arXiv subjects

Xing-Qiu Chen

Publications and source records attributed to Xing-Qiu Chen.

At least 37 records · Page 2Linked to original sources

arXiv2024

Electric field tunable non-linear Hall terahertz detector in Dual quantum spin Hall insulator $\text{TaIrTe}_4$

Nonlinear Hall effect (NHE) can be generated via Berry curvature dipole (BCD) on nonequilibrium Fermi surface in a non-magnetic system without inversion symmetry.To achieve a large BCD, strong local Berry curvatures and their variation with respect to momentum are necessary and hence topological materials with strong inter-band coupling emerge as promising candidates. In this study, we propose a switchable and robust BCD in the newlydiscovered dual quantum spin Hall insulator (QSHI) $\text{TaIrTe}_4$ by applying out-of-plane electric fields. Switchable BCD could be found along with topological phase transitions or insulator-metal transition in the primitive cell and CDW phases of $\text{TaIrTe}_4$ monolayer. This work presents an instructive strategy for achieving a switchable and robust BCD within dual QSHIs, which should be helpful for designing the NHE-based THz radiations detector.

cond-mat.mtrl-sci↗

arXiv2024

Prediction of dual quantum spin Hall insulator in NbIrTe$_4$ monolayer

Dual quantum spin Hall insulator (QSHI) is a newly discovered topological state in the 2D material TaIrTe$_4$, exhibiting both a traditional $Z_2$ band gap at charge neutrality point and a van Hove singularity (VHS) induced correlated $Z_2$ band gap with weak doping. Inspired by the recent progress in theoretical understanding and experimental measurements, we predicted a promising dual QSHI in the counterpart material of the NbIrTe4 monolayer by first-principles calculations. In addition to the well-known band inversion at the charge neutrality point, two new band inversions were found after CDW phase transition when the chemical potential is near the VHS, one direct and one indirect $Z_2$ band gap. The VHS-induced non-trivial band gap is around 10 meV, much larger than that from TaIrTe$_4$. Furthermore, since the new generated band gap is mainly dominated by the $4d$ orbitals of Nb, electronic correlation effects should be relatively stronger in NbIrTe$_4$ as compared to TaIrTe$_4$. Therefore, the dual QSHI state in the NbIrTe$_4$ monolayer is expected to be a good platform for investigating the interplay between topology and correlation effects.

cond-mat.str-el↗

arXiv2024

Switchable quantized signal between longitudinal conductance and Hall conductance in dual quantum spin Hall insulator TaIrTe$_4$

Topological insulating states in two-dimensional (2D) materials are ideal systems to study different types of quantized response signals due to their in gap metallic states. Very recently, the quantum spin Hall (QSH) effect was discovered in monolayer $\text{TaIrTe}_4$ via the observation of quantized longitudinal conductance that rarely exists in other 2D topological insulators. The non-trivial $Z_2$ topological charges can exist at both charge neutrality point and the van Hove singularity point with correlation effect induced band gap. Based on this model 2D material, we studied the switch of quantized signals between longitudinal conductance and transversal Hall conductance via tuning external magnetic field. In $Z_2$ topological phase of monolayer $\text{TaIrTe}_4$, the zero Chern number can be understood as 1-1=0 from the double band inversion from spin-up and spin-down channels. After applying a magnetic field perpendicular to the plane, the Zeeman split changes the band order for one branch of the band inversion from spin-up and spin-down channels, along with a sign charge of the Berry phase. Then the net Chern number of 1-1=0 is tuned to 1+1=2 or -1-1=-2 depending on the orientation of the magnetic field. The quantized signal not only provides another effective method for the verification of topological state in monolayer $\text{TaIrTe}_4$, but also offers a strategy for the utilization of the new quantum topological states based on switchable quantized responses.

cond-mat.mes-hall↗

arXiv2024

Layer-by-layer phase transformation in Ti$_3$O$_5$ revealed by machine learning molecular dynamics simulations

Reconstructive phase transitions involving breaking and reconstruction of primary chemical bonds are ubiquitous and important for many technological applications. In contrast to displacive phase transitions, the dynamics of reconstructive phase transitions are usually slow due to the large energy barrier. Nevertheless, the reconstructive phase transformation from $β$- to $λ$-Ti$_3$O$_5$ exhibits an ultrafast and reversible behavior. Despite extensive studies, the underlying microscopic mechanism remains unclear. Here, we discover a kinetically favorable in-plane nucleated layer-by-layer transformation mechanism through metadynamics and large-scale molecular dynamics simulations. This is enabled by developing an efficient machine learning potential with near first-principles accuracy through an on-the-fly active learning method and an advanced sampling technique. Our results reveal that the $β$-$λ$ phase transformation initiates with the formation of two-dimensional nuclei in the $ab$-plane and then proceeds layer-by-layer through a multistep barrier-lowering kinetic process via intermediate metastable phases. Our work not only provides important insight into the ultrafast and reversible nature of the $β$-$λ$ transition, but also presents useful strategies and methods for tackling other complex structural phase transitions.

cond-mat.mtrl-sci↗

arXiv2023

Ferroelectrically switchable magnetic multistates in MnBi$_2$Te$_4$(Bi$_2$Te$_3$)$_n$ and MnSb$_2$Te$_4$(Sb$_2$Te$_3$)$_n$ (n = 0, 1) thin films

Ferroelectric control of two-dimensional magnetism is promising in fabricating electronic devices with high speed and low energy consumption. The newly discovered layered MnBi$_2$Te$_4$(Bi$_2$Te$_3$)$_n$ and their Sb counterparts exhibit A-type antiferromagnetism with intriguing topological properties. Here, we propose to obtain tunable magnetic multistates in their thin films by ferroelectrically manipulating the interlayer magnetic couplings (IMCs) based on the Heisenberg model and first-principles calculations. Our strategy relies on that interfacing the thin films with appropriate ferroelectric materials can switch on/off an interlayer hopping channel between Mn-$e_g$ orbitals as the polarizations reversed, thus resulting in a switchable interlayer antiferromagnetism-to-ferromagnetism transition. On the other hand, the interface effect leads to asymmetric energy barrier heights for the two polarization states. These properties allow us to build ferroelectrically switchable triple and quadruple magnetic states with multiple Chern numbers in thin films. Our study reveals that ferroelectrically switchable magnetic and topological multistates in MnBi$_2$Te$_4$ family can be obtained by rational design for multifunctional electronic devices, which can also be applied to other two-dimensional magnetic materials.

cond-mat.mtrl-sci↗

arXiv2023

Symmetry breaking induced insulating electronic state in Pb$_{9}$Cu(PO$_4$)$_6$O

The recent experimental claim of room-temperature ambient-pressure superconductivity in a Cu-doped lead-apatite (LK-99) has ignited substantial research interest in both experimental and theoretical domains. Previous density functional theory (DFT) calculations with the inclusion of an on-site Hubbard interaction $U$ consistently predict the presence of flat bands crossing the Fermi level. This is in contrast to DFT plus dynamical mean field theory calculations, which reveal the Mott insulating behavior for the stoichiometric Pb$_{9}$Cu(PO$_4$)$_6$O compound. Nevertheless, the existing calculations are all based on the $P6_3/m$ structure, which is argued to be not the ground-state structure. Here, we revisit the electronic structure of Pb$_{9}$Cu(PO$_4$)$_6$O with the energetically more favorable $P\bar{3}$ structure, fully taking into account electronic symmetry breaking. We examine all possible configurations for Cu substituting the Pb sites. Our results show that the doped Cu atoms exhibit a preference for substituting the Pb2 sites than the Pb1 sites. In both cases, the calculated substitutional formation energies are large, indicating the difficulty in incorporating Cu at the Pb sites. We find that most of structures with Cu at the Pb2 site tend to be insulating, while the structures with both two Cu atoms at the Pb1 sites (except one configuration) are predicted to be metallic by DFT+$U$ calculations. However, when accounting for the electronic symmetry breaking, some Cu-doped configurations previously predicted to be metallic (including the structure studied in previous DFT+$U$ calculations) become insulating. Our work highlights the importance of symmetry breaking in obtaining correct electronic state for Pb$_{9}$Cu(PO$_4$)$_6$O, thereby reconciling previous DFT+$U$ and DFT+DMFT calculations.

cond-mat.mtrl-sci↗

arXiv2023

Hardness and fracture toughness models by symbolic regression

Superhard materials with good fracture toughness have found wide industrial applications, which necessitates the development of accurate hardness and fracture toughness models for efficient materials design. Although several macroscopic models have been proposed, they are mostly semiempirical based on prior knowledge or assumptions, and obtained by fitting limited experimental data. Here, through an unbiased and explanatory symbolic regression technique, we built a macroscopic hardness model and fracture toughness model, which only require shear and bulk moduli as inputs. The developed hardness model was trained on an extended dataset, which not only includes cubic systems, but also contains non-cubic systems with anisotropic elastic properties. The obtained models turned out to be simple, accurate, and transferable. Moreover, we assessed the performance of three popular deep learning models for predicting bulk and shear moduli, and found that the crystal graph convolutional neural network and crystal explainable property predictor perform almost equally well, both better than the atomistic line graph neural network. By combining the machine-learned bulk and shear moduli with the hardness and fracture toughness prediction models, potential superhard materials with good fracture toughness can be efficiently screened out through high-throughput calculations.

cond-mat.mtrl-sci↗

arXiv2023

First-principles study on the electronic structure of Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O ($x$=0, 1)

Recently, Lee et al. reported the experimental discovery of room-temperature ambient-pressure superconductivity in a Cu-doped lead-apatite (LK-99) (arXiv:2307.12008, arXiv:2307.12037). Remarkably, the superconductivity persists up to 400 K at ambient pressure. Despite strong experimental evidence, the electronic structure of LK-99 has not yet been studied. Here, we investigate the electronic structures of LK-99 and its parent compound using first-principles calculations, aiming to elucidate the doping effects of Cu. Our results reveal that the parent compound Pb$_{10}$(PO$_4$)$_6$O is an insulator, while Cu doping induces an insulator-metal transition and thus volume contraction. The band structures of LK-99 around the Fermi level are featured by a half-filled flat band and a fully-occupied flat band. These two flat bands arise from both the $2p$ orbitals of $1/4$-occupied O atoms and the hybridization of the $3d$ orbitals of Cu with the $2p$ orbitals of its nearest-neighboring O atoms. Interestingly, we observe four van Hove singularities on these two flat bands. Furthermore, we show that the flat band structures can be tuned by including electronic correlation effects or by doping different elements. We find that among the considered doping elements (Ni, Cu, Zn, Ag, and Au), both Ni and Zn doping result in the gap opening, whereas Au exhibits doping effects more similar to Cu than Ag. Our work provides a foundation for future studies on the role of unique electronic structures of LK-99 in superconductivity.

cond-mat.mtrl-sci↗

arXiv2023

Comprehensive ab initio study of effects of alloying elements on generalized stacking fault energies of Ni and Ni$_3$Al

Excellent high-temperature mechanical properties of Ni-based single crystal superalloys (NSCSs) are attributed to the yield strength anomaly of Ni$_{3}$Al that is intimately related to generalized stacking fault energies (GSFEs). Therefore, clarifying the effects of alloying elements on the GSFEs is of great significance for alloys design. Here, by means of ab initio density functional theory calculations, we systematically calculated the GSFEs of different slip systems of Ni and Ni$_{3}$Al without and with alloying elements using the alias shear method. We obtained that for Ni, except for magnetic elements Mn, Fe, and Co, most of alloying elements decrease the unstable stacking fault energy ($γ_{usf}$) of the $[01\bar{1}](111)$ and $[11\bar{2}](111)$ slip systems and also decrease the stable stacking fault energy ($γ_{sf}$) of the $[11\bar{2}](111)$ slip system. For Ni$_{3}$Al, most of alloying elements in groups IIIB-VIIB show a strong Al site preference. Except for Mn and Fe, the elements in groups VB-VIIB and the first column of group VIII increase the values of $γ_{usf}$ of different slip systems of Ni$_{3}$Al. On the other hand, the elements in groups IIIB-VIIB also increase the value of $γ_{sf}$. We found that Re is an excellent strengthening alloying element that significantly increases the slip barrier of the tailing slip process for Ni, and also enhances the slip barrier of the leading slip process of three slip systems for Ni$_{3}$Al. W and Mo exhibit similar effects as Re. We predicted that Os, Ru, and Ir are good strengthening alloying elements as well, since they show the strengthening effects on both the leading and tailing slip process for Ni and Ni$_{3}$Al.

cond-mat.mtrl-sci↗

arXiv2023

On parent structures of near-ambient nitrogen-doped lutetium hydride superconductor

Recently, near-ambient superconductivity has been experimentally evidenced in a nitrogen-doped lutetium hydride by Dasenbrock-Gammon \emph{et al.} [Nature 615, 244 (2023)], which yields a remarkable maximum $T_c$ of 294 K at just 10 kbar. However, due to the difficulty of x-ray diffraction (XRD) in identifying light elements such as hydrogen and nitrogen, the crystal structure of the superconductor remains elusive, in particular for the actual stoichiometry of hydrogen and nitrogen and their atomistic positions. This holds even for its parent structure. Here, we set out to address this issue by performing a thorough density functional theory study on the structural, electronic, dynamical, and optical properties of lutetium hydrides. Through thermal and lattice dynamic analysis as well as XRD and superconductor color comparisons, we unambiguously clarified that the parent structures are a mixture of dominant LuH$_2$ phase of the CaF$_2$-type (instead of originally proposed LuH$_3$ structure of $Fm\bar{3}m$ space group) and minor LuH phase of the NaCl-type.

cond-mat.mtrl-sci↗

arXiv2023

Combining Machine Learning and Many-Body Calculations: Coverage-Dependent Adsorption of CO on Rh(111)

Adsorption of carbon monoxide (CO) on transition-metal surfaces is a prototypical process in surface sciences and catalysis. Despite its simplicity, it has posed great challenges to theoretical modeling. Pretty much all existing density functionals fail to accurately describe surface energies, CO adsorption site preference, as well as adsorption energies simultaneously. Although the random phase approximation (RPA) cures these density functional theory failures, its large computational cost makes it prohibitive to study the CO adsorption for any but the simplest ordered cases. Here, we address these challenges by developing a machine-learned force field (MLFF) with near RPA accuracy for the prediction of coverage-dependent adsorption of CO on the Rh(111) surface through an efficient on-the-fly active learning procedure and a $Δ$-machine learning approach. We show that the RPA-derived MLFF is capable to accurately predict the Rh(111) surface energy, CO adsorption site preference as well as adsorption energies at different coverages that are all in good agreement with experiments. Moreover, the coverage-dependent ground-state adsorption patterns and adsorption saturation coverage are identified.

cond-mat.mtrl-sci↗

arXiv2022

Anisotropic linear and nonlinear charge-spin conversion in topological semimetal SrIrO3

Over the past decade, utilizing spin currents in the linear response of electric field to manipulate magnetization states via spin-orbit torques (SOTs) is one of the core concepts for realizing a multitude of spintronic devices. Besides the linear regime, recently, nonlinear charge-spin conversion under the square of electric field has been recognized in a wide variety of materials with nontrivial spin textures, opening an emerging field of nonlinear spintronics. Here, we report the investigation of both linear and nonlinear charge-spin conversion in one single topological semimetal SrIrO3(110) thin film that hosts strong spin-orbit coupling and nontrivial spin textures in the momentum space. In the nonlinear regime, the observation of crystalline direction dependent response indicates the presence of anisotropic surface states induced spin-momentum locking near the Fermi level. Such anisotropic spin textures also give rise to spin currents in the linear response regime, which mainly contributes to the fieldlike SOT component. Our work demonstrates the power of combination of linear and nonlinear approaches in understanding and utilizing charge-spin conversion in topological materials.

cond-mat.mtrl-sci↗

arXiv2022

Large spin Hall conductivity and excellent hydrogen evolution reaction activity in unconventional PtTe1.75 monolayer

Two-dimensional (2D) materials have gained lots of attention due to the potential applications. In this work, we propose that based on first-principles calculations, the (2$\times$2) patterned PtTe$_2$ monolayer with kagome lattice formed by the well-ordered Te vacancy (PtTe$_{1.75}$) hosts large spin Hall conductivity (SHC) and excellent hydrogen evolution reaction (HER) activity. The unconventional nature relies on the $A1@1b$ band representation (BR) of the highest valence band without SOC. The large SHC comes from the Rashba spin-orbit coupling (SOC) in the noncentrosymmetric structure induced by the Te vacancy. Even though it has a metallic SOC band structure, the $\mathbb Z_2$ invariant is well defined due to the existence of the direct band gap and is computed to be nontrivial. The calculated SHC is as large as 1.25$\times 10^3 \frac{\hbar}{e} (Ω~cm)^{-1}$ at the Fermi level ($E_F$). By tuning the chemical potential from $E_F-0.3$ to $E_F+0.3$ eV, it varies rapidly and monotonically from $-1.2\times 10^3$ to 3.1$\times 10^3 \frac{\hbar}{e} (Ω~cm)^{-1}$. In addition, we also find the Te vacancy in the patterned monolayer can induce excellent HER activity. Our results not only offer a new idea to search 2D materials with large SHC, i.e., by introducing inversion-symmetry breaking vacancies in large SOC systems, but also provide a feasible system with tunable SHC (by applying gate voltage) and excellent HER activity.

cond-mat.mtrl-sci↗

arXiv2022

Coexistence of Weyl semimetal and Weyl nodal loop semimetal phases in a collinear antiferromagnet

Antiferromagnets (AFMs) with anomalous quantum responses have lead to new progress for the understanding of their magnetic and electronic structures from symmetry and topology points of view. Two typical topological states are the collinear antiferromagnetic Weyl semimetal (WSM) and Weyl nodal loop semimetal (WNLSM). In comparison with the counterparts in ferromagnets and non-collinear AFMs, the WSMs and WNLSMs in collinear AFMs are still waiting for experimental verification. In this work, we theoretically predicted the coexistence of Weyl points (WPs) and Weyl nodal loops (WNLs) in transition metal oxide RuO2. Owing to the small magnetocrystalline anisotropy energy, the WPs and WNLs can transform to each other via tuning the Neel vector. Moreover, since the WPs are very close to Fermi level and the WNLs are even crossing Fermi level, the topological states in RuO2 can be easily probed by photoemission and STM methods. Our result provides a promising material platform for the study of WSM and WNLSM states in collinear AFMs.

cond-mat.mtrl-sci↗

arXiv2022

Two-dimensional Obstructed Atomic Insulators with Fractional Corner Charge in MA$_2$Z$_4$ Family

According to topological quantum chemistry, a class of electronic materials have been called obstructed atomic insulators (OAIs), in which a portion of valence electrons necessarily have their centers located on some empty $\textit{Wyckoff}$ positions without atoms occupation in the lattice. The obstruction of centering these electrons coinciding with their host atoms is nontrivial and results in metallic boundary states when the boundary is properly cut. Here, on basis of first-principles calculations in combination with topological quantum chemistry analysis, we propose two dimensional MA$_2$Z$_4$ (M = Cr, Mo and W; A = Si and Ge, Z = N, P and As) monolayer family are all OAIs. A typical case is the recently synthesized MoSi$_2$N$_4$. Although it is a topological trivial insulator with the occupied electronic states being integer combination of elementary band representations, it has valence electrons centering empty $\textit{Wyckoff}$ positions. It exhibits unique OAI-induced metallic edge states along the (1$\bar{1}$0) edge of MoSi$_2$N$_4$ monolayer and the in-gap corner states at three vertices of certain hexagonal nanodisk samples respecting C$_3$ rotation symmetry. The readily synthesized MoSi$_2$N$_4$ is quite stable and has a large bulk band gap of 1.94 eV, which makes the identification of these edge and corner states most possible for experimental clarification.

cond-mat.mtrl-sci↗

arXiv2021

Novel Two-Dimensional Layered MSi$_2$N$_4$ (M = Mo, W): New Promising Thermal Management Materials

With the miniaturization and integration of nanoelectronic devices, efficient heat removal becomes a key factor affecting the reliable operation of the nanoelectronic device. With the high intrinsic thermal conductivity, good mechanical flexibility, and precisely controlled growth, two-dimensional (2D) materials are widely accepted as ideal candidates for thermal management materials. In this work, by solving the phonon Boltzmann transport equation (BTE) based on first-principles calculations, we comprehensively investigated the thermal conductivity of novel 2D layered MSi$_2$N$_4$ (M = Mo, W). Our results point to competitive thermal conductivities (162 W/mK) of monolayer MoSi$_2$N$_4$, which is around two times larger than that of WSi$_2$N$_4$ and seven times larger than that of silicene despite their similar non-planar structures. It is revealed that the high thermal conductivity arises mainly from its large group velocity and low anharmonicity. Our result suggests that MoSi$_2$N$_4$ could be a potential candidate for 2D thermal management materials.

cond-mat.mtrl-sci↗

arXiv2021

Piezoelectric quantum spin Hall insulator with Rashba spin splitting in Janus monolayer $\mathrm{SrAlGaSe_4}$

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 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 nontrivial band topology can hold until considered 1.16 tensile strain. Moreover, a Rashba spin splitting in the conduction bands can exit in PQSHI due to the absence of a horizontal mirror symmetry and the presence of SOC. For monolayer $\mathrm{SrAlGaSe_4}$, both in-plane and much weak out-of-plane piezoelectric polarizations can be induced with a uniaxial strain applied. The calculated piezoelectric strain coefficients $d_{11}$ and $d_{31}$ of monolayer $\mathrm{SrAlGaSe_4}$ are -1.865 pm/V and -0.068 pm/V at 1.06 tensile strain as a representative TI. In fact, many PQSHIs can be realized from 2D $\mathrm{MA_2Z_4}$ family. To confirm that, similar to $\mathrm{SrAlGaSe_4}$, the coexistence of piezoelectricity and topological orders can be realized by strain (about 1.04 tensile strain) in the $\mathrm{CaAlGaSe_4}$ monolayer. Our works suggest that Janus monolayer $\mathrm{SrAlGaSe_4}$ is a pure 2D system for PQSHI, enabling future studies exploring the interplay between piezoelectricity and topological orders, which can lead to novel applications in electronics and spintronics.

cond-mat.mtrl-sci↗

arXiv2020

Structure effect on intrinsic piezoelectricity in septuple-atomic-layer $\mathrm{MSi_2N_4}$ (M=Mo and W)

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 results show that $\mathrm{MoSi_2N_4}$ and $\mathrm{WSi_2N_4}$ monolayers have the same structural dependence on piezoelectric strain and stress coefficients ($d_{11}$ and $e_{11}$), together with the ionic and electronic contributions to $e_{11}$.Finally, we investigate the intrinsic piezoelectricity of monolayer $\mathrm{MA_2Z_4}$ (M=Cr, Mo and W; A=Si and Ge; Z=N and P) with $α_1$ and $α_2$ phases expect $\mathrm{CrGe_2N_4}$, because they all are semiconductors and their enthalpies of formation between $α_1$ and $α_2$ phases are very close. The most important result is that monolayer $\mathrm{MA_2Z_4}$ containing P atom have more stronger piezoelectric polarization than one including N atom. The largest $d_{11}$ among $\mathrm{MA_2N_4}$ materials is 1.85 pm/V, which is close to the smallest $d_{11}$ of 1.65 pm/V in $\mathrm{MA_2P_4}$ monolayers. For $\mathrm{MA_2P_4}$, the largest $d_{11}$ is up to 6.12 pm/V. Among the 22 monolayers, $α_1$-$\mathrm{CrSi_2P_4}$, $α_1$-$\mathrm{MoSi_2P_4}$, $α_1$-$\mathrm{CrGe_2P_4}$, $α_1$-$\mathrm{MoGe_2P_4}$ and $α_2$-$\mathrm{CrGe_2P_4}$ have large $d_{11}$, which are greater than or close to 5 pm/V, a typical value for bulk piezoelectric materials.

cond-mat.mtrl-sci↗