Graphite-like carbon nitride (g-$\mathrm{C_3N_4}$) is considered as a promising candidate for energy materials. In this work, the biaxial strain (-4\%-4\%) effects on piezoelectric properties of g-$\mathrm{C_3N_4}$ 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-$\mathrm{C_3N_4}$, and almost unchanged electronic contribution, which is different from $\mathrm{MoS_2}$ monolayer (the enhanced electronic contribution and reduced ionic contribution). To prohibit current leakage, a piezoelectric material should be a semiconductor, and g-$\mathrm{C_3N_4}$ 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-$\mathrm{C_3N_4}$ monolayer, which gives a useful guidence for developing efficient energy conversion devices.
Shear piezoelectricity in poly(vinylidenefluoride-co-trifluoroethylene): full piezotensor coefficients by molecular modeling, biaxial transverse response, and use in suspended energy-harvesting nanostructures
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 stra…
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…
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 $\mat…
The combination of piezoelectricity with other unique properties (like topological insulating phase and intrinsic ferromagnetism) in two-dimensional (2D) materials is much worthy of intensive study. In this work, the piezoelectric properties of 2D topological insulators InXO (X=Se and Te) from monolayer InX (X=Se and Te) with double-side oxygen functionalization are studied by density functional theory (DFT). The large piezoelectric strain coefficients (e.g. $d_{11}$=-13.02 pm/V for InSeO and $d_{11}$=-9.64 pm/V for InTeO) are predicted, which are comparable and even higher than ones of many o…
For two-dimensional (2D) material, piezoelectric ferromagnetism (PFM) 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 (FM) semiconductor with large vertical piezoelectric response and high Curie temperature. The predicted out-of-plane piezoelectric strain coefficient $d_{31}$ is -1.58 pm/V, which is higher than ones of most 2D materials (compare absolute values of $d_{31}$). The large out-of-plane piezoelectricity is robust against electronic co…
The realization of multifunctional two-dimensional (2D) materials is fundamentally intriguing, such as combination of piezoelectricity with topological insulating phase or ferromagnetism. In this work, a Janus monolayer $\mathrm{SrAlGaSe_4}$ is built from 2D $\mathrm{MA_2Z_4}$ family with dynamic, mechanical and thermal stabilities, which is piezoelectric due to lacking inversion symmetry. The unstrained $\mathrm{SrAlGaSe_4}$ 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 the bia…
Electronic Phase Transformations and Energy Gap Variations in Uniaxial and Biaxial Strained Monolayer VS$_2$ TMDs: A Comprehensive DFT and Beyond-DFT Study
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 …
Motived by experimentally synthesized $\mathrm{MoSi_2N_4}$ (\textcolor[rgb]{0.00,0.00,1.00}{Science 369, 670-674 (2020})), the intrinsic piezoelectricity in monolayer $\mathrm{XSi_2N_4}$ (X=Ti, Zr, Hf, Cr, Mo and W) are studied by density functional theory (DFT). Among the six monolayers, the $\mathrm{CrSi_2N_4}$ has the best piezoelectric strain coefficient $d_{11}$ of 1.24 pm/V, and the second is 1.15 pm/V for $\mathrm{MoSi_2N_4}$. Taking $\mathrm{MoSi_2N_4}$ as a example, strain engineering is applied to improve $d_{11}$. It is found that tensile biaxial strain can enhance $d_{11}$ of $\mat…
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…
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_2SS…
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 anomalo…
We predict that monolayer FeCl$_2$ is a two-dimensional piezoelectric ferromagnet (PFM) with easy-axis magnetism and a Curie temperature of 260 K. Our ab-initio calculations combined with data mining reveal 2H-FeCl$_2$ as the only easy-axis 2D monolayer PFM, and that its magnetic anisotropy increases many-fold with moderate hole doping. We develop an analysis based on magnetic anisotropy energy densities that explain the magnetic and doping-dependent behavior of FeCl$_2$, as well as VSe$_2$ and CrI$_3$, and can enable the design of future 2D magnetically ordered materials.
The recently experimentally synthesized monolayer $\mathrm{MoSi_2N_4}$ and $\mathrm{WSi_2N_4}$ (\textcolor[rgb]{0.00,0.00,1.00}{Science 369, 670-674 (2020})) lack inversion symmetry, which allows them to become piezoelectric. In this work, based on ab initio calculations, we report structure effect on intrinsic piezoelectricity in septuple-atomic-layer $\mathrm{MSi_2N_4}$ (M=Mo and W), and six structures ($α_i$ ($i$=1 to 6)) are considered with the same space group.It is found that $\mathrm{MSi_2N_4}$ (M=Mo and W) with $α_i$ ($i$=1 to 6) all are indirect band gap semiconductors. Calculated res…
Photocatalytic water splitting is an effective way to obtain renewable clean energy. The challenge is to design tunable photocatalyst to meet the needs in different environments. At the same time, the oxygen and hydrogen evolution reactions (OER and HER) on the photocatalyst should be separated, which will be conducive to the separation of products. The electronic, optical and photocatalytic properties of Janus X2PAs (X = Si, Ge and Sn) monolayers are explored by first-principles calculation. All the strain-free X2PAs monolayers exhibit excellent photocatalytic properties with suitable band ed…
Low-dimensional (LD) transition metal dichalcogenides (TMDs) in the form of nanoflakes, which consist of one or several layers, are the subject of intensive fundamental and applied research. Due to the size-induced transition from a bulk to nanoscale, they can be both nonpolar, piezoelectric or even ferroelectric. Also, in terms of electronic properties, they can be direct-band semiconductors, semi-metals or even metals. The tuning of the electronic properties in the LD-TMDs are commonly related with applied strains and strain gradients, which can affect strongly their polar properties via the…
The electronic properties of a field-effect transistor with two different structures of MoSi$_2$N$_4$ and WSi$_2$N$_4$ monolayers as the channel material in the presence of biaxial strain are investigated. The band structures show that these compounds are semiconductors with an indirect bandgap. Their band gaps can be adjusted by applying in-plane biaxial strain. In the following, the variation of the energies of the valleys and corresponding effective masses with respect to the strain are explored. Finally, the strained MoSi$_2$N$_4$ or WSi$_2$N$_4$ are used as the channel of a p-type FET and…
The discovery of two dimensional (2D) magnetic materials has brought great research value for spintronics and data storage devices. However, their air-stability as well as the oxidation mechanism has not been unveiled, which limits their further applications. Here, by first-principles calculations, we carried out a detailed study on the oxidation process of monolayer CrSe2 and biaxial tensile strain effect. We found dissociation process of O2 on pristine CrSe2 sheet is an endothermic reaction with a reaction energy barrier of 0.53 eV, indicating its thermodynamics stability. However, such a pr…
Integration of promising piezoelectric and photocatalytic properties in Janus In$XY$ ($X$ = S, Se, Te; $Y$ = Cl, Br, I) monolayers and their heterojunctions
A two-dimensional (2D) material with piezoelectricity, topological and ferromagnetic (FM) orders, namely 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 $\mathrm{Fe_2IX}$ (X=Cl and Br) with dynamic, mechanical and thermal stabilities is predict to be room-temperature PQAHI. At the absence of spin-orbit coupling (SOC), monolayer $\mathrm{Fe_2IX}$ (X=Cl and Br) is a half Dirac semimetal state. When the SOC is included, these monolayers become qua…
Ferrovalley materials can achieve manipulation of the valley degree of freedom with intrinsic spontaneous valley polarization introduced by their intrinsic ferromagnetism. A good ferrovalley material should possess perpendicular magnetic anisotropy (PMA), valence band maximum (VBM)/conduction band minimum (CBM) at valley points, strong ferromagnetic (FM) coupling and proper valley splitting. In this work, the monolayer $\mathrm{GdCl_2}$ is proposed as a potential candidate material for valleytronic applications by the first-principles calculations. It is proved that monolayer $\mathrm{GdCl_2}$…
First-principles study on physical properties of a single ZnO monolayer with graphene-like structure
通过第一性原理计算，研究了具有类石墨烯结构的单层ZnO（SZOML）的弹性、压电、电子和光学性质。声子色散曲线包含三个声学分支和三个光学分支。在$Γ$点，面外声学模式具有渐近行为$ω(q)=Bq^2$，其中$B=1.385 \times 10^{-7}$ m $^2$ /s，而两个面内声学模式具有声速$2.801$ km/s和$8.095$ km/s;其他三个光学模式具有频率250 cm $^{-1}$，566 cm $^{-1}$和631 cm $^{-1}$。弹性和压电常数从弛豫离子模型获得。研究发现，SZOML比石墨烯柔软得多，但它是一种压电材料。电子带隙为3.576 eV，这意味着SZOML是宽带隙半导体。在线性光谱中存在许多峰，其中在3.58 eV处的第一个峰对应于SZOML的带隙。
Chemical vapor deposition has been most recently employed to fabricate centimeter-scale high-quality single-layer MoSi2N4 (Science; 2020;369; 670). Motivated by this exciting experimental advance, herein we conduct extensive first-principles based simulations to explore the stability, mechanical properties, lattice thermal conductivity, piezoelectric and flexoelectric response, and photocatalytic and electronic features of MA2Z4 (M = Cr, Mo, W; A = Si, Ge; Z = N, P) monolayers. The considered nanosheets are found to exhibit dynamical stability and remarkably high mechanical properties. Moreove…
Spin-orbit coupling (SOC) combined with electronic correlation can induce topological phase transition, producing novel electronic states. Here, we investigate the impact of SOC combined with correlation effects on physical properties of monolayer $\mathrm{OsBr_2}$, based on first-principles calculations with generalized gradient approximation plus $U$ (GGA+$U$) approach. With intrinsic out-of-plane magnetic anisotropy, $\mathrm{OsBr_2}$ undergoes threefold topological phase transition with increasing $U$, and valley-polarized quantum anomalous Hall insulator (VQAHI) to half-valley-metal (HVM)…
Twelve two-dimensional group-IV monochalcogenide monolayers (SiS, SiSe, SiTe, GeS, GeSe, GeTe, SnS, SnSe, SnTe, PbS, PbSe, and PbTe) with a buckled honeycomb atomistic structure--belonging to symmetry group P3m1--and an out-of-plane intrinsic electric polarization are shown to be metastable by three independendent methods. First, we uncover a coordination-preserving structural transformation from the low-buckled honeycomb structure onto the lower-energy Pnm2$_1$ (or Pmmn for PbS, PbSe, and PbTe) phase to estimate {\em energy barriers} $E_B$ that must be overcome during such structural transfor…
Mechanical control of electronic and magnetic properties of 2D Van-der-Waals heterostructures gives new possibilities for further development of spintronics and information-related technologies. Using the density functional theory, we investigate the structural, electronic, and magnetic properties of silicene monolayer with substituted Chromium atoms and under a small biaxial strain ($-6\%< ε< 8\%$). Our results indicate that the Cr-doped silicene nanosheets without strain have magnetic metallic, half-metallic or semiconducting properties depending on the type of substitution. We also show tha…
