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 $\mathrm{MoSi_2N_4}$, and the $d_{11}$ at 4\% can improve by 107\% with respect to unstrained one. By replacing the N by P or As in $\mathrm{MoSi_2N_4}$, the $d_{11}$ can be raise substantially. For $\mathrm{MoSi_2P_4}$ and $\mathrm{MoSi_2As_4}$, the $d_{11}$ is as high as 4.93 pm/V and 6.23 pm/V, which is mainly due to smaller $C_{11}-C_{12}$ and very small minus or positive ionic contribution to piezoelectric stress coefficient $e_{11}$ with respect to $\mathrm{MoSi_2N_4}$. The discovery of this piezoelectricity in monolayer $\mathrm{XSi_2N_4}$ enables active sensing, actuating and new electronic components for nanoscale devices, and is recommended for experimental exploration.
Piezoelectricity offers precise and robust conversion between electricity and mechanical force. Here we report the first experimental evidence of piezoelectricity in a single layer of molybdenum disulfide (MoS2) crystal as a result of inversion symmetry breaking of the atomic structure, with measured piezoelectric coefficient e11 = 2.9e-10 C/m. Through the angular dependence of electro-mechanical coupling, we uniquely determined the two-dimensional (2D) crystal orientation. We observed that only MoS2 membranes with odd number of layers exhibited piezoelectricity, in sharp contrast to the conve…
The ground-state structure of monolayers and nanoplatelets of SnS with a thickness from two to five monolayers is calculated from first principles. It is shown that nanoobjects with only odd number of monolayers are ferroelectric. The ferroelectric, piezoelectric, and elastic properties of these polar structures are calculated. The appearance of polarization in these nanoobjects is explained by an uncompensated polarization that exists in an antiferroelectric structure of bulk SnS. The mechanism of ferroelectricity, in which the ferroelectric distortion is associated with short-range ordering …
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…
We find that several layer-phase group-III monochalcogenides, including GaS, GaSe and InSe, are piezoelectric in the monolayer form. First-principles calculations reveal that the piezoelectric coefficients of monolayer GaS, GaSe and InSe are on the same order of magnitude as the earlier discovered two-dimensional piezoelectric materials, such as BN and MoS2 monolayers. Our study expands the family of two dimensional piezoelectric materials, suggesting that strong piezoelectric response can occur in a wide range of two dimensional materials with broken inversion symmetry. The co-existence of pi…
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 ($d…
Two-dimensional van der Waals (2D vdW) materials that display ferromagnetism and piezoelectricity have received increased attention. Despite numerous 2D materials have so far been reported as ferromagnetic, developing an air stable and transferable vdW material that is multiferroic has been challenging. To address this problem, we report our work on layered transition metal silicates that are derivatives of kaolinites and lizardites with transition metal substituting on Al$^{3+}$ and Mg$^{2+}$ sites using ab-initio calculations. Using Density Functional Theory (DFT), we show that these compoun…
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 $\mathrm{Li_2Fe_2SS…
Two-dimensional materials that exhibit spontaneous electric polarization are of notable interest for functional materials. However, despite many two-dimensional polar materials are predicted in theory, the number of experimentally confirmed two-dimensional ferroelectrics are still far less than bulk ferroelectrics. We provide strong evidence that the Pmn2$_1$ phase of arsenic chalcogenides As$_2$X$_3$ (X=S, Se, and Te), which include the recently isolated monolayer orpiment, are intrinsic ferroelectrics and demonstrate strong in-plane piezoelectricity. We found the calculated energy barriers f…
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…
We predict enormous piezoelectric effects in intrinsic monolayer group IV monochalcogenides (MX, M=Sn or Ge, X=Se or S), including SnSe, SnS, GeSe and GeS. Using first-principle simulations based on the modern theory of polarization, we find that their characteristic piezoelectric coefficients are about two orders of magnitude larger than those of other 2D materials, such as MoS2 and GaSe, and bulk quartz and AlN which are widely used in industry. This enhancement is a result of the unique "puckered" C2v symmetry and weaker chemical bonds of monolayer group IV monochalcogenides. Given the achi…
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…
Prediction of Magnetoelectric Multiferroic Janus Monolayers VOXY(X/Y = F, Cl, Br, or I, and X$\not=$Y) with in-plane ferroelectricity and out-of-plane piezoelectricity
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…
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…
Experimental realization of single-layer MoSi2N4 is among the latest groundbreaking advances in the field of two-dimensional (2D) materials. Inspired by this accomplishment, herein we conduct first-principles calculations to explore the stability of MC2N4 (M= Cr, Mo, W, V, Nb, Ta, Ti, Zr, Hf) monolayers. Acquired results confirm the desirable thermal, dynamical and mechanical stability of MC2N4 (M= Cr, Mo, W, V) nanosheets. Interestingly, CrC2N4, MoC2N4 and WC2N4 monolayers are found to be semiconductors with band gaps of 2.32, 2.76 and 2.86 eV, respectively, using the HSE06 functional, wherea…
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…
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…
Lattices of odd-layered two-dimensional (2D) transition metal dichalcogenides (TMDs) such as WSe2 are non-centrosymmetric, and thus could possess linear piezoelectricity that is attractive for applications such as nanoelectromechanical systems (NEMS) and nanogenerators. Measuring the electromechanical coupling of 2D TMDs, however, is rather challenging, since its D3h point group symmetry makes conventional piezoresponse force microscopy (PFM) inapplicable. Here we develop a lateral excitation scanning probe microscopy (SPM) technique that enables mapping of the piezoelectric response of atomic…
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 Se atomic layer in $\mathrm{MoSe_2}$ by S 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 and mech…
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…
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 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…
Since the first realization of reversible charge doping in graphene via field-effect devices, it has become evident how the induction a gap could further enhance its potential for technological applications. Here we show that the gap opening due to a sublattice symmetry breaking has also a profound impact on the polar response of graphene. By combining ab-initio calculations and analytical modelling we show that for realistic band-gap values ($Δ\lesssim 0.5$ eV) the piezoelectric coefficient and the Born effective charge of graphene attain a giant value, independent on the gap. In particular t…
For two-dimensional (2D) materials, a pure large out-of-plane piezoelectric response, compatible with the nowadays bottom/top gate technologies, is highly desired. In this work, the piezoelectric properties of penta-graphene (CCC) monolayer are studied with pure out-of-plane piezoelectric effect by density functional theory (DFT). However, the $d_{36}$ is very small, and only -0.065 pm/V. Two strategies are proposed to enhance piezoelectric properties of CCC monolayer. Firstly, both biaxial and uniaxial strains are applied, but the enhancement is very small, and at -2\% biaxial (-4\% uniaxial)…
Integration of promising piezoelectric and photocatalytic properties in Janus In$XY$ ($X$ = S, Se, Te; $Y$ = Cl, Br, I) monolayers and their heterojunctions
