrm{WSi_2N_4}$ of which have been synthesized in experiment(\textcolor[rgb]{0.00,0.00,1.00}{Science 369, 670-674 (2020)}). The predicted $\mathrm{MSiGeN_4}$ (M=Mo and W) monolayers exhibit dynamic, thermodynamical and mechanical stability, and they are indirect band-gap semiconductors. The inclusion of spin-orbit coupling (SOC) gives rise to the Rashba-type spin splitting, which is observed in the valence bands, being different from common conduction bands. Calculated results show valley polarization at the edge of the conduction bands due to SOC together with inversion symmetry breaking. It is found that $\mathrm{MSiGeN_4}$ (M=Mo and W) monolayers have high electron mobilities. Both in-plane and much weak out-of-plane piezoelectric polarizations can be observed, when a uniaxial strain in the basal plane is applied. The values of piezoelectric strain coefficient $d_{11}$ of the Janus $\mathrm{MSiGeN_4}$ (M=Mo and W) monolayers fall between those of the $\mathrm{MSi_2N_4}$ (M=Mo and W) and $\mathrm{MGe_2N_4}$ (M=Mo and W) monolayers, as expected. It is proved that strain can tune the positions of valence band maximum (VBM) and conduction band minimum (CBM), and enhance the the strength of conduction bands convergence caused by compressive strain. It is also found that tensile biaxial strain can enhance $d_{11}$ of $\mathrm{MSiGeN_4}$ (M=Mo and W) monolayers, and the compressive strain can improve the $d_{31}$ (absolute values)., Comment: 10 pages, 11 figures

The compounds exhibit piezoelectricity, which demands to break inversion symmetry, and then to be a semiconductor. For Ga2O3, the orthorhombic case (ϵ-Ga2O3) of common five phases breaks inversion symmetry. Here, the piezoelectric tensor of ϵ-Ga2O3 is reported by using density functional perturbation theory (DFPT). To confirm semiconducting property of ϵ-Ga2O3, its electronic structures are studied by using generalized gradient approximation (GGA) and Tran and Blaha’s modified Becke and Johnson (mBJ) exchange potential. The gap value of 4.66 eV is predicted with mBJ method, along with the effective mass tensor for electron at the conduction band minimum (CBM) [about 0.24 m0]. The mBJ gap is very close to the available experimental value. The elastic tensor Cij are calculated by using the finite difference method (FDM), and piezoelectric stress tensor eij are attained by DFPT, and then piezoelectric strain tensor dij are calculated from Cij and eij. In this process, average mechanical properties of ϵ-Ga2O3 are estimated, such as bulk modulus, Shear modulus, Young’s modulus and so on. The calculated dij are comparable and even higher than commonly used piezoelectric materials such as α-quartz, ZnO, AlN and GaN.

Experimentally synthesized $\mathrm{MoSi_2N_4}$ (\textcolor[rgb]{0.00,0.00,1.00}{Science 369, 670-674 (2020)}) is a piezoelectric semiconductor. Here, we systematically study the large biaxial (isotropic) strain effects (0.90 to 1.10) on electronic structures and transport coefficients of monolayer $\mathrm{MoSi_2N_4}$ by density functional theory (DFT). With $a/a_0$ from 0.90 to 1.10, the energy band gap firstly increases, and then decreases, which is due to transformation of conduction band minimum (CBM). Calculated results show that the $\mathrm{MoSi_2N_4}$ monolayer is mechanically stable in considered strain range. It is found that the spin-orbital coupling (SOC) effects on Seebeck coefficient depend on the strain. In unstrained $\mathrm{MoSi_2N_4}$, the SOC has neglected influence on Seebeck coefficient. However, the SOC can produce important influence on Seebeck coefficient, when the strain is applied, for example 0.96 strain. The compressive strain can change relative position and numbers of conduction band extrema (CBE), and then the strength of conduction bands convergence can be enhanced, to the benefit of n-type $ZT_e$. Only about 0.96 strain can effectively improve n-type $ZT_e$. Our works imply that strain can effectively tune the electronic structures and transport coefficients of monolayer $\mathrm{MoSi_2N_4}$, and can motivate farther experimental exploration., Comment: 7 pages,7 figures

The Janus structure, by combining properties of different transition metal dichalcogenide (TMD) monolayers in a single polar material, has attracted increasing research interest because of their particular structure and potential application in electronics, optoelectronics and piezoelectronics. In this work, Janus SnSSe monolayer is predicted by means of first-principles calculations, which exhibits dynamic and mechanical stability. By using generalized gradient approximation (GGA) plus spin-orbit coupling (SOC), the Janus SnSSe monolayer is found to be an indirect band-gap semiconductor, whose gap can easily be tuned by strain. High carrier mobilities are obtained for SnSSe monolayer, and the hole mobility is higher than the electron mobility. For SnSSe monolayer, a uniaxial strain in the basal plane can induce both strong in-plane and much weaker out-of-plane piezoelectric polarizations, which reveals the potential as a piezoelectric two-dimensional (2D) material. The high absorption coefficients in the visible light region are observed, suggesting a potential photocatalytic application. Calculated results show that SnSSe monolayer has very high power factor, making it a promising candidate for thermoelectric applications. Our works reveal that the Janus SnSSe structure can be fabricated with unique electronic, optical, piezoelectric and transport properties, and can motivate related experimental works., 9 pages, 10 figures

A two-dimensional (2D) material system with both piezoelectricity and ferromagnetic (FM) order, referred to as a 2D piezoelectric ferromagnetism (PFM), may open up unprecedented opportunities for intriguing physics. Inspired by experimentally synthesized Janus monolayer MoSSe from $\mathrm{MoS_2}$, in this work, the Janus monolayer $\mathrm{CrBr_{1.5}I_{1.5}}$ with dynamic, mechanical and thermal stabilities is predicted, which is constructed from synthesized ferromagnetic $\mathrm{CrI_3}$ monolayer by replacing the top I atomic layer with Br atoms. Calculated results show that monolayer $\mathrm{CrBr_{1.5}I_{1.5}}$ is an intrinsic FM half semiconductor with valence and conduction bands being fully spin-polarized in the same spin direction. Furthermore, monolayer $\mathrm{CrBr_{1.5}I_{1.5}}$ possesses a sizable magnetic anisotropy energy (MAE). By symmetry analysis, it is found that both in-plane and out-of-plane piezoelectric polarizations can be induced by a uniaxial strain in the basal plane. The calculated in-plane $d_{22}$ value of 0.557 pm/V is small. However, more excitingly, the out-of-plane $d_{31}$ is as high as 1.138 pm/V, which is obviously higher compared with ones of other 2D known materials. The strong out of-plane piezoelectricity is highly desirable for ultrathin piezoelectric devices. Moreover, strain engineering is used to tune piezoelectricity of monolayer $\mathrm{CrBr_{1.5}I_{1.5}}$. It is found that compressive strain can improve the $d_{22}$, and tensile strain can enhance the $d_{31}$. A FM order to antiferromagnetic (AFM) order phase transition can be induced by compressive strain, and the critical point is about 0.95 strain. That is to say that a 2D piezoelectric antiferromagnetism (PAFM) can be achieved by compressive strain, and the corresponding $d_{22}$ and $d_{31}$ are 0.677 pm/V and 0.999 pm/V at 0.94 strain, respectively., 10 pages, 15 figures

Graphite-like carbon nitride (g- C 3 N 4 ) is considered as a promising candidate for energy materials. In this work, the biaxial strain (−4%–4%) effects on piezoelectric properties of g- C 3 N 4 monolayer are studied by density functional theory (DFT). It is found that the increasing strain can reduce the elastic coefficient C 11 - C 12 , and increases piezoelectric stress coefficient e 11 , which lead to the enhanced piezoelectric strain coefficient d 11 . Compared to unstrained one, strain of 4% can raise the d 11 by about 330%. From −4% to 4%, strain can induce the improved ionic contribution to e 11 of g- C 3 N 4 , and almost unchanged electronic contribution, which is different from MoS 2 monolayer (the enhanced electronic contribution and reduced ionic contribution). It is found that the biaxial strain indeed is a more effective strategy for g- C 3 N 4 than MoS 2 monolayer with the increase being only 46%. To prohibit current leakage, a piezoelectric material should be a semiconductor, and g- C 3 N 4 monolayer is always a semiconductor in considered strain range. Calculated results show that the gap increases from compressive strain to tensile one. At 4% strain, the first and second valence bands cross, which has important effect on transition dipole moment (TDM). Our works provide a strategy to achieve enhanced piezoelectric effect of g- C 3 N 4 monolayer, which gives a useful guidance for developing efficient energy conversion devices.