Interlayer Coupling Induced Ferroelectricity in Bilayer α-As

Interlayer Coupling Induced Ferroelectricity in Bilayer α-As | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Interlayer Coupling Induced Ferroelectricity in Bilayer α-As In Kee Park, Geunsik Lee This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7653762/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Ferroelectric (FE) instability in the puckered lattice of arsenic (α-As) is investigated using density functional theory (DFT) calculations. A bilayer (BL) structure with the most stable AA-stacked configuration is found to exhibit spontaneous ferroelectric polarization arising from an intralayer distortion analogous to that observed in α-Bi monolayers. Unlike conventional two-dimensional (2D) ferroelectricity, which is typically driven by sliding-induced charge transfer, the observed polarization in α-As primarily originates from a lattice contraction along the armchair direction caused by inverted band occupation facilitated through interlayer electron hopping. The calculated polarization reaches 0.63 × 10 -10 C/m with the associated transition barrier 5.4 meV/u.c., and our molecular dynamics simulations using machine-learned interatomic potential shows the FE ordering persisting up to ~100 K or 300 K under a uniaxial compression of 0% or -4%, respectively. These results provide new insight into distinct mechanism of 2D ferroelectricity governed by interlayer electronic coupling. Hard Condensed-matter Physics 2d ferroelectrics DFT modeling Figures Figure 1 Figure 2 Figure 3 Figure 4 Full Text Ferroelectric (FE) materials have attracted considerable attention due to their spontaneous polarization which can be reversed by applying an external electric field [1-3]. Notable applications include non-volatile data storage [4], neuromorphic computing [5,6], and energy harvesting and sensing, enabled by their intrinsic pyroelectric and piezoelectric properties [7,8]. However, as devices dimensions continue to shrink, there is an increasing demand for materials that enable fast operation, long retention time, and low energy consumption. For this, two-dimensional (2D) FEs have emerged as promising candidates owing to their distinctive advantages. The van der Waals (vdW) layered structures of 2D FEs are free from the strong depolarization effects along the out-of-plane direction that typically hinder polarization in conventional three-dimensional FEs [9-11]. Atomically smooth surfaces allow for clean exfoliation without surface defects and dangling bonds, making 2D FEs ideal for designing multifunctional devices such as heterostructures and multiferroic systems [12]. Additionally, mechanical flexibility of 2D materials supports wearable and flexible electronics [8,13]. Finally, their reduced dimensionality leads to weakened internal fields, enabling low-power and ultrafast FE switching [14]. Extensive research has been devoted to 2D FE materials. Notable examples are CuInP₂S₆ [15] and In₂Se₃ [16]. Although systematic efforts based on symmetry analysis have been made to identify potential FE materials [17], only a limited number were confirmed to exhibit intrinsic FE polarization. This limitation has prompted alternative approach to induce FE through external perturbations, which is often referred to as hidden ferroelectricity. Representative examples are strain-induced ferroelectricity in perovskite [18, 19] and electric field-induced FE transition in MX (M = Si, Ge, Sn; X = S, Se, Te) system [20]. Another compelling strategy is sliding ferroelectricity, where a non-ferroelectric layered system acquires FE polarization through interlayer charge transfer induced by lateral sliding that breaks inversion symmetry. This phenomenon has been demonstrated in bilayer hBN [21, 22], WTe₂ [23], graphene [24], and MoS₂ [25]. Within the various layered materials, α phase of group-V elements with puckered lattice structure, also known as black phosphorus structure, have attracted considerable attention due to their in-plane anisotropic properties and highly tunable band gap with thickness [26, 27]. Monolayer α-P and α-As lack spontaneous polarization due to their centrosymmetric lattice structure. However, compressive strain along the armchair direction induces instability against a buckling mode, thereby inducing FE polarization in α-P [28, 29]. Recent study also reports sliding FE in multilayer (three or more) α-P driven by work function differences between stacking configurations [30]. In contrast, α-Sb and α-Bi favor a buckled structure that leads to spontaneous polarization [31]. Notably, recent experimental study has demonstrated FE switching in monolayer α-Bi under applied voltage [32]. In addition, the interlayer coupling is significant as one can expect from a band gap reduction from 1.5 to 0.3 eV for monolayer to bulk α-P [33]. Raman measurements of α-P reveal that interlayer force constants and interlayer binding are two to three times stronger than that of graphene and MoS₂ [34]. For α-As and α-Sb, surface energy and optimized lattice constants vary significantly with respect to the number of layers [35]. In this study, we investigate the interlayer interaction and FE properties of BL α-As. Through systematic scanning diverse stacking configurations, we identify metastable structures and characterize their FE properties. We reveal the emergence of a ferroelectric phase in BL, unlike monolayer counterpart, elucidating the crucial role of interlayer coupling in stabilizing novel FE phase. The underlying mechanism differs from that of conventional sliding ferroelectrics and is related to lattice contraction caused by significant interlayer electron hopping. Our results provide insight into new mechanisms for achieving ferroelectricity beyond conventional approaches. First-principles calculations were performed using density functional theory (DFT) (see Section 1 in Supplemental Material for details [43]). Figure 1(a) depicts the crystal structure of monolayer (ML) α-As in which two atomically flat zigzag chains run along the a -axis to form the puckered lattice. An identical motif is found in α-Bi [32] and group-IV monochalcogenides [36], but in those materials this geometry is known to be unstable with respect to the out-of-plane buckling (B 1u ) mode, indicated by the arrows, which induces a ferroelectric polarization along positive or negative b- axis. In contrast, as shown in Fig. 1(b), our calculations reveal that ML prefers to remain flat, which is also valid for AB-stacked bulk phase. To assess how interlayer interactions affect the structural stability against B 1u mode in BL α-As, various stacking registries were considered, as illustrated in Fig. 1(c). We define the second layer’s displacement relative to the first one by fractional in-plane coordinates (Δ a , Δ b ). Restricting Δ a , Δ b to 0.0 or 0.5 yields four distinct stackings, denoted as AA, AB, AC, and AD corresponding to (0.0, 0.0), (0.5, 0.0), (0.5, 0.5), and (0.0, 0.5), respectively. For each registry, we performed full geometry optimization under the constraint that the in-plane fractional coordinates remain fixed. Related to B 1u distortion, three initial geometries were considered, the perfectly flat and two buckled variants with Δz = 0.2 Å, featuring either parallel or antiparallel polarizations between the bottom and top layers (Fig. S1). This method allowed us to find out the most stable bilayer configuration as a function of stacking. Figures 2(a) shows the heat maps of the potential energy surface (PES) calculated with the initially flat and buckled (parallel polarization) geometries, where the antiparallel buckling was checked to give nearly the same result as that of parallel case (Fig. S2). The optimized structure can exhibit non-zero buckling with parallel or anti-parallel polarizations between top and bottom layers, or zero buckling. Notably the ferroelectric behavior depends on the initial configurations of buckling and stacking. For example, the registries near Δ b = 0.5 (AC and AD) have relatively high potential energy (Table 1) and exhibit the antiparallel polarizations irrespective of whether the initial structure is buckled or not. Meanwhile, relatively stable registries (AA and AB) near Δ b = 0.0 leads to zero polarization except AA-stacked ferroelectric phase (AA-FE) obtained with initially buckled structure, where for AB almost identical structures of zero buckling were obtained for two initial cases. As listed in Table 1, the most stable structure is found to be AA-FE with the buckling heights 0.14, 0.15 Å for the zigzag chains at interface, surface layers, respectively. Relative to AA-FE, the potential energies of AA and AB are higher by 5.9 and 20.4 meV/u.c, respectively. The newly found AA-FE with a lower energy than AA indicates that AA structure is unstable dynamically. Indeed, our calculated phonon band structure exhibits imaginary modes for AA, as shown in Fig. 2(b), and AA-FE and AB are confirmed to be stable dynamically. Actually, AA corresponds to the transition state connecting two bistable states of AA-FE, shown in Fig. 2(c). By nudged elastic band (NEB) calculation the minimum energy path connecting two oppositely polarized AA-FE structures (Fig. 2(d)) involves the transition state corresponding to the structure with zero buckling height, matching with the AA configuration. The associated energy barrier (5.4 meV/u.c.) is comparable to ML α-Bi (43 meV/u.c.) [32], BL hBN (9 meV/u.c.) [21] and BL WTe 2 (0.6 meV/u.c.) [37]. These systems have been experimentally shown to undergo polarization switching under external voltage [22, 23], which highlights possibility of polarization control in BL α-As. The electric polarization calculated for AA-FE is 0.63 10 -10 C/m, which is approximately 1.5 times greater than that reported for ML α-Bi (~0.4 10 -10 C/m) [32] and exceeds by the several orders of magnitude those found in typical sliding FE systems such as BL hBN (2.08 pC/m ~ 0.02 10 -10 C/m) or BL MoS 2 (0.33 pC/m ~ 0.003 10 -10 C/m) [21]. This is particularly noteworthy because ML α-As does not exhibit intrinsic ferroelectricity, indicating that the ferroelectric state emerges exclusively in the BL system through interlayer coupling. Bulk α-As is known to favor AB stacking as its ground state, but our calculations for BL show that the AA-FE and AA are more stable than AB. Previous theoretical studies have shown competing stability between AB and AA stackings with very little energy difference (~10 meV/atom) and the results are controversial with dependence on DFT functional [38, 39]. Crucially, those studies, including one using diffuse Monte Carlo method [40] have not considered buckling distortion to lower the total energy, particularly for the AA stacking. From our calculation, the energy difference between AA-FE and AB is 20.4 meV/u.c. or 1.2 meV/Å 2 , which is comparable to stacking fault energies of other 2D materials such as hBN and graphene (~1.0 meV/Å 2 ) [41]. This suggests that AA-FE stacking is readily formed once BL α-As is synthesized. It is worthy to note that AA-stacked bulk α-As is unstable with respect to forming the gray arsenic (Fig. S9). To elucidate the origin of ferroelectric distortion in AA-stacked BL α-As, we studied the electronic structure. For ML α-As, the band structure shown in Fig. 3(a) has the band gap ~1.0 eV. It is also shown that the valence band maximum (VBM) orbital at Γ point has the p z orbital symmetries of bonding type σ and antibonding type π* along the vertical and horizontal directions, respectively. For the conduction band minimum (CBM) orbitals, it is reversed. For BL α-As with AA configuration (Fig. 3(b)), the band structure becomes metallic with the reversed orbital symmetry between VBM and CBM due to the significant interlayer hopping. In other words, the bonding type π at Γ is occupied while the antibonding type π* is empty. This band inversion is attributed to the proximity of atoms between layers, appearing in the AA stacking. As shown in Fig. S4, the first nearest-neighbor interlayer atomic distance in the AA-FE is significantly shorter (3.13 Å) than that in the AB (3.72 Å), leading to a band splitting as large as ~1.5 eV by the interlayer hopping. Charge density difference plot (Fig. S5) confirms that this reorganization of orbital occupation. Furthermore, the π band inversion makes the interatomic bonds within the zigzag chains stronger while simultaneously weakening the vertical intralayer bonds. As a result, the lattice compresses significantly along the armchair direction such as b = 4.68 Å for ML, reduced to b = 4.35 Å for AA-FE (see Table 1). It has been reported that the compressive strain along the armchair direction makes the buckled structure stable and induces ferroelectricity in α-P [29]. Consistently, a similar behavior is observed for α-As, as one can see the potential energy curves in Fig. 3(c). ML α-As exhibits a paraelectric or ferroelectric behavior for uncompressed b = b 0 = 4.68 Å or the compressed lattice ( b = 0.93 b₀), respectively, about the B 1u distortion. It is worth noting that the potential energy gain associated with FE distortion reduces as the system is changed from ML to BL. Specifically, while for BL the distortion lowers the potential energy by 5.9 meV/u.c. ~ 0.7 meV/As (AA-FE vs AA in Table 1), for the compressed ML with b = b 0 it stabilizes by 17 meV/u.c. ~ 4.3 meV/As (Fig. 2(d)). Previous studies have shown that the distortion in the ML arises from degeneracy lifting of the p z orbitals of surface atoms [31]. In the BL, we confirm that the interfacial atoms exhibit a favorable bonding type interaction across the vdW gap (Fig. S5). Hence, the reduced energy gain in AA-FE, as compared to the compressed ML, and resulting suppression of buckling height can be attributed to the diminished surface effect. The interlayer-hopping induced band inversion is further confirmed by the hybrid functional that is more suitable for quantitatively accurate prediction of band structure. As shown in Fig. S6, our HSE06 calculation for ML α-As exhibits a significantly enlarged band gap of ~1.4 eV at Γ, which is ~0.8 eV larger than that by PBE+D3. Despite this enlarged gap in ML, AA-FE still exhibits a pronounced band inversion with the energy difference of ~0.9 eV at Γ, exceeding the value (~0.8 eV) by PBE+D3. This result indicates that the band inversion behavior for BL would not originate from shortcoming of DFT method used, and reinforces the robustness of the proposed FE mechanism related to the remarkable interlayer interaction. To assess the thermal stability of ferroelectricity in AA-FE, molecular dynamics were conducted using machine-learned interatomic potential (see Section 2 in Supplemental Material for details [43]). Five independent trajectories with each 20 ps long are generated with varying the temperature from 10 K up to 300 K by 25 K step, and statistical analysis was performed on the final 15 ps with 15,000 snapshots for each trajectory. The ferroelectricity is characterized by measuring the buckling height of the zigzag chains. Since calculation of electric polarization for many snapshots in a trajectory is computationally demanding, we first confirmed monotonically increasing behavior of electric polarization with the buckling height (Fig. S8). Then, for every trajectory, we extracted a distribution of the bucking heights whose non-zero mean value indicates a finite polarization value. In Fig. 4(a), the mean buckling height is plotted as a function of temperature. At low temperatures, the average buckling height exceeds 0.15 Å in the magnitude, corresponding to a polarization predicted to be greater than 0.63 × 10⁻¹⁰ C/m from Fig. 2(c). With increasing the temperature, gradual reduction in the mean buckling height is observed, indicating a gradual decrease in polarization density. This behavior reflects the thermal destabilization of the buckled structure, suggesting that the ferroelectric order becomes increasingly suppressed with raising temperature, where the polarization essentially vanishes at 125 K due to dynamical switching between positive and negative values (Fig. S10). From our simulations, the critical temperature of BL α-As is ~100 K. To show potential ferroelectricity at room temperature, additional molecular dynamics were performed at 300 K with a uniaxial compressive strain along the armchair axis from 0% to -5% whose equivalent lattice parameters are b = 4.35 Å to 4.13 Å, respectively. In consistency with strain-enhanced ferroelectric transition barrier (Fig. S12), our result in Fig. 4(b) shows room temperature ferroelectric phase beyond 4% compression. It is insightful to compare the electronic structure of α-As with those of other group-V elements (Fig. S13). For α-P monolayer, there is strong hybridization between s and p orbitals [42], suppressing the need for p z degeneracy lifting via buckling distortion. In contrast, for heavier pnictogens such as antimony and bismuth, s and p orbitals are largely decoupled with the pronouncing inert pair effect. This decoupling makes the p z electrons with dangling bonds unstable with respect to the ferroelectric distortion. Positioned between these two extremes in the periodic table, arsenic exhibits an intermediate behavior; its monolayer remains flat, similar to phosphorus. However, in the bilayer configuration, the interlayer electron hopping induces the symmetry breaking as observed in heavier elements. This highlights the unique characteristics of As, which bridges the behavior of lighter and heavier group-V elements. In summary, we have demonstrated the emergence of a novel ferroelectric phase in bilayer α-As that is absent in its monolayer counterpart. Through systematic DFT calculations, we identified the AA-FE configuration as the most stable structure, exhibiting spontaneous polarization due to ferroelectric buckling. This ferroelectric state deviates from the conventional sliding ferroelectricity mechanism and is instead driven by significant interlayer electron hopping that leads to significant lattice compression. Our findings highlight the crucial role of interlayer interactions in generating novel ferroelectric states in 2D materials. Declarations ACKNOWLEDGMENTS This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (Grants No. RS-2023–00257666, No. RS-2025-00522876, No. RS-2024-00508578, and No. NRF-2021M3H4A1A02055684). Computation resources were supported by KISTI (Grants No. KSC-2024-CRE-0201 and No. KSC-2024-CRE-0482). References J. Wang, J. B. Neaton, H. Zheng, V. Nagarajan, S. B. Ogale, B. Liu, D. Viehland, V. Vaithyanathan, D. G. Schlom, U. V. Waghmare et al. , Epitaxial BiFeO 3 multiferroic thin film heterostructures, Science 299 , 1719 (2003). S. Horiuchi and Y. Tokura, Organic ferroelectrics, Nat. Mater. 7 , 357 (2008). A. J. Lovinger, Ferroelectric polymers, Science 220 , 4602 (1983). A. K. Tripathi, A. J. J. M. Van Breemen, J. Shen, Q. Gao, M. G. Ivan, K. Reimann, E. R. Meinders, and G. H. Gelinck, Multilevel information storage in ferroelectric polymer memories, Adv. Mater. 23 , 4146 (2011). L. Chen, M. E. Pam, S. Li, and K.-W. Ang, Ferroelectric memory based on two-dimensional materials for neuromorphic computing, Neuromorph. Comput. Eng. 2 , 022001 (2022). D. Ielmini and S. Ambrogio, Emerging neuromorphic devices, Nanotechnology 31 , 092001 (2019). J. F. Scott, Application of modern ferroelectrics, Science 315 , 5814 (2007). C. Cui, F. Xue, W. J. Hu, and L. J. Li, Two-dimensional materials with piezoelectric and ferroelectric functionalities, npj 2D Mater. Appl. 2 , 18 (2018). J. Junquera and P. Ghosez, Critical thickness for ferroelectricity in perovskite ultrathin films, Nature 422 , 506 (2003). P. Gao, Z. Zhang, M. Li, R. Ishikawa, B. Feng, H.-J. Liu, Y.-L. Huang, N. Shibata, X. Ma, S. Chen et al., Possible absence of critical thickness and size effect in ultrathin perovskite ferroelectric films, Nat. Commun. 8 , 15549 (2017). Y. Kim, D. Kim, J. Kim, Y. Chang, T. Noh, J. Kong, K. Char, Y. Park, S. Bu, J. Yoon and J. Chung, Critical thickness of ultrathin ferroelectric BaTiO 3 films, Appl. Phys. Lett. 86 , 1 (2005). W. Xu, L. Wang, D. C. M. Yang, A. Hajibabaei, Y. Lee, C. Park, T. W. Lee, and K. S. Kim, Supra-binary polarization in a ferroelectric nanowire, Adv. Mater. 33 , 2101981 (2021). W. Z. Wu, L. Wang, Y. L. Li, F. Zhang, L. Lin, S, M. Niu, D. Chenet, X. Zhang, Y. F. Hao, T. F. Heinz, J. Hone, Z. L. Wang, Piezoelectricity of single-atomic-layer MoS 2 for energy conversion and piezotronics, Nature 514 , 470 (2014). S. Wang, L. Liu, L. Gan, H. Chen, X. Hou, Y. Ding, S. Ma, D. W. Zhang, P. Zhou, Two-dimensional ferroelectric channel transistors integrating ultra-fast memory and neural computing, Nat. Commun. 12 , 1 (2021). A. Belianinov, Q. He, A. Dziaugys, P. Maksymovych, E. Eliseev, A. Borisevich, A. Morozovska, J. Banys, Y. Vysochanskii, and S. V. Kalinin, CuInP 2 S 6 room temperature layered ferroelectric, Nano Lett. 15 , 3808 (2015). W. Ding, J. Zhu, Z. Wang, Y. Gao, D. Xiao, Y. Gu, Z. Zhang, and W. Zhu, Prediction of intrinsic two-dimensional ferroelectrics in In 2 Se 3 and other III 2 -VI 3 van der Waals materials, Nat. Commun. 8 , 1 (2017). L. Chen, B. Liu, Z. Guo, X. Duan, G. Fang, Y. F. Zheng, H. Fang, and Y. Y. Zhang, DFSE: Inverse design of ferroelectrics from spatial symmetry breaking evolution, J. Chem. Theory Comput. 21 , 5346 (2025). R. Xu, S. Liu, I. Grinberg, J. Karthik, A. R. Damodaran, A. M. Rappe, and L. W. Martin, Ferroelectric polarization reversal via successive ferroelastic transitions, Nat. Mater. 14 , 79 (2015). J. H. Haeni, P, Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W. Tian, M. E. Hawley, B. Craigo et al. , Room-temperature ferroelectricity in strained SrTiO 3 , Nature 430 , 758 (2004). F. Sui, Y. Yu, J. Chen, R. Qi, R. Ge, Y. Zheng, B. Liu, R. Jin, S. Gong, F. Yue, Unconventional (anti)ferroelectricity in van der Waals group-IV monochalcogenides, Nat. Commun. 16 , 1 (2025). L. Li and M. Wu, Binary compound bilayer and multilayer with vertical polarizations: Two-dimensional ferroelectrics, multiferroics, and nanogenerators, ACS Nano 11 , 6382 (2017). M. V. Stern, Y. Waschitz, W. Cao, I. Nevo, K. Watanabe, T. Taniguchi, E. Sela, M. Urbakh, O. Hod, and M. B. Shalom, Interfacial ferroelectricity by van der Waals sliding, Science 372 , 142 (2021). Z. Fei, W. Zhao, T. A. Palomaki, B. Sun, M. K. Miller, Z. Zhao, J. Yan, X. Xu, and D. H. Cobden, Ferroelectric switching of a two-dimensional metal, Nature 560 , 336 (2018). Z. Zheng, Q. Ma, Z. Bi, S. de la Barrera, M. H. Liu, N. Mao, Y. Zhang, N. Kiper, K. Watanabe, T. Taniguchi et al., Unconventional ferroelectricity in Moiré heterostructures, Nature 588 , 71 (2020). A. Weston, E. G. Castanon, V. Enaldiev, F. Ferreira, S. Bhattacharjee, S. Xu, H. Corte-León, Z. Wu, N. Clark, A. Summerfield et al. , Interfacial ferroelectricity in marginally twisted 2D semiconductors, Nat. Nanotechnol. 17 , 390 (2022). H. Liu, A. T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tománek, and P. D. Ye, Phosphorene: An unexplored 2D semiconductor with a high hole mobility, ACS Nano 8 , 4033 (2014). Y. Xu, Z. Shi, X. Shi, K. Zhang, and H. Zhang, Recent progress in black phosphorus and black-phosphorus-analogue materials: properties, synthesis and applications, Nanoscale 11 , 14491 (2019). W. Ma, J. Lu, B. Wan, D. Peng, Q. Xu, G. Hu, Y. Peng, C. Pan, and Z. L. Wang, Piezoelectricity in multilayer black phosphorus for piezotronics and nanogenerators, Adv. Mater. 32 , 1905795 (2020). W. Xu, J. D. Zheng, W. Y. Tong, J. L. Wang, Y. P. Shao, Y. K. Zhang, Y. F. Tan, and C. G. Duan, Strain-induced ferroelectric phase transition in group-V monolayer black phosphorus, Adv. Quantum Technol. 6 , 2200169 (2023). W. Shen, J. Shen, F. Wang, and Y. Lu, Emergence of multiple ferroelectric states in multilayer black phosphorus, Phys. Rev. B 111 , 115429 (2025). C. Xiao, F. Wang, S. A. Yang, Y. Lu, Y. Feng, and S. Zhang, Elemental ferroelectricity and antiferroelectricity in group-V monolayer, Adv. Funct. Mater. 28 , 1707383 (2018). J. Gou, H. Bai, X. Zhang, Y. L. Huang, S. Duan, A. Ariando, S. A. Yang, L. Chen, Y. Lu, and A. T. S. Wee, Two-dimensional ferroelectricity in a single-element bismuth monolayer, Nature (London) 617 , 67 (2023). V. Tran, R. Soklaski, Y. Liang, and L. Yang, Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus, Phys. Rev. B 89 , 235319 (2014). X. Luo, X. Lu, G. K. W. Koon, A. H. Castro Neto, B. Özyilmaz, Q. Xiong, and S. Y. Quek, Large frequency change with thickness in interlayer breathing mode - Significant interlayer interactions in few layer black phosphorus, Nano Lett. 15 , 3931 (2015). N. Zhao, Y. F. Zhu, and Q. Jiang, Thickness-dependent surface energies of few-layered arsenene and antimonene films in α and β phases, Phys. E Low-Dimens. Syst. Nanostructures 101 , 38 (2018). R. Fei, W. Kang, and L. Yang, Ferroelectricity and phase transitions in monolayer group-IV monochalcogenides, Phys. Rev. Lett. 117 , 097601 (2016). X. Liu, Y. Yang, T. Hu, G. Zhao, C. Chen, and W. Ren, Vertical ferroelectric switching by in-plane sliding of two-dimensional bilayer WTe 2 , Nanoscale 11 , 18575 (2019). K. Mi, J. Xie, M. S. Si, and C. X. Gao, Layer-stacking effect on electronic structures of bilayer arsenene, Europhys. Lett. 117, 27002 (2017). D. Kecik, E. Durgun, and S. Ciraci, Stability of single-layer and multilayer arsenene and their mechanical and electronic properties, Phys. Rev. B 94 , 205409 (2016). Y. Kadioglu, J. A. Santana, H. D. Özaydin, F. Ersan, O. Ü. Aktürk, E. Aktürk, and F. A. Reboredo, Diffusion quantum Monte Carlo and density functional calculations of the structural stability of bilayer arsenene, J. Chem. Phys. 148 , 214706 (2018). S. Zhou, J. Han, S. Dai, J. Sun, and D. J. Srolovitz, Van der Waals bilayer energetics: Generalized stacking-fault energy of graphene, boron nitride, and graphene/boron nitride bilayers, Phys. Rev. B 92 , 155438 (2015). Y. Kim, I. K. Park, D. C. M. Yang, D. Y. Kim, G. Lee, and N. Kim, Synchrotron x-ray diffraction study of inversion symmetry breaking in bulk black phosphorus, Phys. Rev. B 111 , L161407 (2025). See Supplemental Material for DFT calculation methods and machine-learned potential molecular dynamics. Tables Table 1. Optimized lattice parameters and relative total energies by PBE+D3 for monolayer (ML) and bilayer (BL) α-As. For BL, different stacking registries such as AA, AB, AC, AD were considered, where AA-FE refers to AA-stacked ferroelectric. Δ E means the total energy per unit cell relative to the most stable AA-FE. α-As structure a (Å) b (Å) Δ E (meV/u.c.) ML 3.70 4.68 BL AA-FE 3.74 4.35 0.0 AA 3.74 4.39 5.9 AB 3.71 4.61 20.4 AC 3.72 4.54 183.8 AD 3.74 4.51 86.9 Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7653762","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":517363954,"identity":"a7275059-e74a-4dc3-b51f-8af5c2161eb2","order_by":0,"name":"In Kee Park","email":"","orcid":"","institution":"Department of Chemistry, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulsan 44919, Republic of Korea","correspondingAuthor":false,"prefix":"","firstName":"In","middleName":"Kee","lastName":"Park","suffix":""},{"id":517364010,"identity":"989691ef-303a-4397-9679-8c4c4ef4fa54","order_by":1,"name":"Geunsik Lee","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0UlEQVRIiWNgGAWjYFAC5gYGhgoGBjYo14AILYxALWdAWphJ0cLYBraOSC3y/gcbH3ycdziPj//8AYYfNQzG5g0EtBjeSGw2nLntcDGbRDIDY88xBjOZA4S0zGBsk+bddjixTQLoMN4GBhsJQg4z7D/Y/vvvHKAW/sMMjH+J0SLPkNjGzNgA1MKQzMAMtMWMoBYDicRmyZ5j6UCHJRscljkmYUzYlv7DBz/8qLFOnN9/8OHDNzU2hjMI2nIAiQNkE7QDaEsDYTWjYBSMglEw0gEAbK87WAjyV5cAAAAASUVORK5CYII=","orcid":"","institution":"Department of Chemistry, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulsan 44919, Republic of Korea","correspondingAuthor":true,"prefix":"","firstName":"Geunsik","middleName":"","lastName":"Lee","suffix":""}],"badges":[],"createdAt":"2025-09-19 02:44:58","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-7653762/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7653762/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":91962848,"identity":"3c200e0f-3d8c-493a-8539-1734335c94a5","added_by":"auto","created_at":"2025-09-23 07:59:36","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1091103,"visible":true,"origin":"","legend":"","description":"","filename":"MS2.docx","url":"https://assets-eu.researchsquare.com/files/rs-7653762/v1/f6e66ae830c7aa650c1f2c4b.docx"},{"id":91962839,"identity":"7764ef96-06b0-4866-b478-4fe1d76b4600","added_by":"auto","created_at":"2025-09-23 07:59:36","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":342,"visible":true,"origin":"","legend":"","description":"","filename":"rs7653762.json","url":"https://assets-eu.researchsquare.com/files/rs-7653762/v1/5b418b8244a13494fcc82306.json"},{"id":91962847,"identity":"0dde1405-78de-43f9-9686-980ff74ee445","added_by":"auto","created_at":"2025-09-23 07:59:36","extension":"xml","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":94190,"visible":true,"origin":"","legend":"","description":"","filename":"rs76537620enriched.xml","url":"https://assets-eu.researchsquare.com/files/rs-7653762/v1/72a33060c025290361822ecf.xml"},{"id":91963590,"identity":"0a6d7461-2563-4804-9c8f-96c57b52f58f","added_by":"auto","created_at":"2025-09-23 08:07:36","extension":"png","order_by":7,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":49433,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7653762/v1/0b98e78c5c6738ae587a25da.png"},{"id":91962849,"identity":"e535f3fa-0490-4935-939f-a203b3de1cec","added_by":"auto","created_at":"2025-09-23 07:59:36","extension":"png","order_by":8,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":98080,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7653762/v1/d71af22e6e86452a04ba6e74.png"},{"id":91964974,"identity":"d48402ce-b346-479a-9c25-a2069779e750","added_by":"auto","created_at":"2025-09-23 08:15:36","extension":"png","order_by":9,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":51360,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7653762/v1/03714317f21ef250f567c433.png"},{"id":91965834,"identity":"17eb8311-9aab-45c7-85d1-557c3a80a4a2","added_by":"auto","created_at":"2025-09-23 08:27:01","extension":"png","order_by":10,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":21505,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7653762/v1/32ced027b5ca571db4006e6e.png"},{"id":91963594,"identity":"494ff954-f088-4a02-b6a4-25ad2b4477ca","added_by":"auto","created_at":"2025-09-23 08:07:36","extension":"xml","order_by":11,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":93292,"visible":true,"origin":"","legend":"","description":"","filename":"rs76537620structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-7653762/v1/0ae885503495ecee15401111.xml"},{"id":91962851,"identity":"adeba5a8-78d0-40de-b156-b0cd12f6b394","added_by":"auto","created_at":"2025-09-23 07:59:36","extension":"html","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":98492,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7653762/v1/48cca2371afd1cf3cd82fbe2.html"},{"id":91962842,"identity":"787bbe52-472d-4529-abba-ef7566a3840e","added_by":"auto","created_at":"2025-09-23 07:59:36","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":303741,"visible":true,"origin":"","legend":"\u003cp\u003eCrystal structure of monolayer (ML) and stacking registries of bilayer (BL). (a) Crystal structure of ML α-As together with B\u003csub\u003e1u \u003c/sub\u003ephonon mode distortion depicted by the red arrows. (b) Potential energy curves of ML (black) and bulk (red) α-As against the B\u003csub\u003e1u \u003c/sub\u003edistortion using the optimized lattice constants by PBE+D3. The bulk unit cell is composed of two layers with the experimentally reported AB stacking. (c) Top and side views for the BL stacking configuration denoted by fractional displacements of the upper layer (light blue atoms) along \u003cem\u003ea\u003c/em\u003e-axis (Δ\u003csub\u003ea\u003c/sub\u003e) and \u003cem\u003eb\u003c/em\u003e-axis (Δ\u003csub\u003eb\u003c/sub\u003e) with respect to the lower layer (deep blue atoms).\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7653762/v1/a44c9b24ce364d88e45b0361.png"},{"id":91962846,"identity":"bd537acb-d06b-479f-8137-7da51bb17e54","added_by":"auto","created_at":"2025-09-23 07:59:36","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":727112,"visible":true,"origin":"","legend":"\u003cp\u003ePotential energy surface and phonon band structures for different stacking types. (a) Heat maps of the potential energy with varying stacking registry Δ\u003csub\u003ea\u003c/sub\u003e, Δ\u003csub\u003eb\u003c/sub\u003e as defined in Fig. 1(c), calculated for two initial geometries, flat and buckled. (b) Phonon band structures of relatively stable stacking types (AA, AA-FE, AB). (c) Minimum energy path connecting two bistable states of AA-FE (black, left), and the polarization (red, right). (d) Atomic structures are given for two stable structures with Δz = \u003cimg width=\"12\" height=\"19\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAcBAMAAACe6vIUAAAAAXNSR0IArs4c6QAAABtQTFRFAAAAAAAAAAA6ADqQkDoAkNv/2////7Zm///bxPh3hAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAFiUAABYlAUlSJPAAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAJklEQVQoU2NgoD7gcE6AGko2i10QDIQCQAaRbQqKXgx/otiBLgsABIEK+V7wD6AAAAAASUVORK5CYII=\"/\u003e0.136 Å (AA-FE stacking) and the transition state with Δz = 0.0 Å (AA stacking).\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7653762/v1/8754f736b72933e395fc5cf7.png"},{"id":91963591,"identity":"787eedd3-47c4-42a7-9bf5-82f466660bad","added_by":"auto","created_at":"2025-09-23 08:07:36","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":325694,"visible":true,"origin":"","legend":"\u003cp\u003eElectronic band structures of monolayer (ML) and bilayer (BL) α-As and potential energy curves along the B\u003csub\u003e1u\u003c/sub\u003e mode. (a) Electronic band structure of ML and (b) BL of AA stacking. The colored arrows and boxes show the iso-surface plot of the Bloch orbitals at the Γ point corresponding to the VBM and CBM. (c) Potential energy curve of ML α-As about the B\u003csub\u003e1u \u003c/sub\u003edistortion calculated using the lattice constant optimized for ML α-As (b\u003csub\u003e0 \u003c/sub\u003e= 4.68 Å, black) and the compressed lattice (0.93 b\u003csub\u003e0\u003c/sub\u003e, red) corresponding to the optimized lattice constant of BL AA-FE.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7653762/v1/76cb03842f3f9b86d21be372.png"},{"id":91962840,"identity":"bdb5f514-8581-4541-9709-300c2cb57e48","added_by":"auto","created_at":"2025-09-23 07:59:36","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":128335,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7653762/v1/7a5f51f168988b0919f31102.png"},{"id":91966082,"identity":"1b1ba389-674a-4847-99ef-af16b8ac5e5a","added_by":"auto","created_at":"2025-09-23 08:28:06","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1834673,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7653762/v1/cec1aed2-f9e9-40a1-b030-2dd3a8f2fc2a.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eInterlayer Coupling Induced Ferroelectricity in Bilayer α-As\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"Full Text","content":"\u003cp\u003eFerroelectric (FE) materials have attracted considerable attention due to their spontaneous polarization which can be reversed by applying an external electric field [1-3]. Notable applications include non-volatile data storage [4], neuromorphic computing [5,6], and energy harvesting and sensing, enabled by their intrinsic pyroelectric and piezoelectric properties [7,8]. However, as devices dimensions continue to shrink, there is an increasing demand for materials that enable fast operation, long retention time, and low energy consumption. For this, two-dimensional (2D) FEs have emerged as promising candidates owing to their distinctive advantages. \u003c/p\u003e\n\u003cp\u003eThe van der Waals (vdW) layered structures of 2D FEs are free from the strong depolarization effects along the out-of-plane direction that typically hinder polarization in conventional three-dimensional FEs [9-11]. Atomically smooth surfaces allow for clean exfoliation without surface defects and dangling bonds, making 2D FEs ideal for designing multifunctional devices such as heterostructures and multiferroic systems [12]. Additionally, mechanical flexibility of 2D materials supports wearable and flexible electronics [8,13]. Finally, their reduced dimensionality leads to weakened internal fields, enabling low-power and ultrafast FE switching [14].\u003c/p\u003e\n\u003cp\u003eExtensive research has been devoted to 2D FE materials. Notable examples are CuInP₂S₆ [15] and In₂Se₃ [16]. Although systematic efforts based on symmetry analysis have been made to identify potential FE materials [17], only a limited number were confirmed to exhibit intrinsic FE polarization. This limitation has prompted alternative approach to induce FE through external perturbations, which is often referred to as hidden ferroelectricity. Representative examples are strain-induced ferroelectricity in perovskite [18, 19] and electric field-induced FE transition in MX (M = Si, Ge, Sn; X = S, Se, Te) system [20]. Another compelling strategy is sliding ferroelectricity, where a non-ferroelectric layered system acquires FE polarization through interlayer charge transfer induced by lateral sliding that breaks inversion symmetry. This phenomenon has been demonstrated in bilayer hBN [21, 22], WTe₂ [23], graphene [24], and MoS₂ [25].\u003c/p\u003e\n\u003cp\u003eWithin the various layered materials, α phase of group-V elements with puckered lattice structure, also known as black phosphorus structure, have attracted considerable attention due to their in-plane anisotropic properties and highly tunable band gap with thickness [26, 27]. Monolayer α-P and α-As lack spontaneous polarization due to their centrosymmetric lattice structure. However, compressive strain along the armchair direction induces instability against a buckling mode, thereby inducing FE polarization in α-P [28, 29]. Recent study also reports sliding FE in multilayer (three or more) α-P driven by work function differences between stacking configurations [30]. In contrast, α-Sb and α-Bi favor a buckled structure that leads to spontaneous polarization [31]. Notably, recent experimental study has demonstrated FE switching in monolayer α-Bi under applied voltage [32]. In addition, the interlayer coupling is significant as one can expect from a band gap reduction from 1.5 to 0.3 eV for monolayer to bulk α-P [33]. Raman measurements of α-P reveal that interlayer force constants and interlayer binding are two to three times stronger than that of graphene and MoS₂ [34]. For α-As and α-Sb, surface energy and optimized lattice constants vary significantly with respect to the number of layers [35]. \u003c/p\u003e\n\u003cp\u003eIn this study, we investigate the interlayer interaction and FE properties of BL α-As. Through systematic scanning diverse stacking configurations, we identify metastable structures and characterize their FE properties. We reveal the emergence of a ferroelectric phase in BL, unlike monolayer counterpart, elucidating the crucial role of interlayer coupling in stabilizing novel FE phase. The underlying mechanism differs from that of conventional sliding ferroelectrics and is related to lattice contraction caused by significant interlayer electron hopping. Our results provide insight into new mechanisms for achieving ferroelectricity beyond conventional approaches.\u003c/p\u003e\n\u003cp\u003eFirst-principles calculations were performed using density functional theory (DFT) (see Section 1 in Supplemental Material for details [43]). Figure 1(a) depicts the crystal structure of monolayer (ML) α-As in which two atomically flat zigzag chains run along the \u003cem\u003ea\u003c/em\u003e-axis to form the puckered lattice. An identical motif is found in α-Bi [32] and group-IV monochalcogenides [36], but in those materials this geometry is known to be unstable with respect to the out-of-plane buckling (B\u003csub\u003e1u\u003c/sub\u003e) mode, indicated by the arrows, which induces a ferroelectric polarization along positive or negative \u003cem\u003eb-\u003c/em\u003eaxis. In contrast, as shown in Fig. 1(b), our calculations reveal that ML prefers to remain flat, which is also valid for AB-stacked bulk phase. \u003c/p\u003e\n\u003cp\u003eTo assess how interlayer interactions affect the structural stability against B\u003csub\u003e1u\u003c/sub\u003e mode in BL α-As, various stacking registries were considered, as illustrated in Fig. 1(c). We define the second layer’s displacement relative to the first one by fractional in-plane coordinates (Δ\u003csub\u003ea\u003c/sub\u003e, Δ\u003csub\u003eb\u003c/sub\u003e). Restricting Δ\u003csub\u003ea\u003c/sub\u003e, Δ\u003csub\u003eb\u003c/sub\u003e to 0.0 or 0.5 yields four distinct stackings, denoted as AA, AB, AC, and AD corresponding to (0.0, 0.0), (0.5, 0.0), (0.5, 0.5), and (0.0, 0.5), respectively. For each registry, we performed full geometry optimization under the constraint that the in-plane fractional coordinates remain fixed. Related to B\u003csub\u003e1u\u003c/sub\u003e distortion, three initial geometries were considered, the perfectly flat and two buckled variants with Δz = 0.2 Å, featuring either parallel or antiparallel polarizations between the bottom and top layers (Fig. S1). This method allowed us to find out the most stable bilayer configuration as a function of stacking. \u003c/p\u003e\n\u003cp\u003eFigures 2(a) shows the heat maps of the potential energy surface (PES) calculated with the initially flat and buckled (parallel polarization) geometries, where the antiparallel buckling was checked to give nearly the same result as that of parallel case (Fig. S2). The optimized structure can exhibit non-zero buckling with parallel or anti-parallel polarizations between top and bottom layers, or zero buckling. Notably the ferroelectric behavior depends on the initial configurations of buckling and stacking. For example, the registries near Δ\u003csub\u003eb\u003c/sub\u003e = 0.5 (AC and AD) have relatively high potential energy (Table 1) and exhibit the antiparallel polarizations irrespective of whether the initial structure is buckled or not. Meanwhile, relatively stable registries (AA and AB) near Δ\u003csub\u003eb\u003c/sub\u003e = 0.0 leads to zero polarization except AA-stacked ferroelectric phase (AA-FE) obtained with initially buckled structure, where for AB almost identical structures of zero buckling were obtained for two initial cases. As listed in Table 1, the most stable structure is found to be AA-FE with the buckling heights 0.14, 0.15 Å for the zigzag chains at interface, surface layers, respectively. Relative to AA-FE, the potential energies of AA and AB are higher by 5.9 and 20.4 meV/u.c, respectively. \u003c/p\u003e\n\u003cp\u003eThe newly found AA-FE with a lower energy than AA indicates that AA structure is unstable dynamically. Indeed, our calculated phonon band structure exhibits imaginary modes for AA, as shown in Fig. 2(b), and AA-FE and AB are confirmed to be stable dynamically. Actually, AA corresponds to the transition state connecting two bistable states of AA-FE, shown in Fig. 2(c). By nudged elastic band (NEB) calculation the minimum energy path connecting two oppositely polarized AA-FE structures (Fig. 2(d)) involves the transition state corresponding to the structure with zero buckling height, matching with the AA configuration. The associated energy barrier (5.4 meV/u.c.) is comparable to ML α-Bi (43 meV/u.c.) [32], BL hBN (9 meV/u.c.) [21] and BL WTe\u003csub\u003e2\u003c/sub\u003e (0.6 meV/u.c.) [37]. These systems have been experimentally shown to undergo polarization switching under external voltage [22, 23], which highlights possibility of polarization control in BL α-As. The electric polarization calculated for AA-FE is 0.63 \u003cimg width=\"11\" height=\"20\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAeCAMAAAD95QUdAAAAAXNSR0IArs4c6QAAADlQTFRFAAAAAAAAAABmADo6ADqQAGa2OjqQOma2ZpDbZrbbtmYAtmY6tv//25A625Bm2////7Zm/9uQ///b9bYqqgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAFiUAABYlAUlSJPAAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAYElEQVQoU9WRURKAIAhEIbMsI6v7HzYSMDxBk1/Mc93dEYBfnnMq1ntPdSIcFRHOcmeIMJpYkAOiYtD86sPQA7hWHLbupx6NJWpaZB+HxNQhS2lpb4+sFQ+tzo55+XozN5GFAq1I+ufzAAAAAElFTkSuQmCC\" alt=\"image\"\u003e 10\u003csup\u003e-10 \u003c/sup\u003eC/m, which is approximately 1.5 times greater than that reported for ML α-Bi (~0.4 \u003cimg width=\"11\" height=\"20\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAeCAMAAAD95QUdAAAAAXNSR0IArs4c6QAAADlQTFRFAAAAAAAAAABmADo6ADqQAGa2OjqQOma2ZpDbZrbbtmYAtmY6tv//25A625Bm2////7Zm/9uQ///b9bYqqgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAFiUAABYlAUlSJPAAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAYElEQVQoU9WRURKAIAhEIbMsI6v7HzYSMDxBk1/Mc93dEYBfnnMq1ntPdSIcFRHOcmeIMJpYkAOiYtD86sPQA7hWHLbupx6NJWpaZB+HxNQhS2lpb4+sFQ+tzo55+XozN5GFAq1I+ufzAAAAAElFTkSuQmCC\" alt=\"image\"\u003e 10\u003csup\u003e-10 \u003c/sup\u003eC/m) [32] and exceeds by the several orders of magnitude those found in typical sliding FE systems such as BL hBN (2.08 pC/m ~ 0.02 \u003cimg width=\"11\" height=\"20\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAeCAMAAAD95QUdAAAAAXNSR0IArs4c6QAAADlQTFRFAAAAAAAAAABmADo6ADqQAGa2OjqQOma2ZpDbZrbbtmYAtmY6tv//25A625Bm2////7Zm/9uQ///b9bYqqgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAFiUAABYlAUlSJPAAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAYElEQVQoU9WRURKAIAhEIbMsI6v7HzYSMDxBk1/Mc93dEYBfnnMq1ntPdSIcFRHOcmeIMJpYkAOiYtD86sPQA7hWHLbupx6NJWpaZB+HxNQhS2lpb4+sFQ+tzo55+XozN5GFAq1I+ufzAAAAAElFTkSuQmCC\" alt=\"image\"\u003e 10\u003csup\u003e-10 \u003c/sup\u003eC/m) or BL MoS\u003csub\u003e2 \u003c/sub\u003e(0.33 pC/m ~ 0.003\u003cimg width=\"15\" height=\"20\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABYAAAAeCAMAAAAfOR5kAAAAAXNSR0IArs4c6QAAADlQTFRFAAAAAAAAAABmADo6ADqQAGa2OjqQOma2ZpDbZrbbtmYAtmY6tv//25A625Bm2////7Zm/9uQ///b9bYqqgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAFiUAABYlAUlSJPAAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAZUlEQVQoU2NgGElAkI0f5l0+DoTHeRlZoOK8jOxI4QET52VkRQkliDi6KEiEhR8oCrcDpomXkRmLKIMQFyMTD2bwg1TD3IPsRlag2ejiENvQxWFuQHULwr3cyP4RQPiYm3MIJAYAQXoCrfLbrGMAAAAASUVORK5CYII=\" alt=\"image\"\u003e 10\u003csup\u003e-10 \u003c/sup\u003eC/m) [21]. This is particularly noteworthy because ML α-As does not exhibit intrinsic ferroelectricity, indicating that the ferroelectric state emerges exclusively in the BL system through interlayer coupling.\u003c/p\u003e\n\u003cp\u003eBulk α-As is known to favor AB stacking as its ground state, but our calculations for BL show that the AA-FE and AA are more stable than AB. Previous theoretical studies have shown competing stability between AB and AA stackings with very little energy difference (~10 meV/atom) and the results are controversial with dependence on DFT functional [38, 39]. Crucially, those studies, including one using diffuse Monte Carlo method [40] have not considered buckling distortion to lower the total energy, particularly for the AA stacking. From our calculation, the energy difference between AA-FE and AB is 20.4 meV/u.c. or 1.2 meV/Å\u003csup\u003e2\u003c/sup\u003e, which is comparable to stacking fault energies of other 2D materials such as hBN and graphene (~1.0 meV/Å\u003csup\u003e2\u003c/sup\u003e) [41]. This suggests that AA-FE stacking is readily formed once BL α-As is synthesized. It is worthy to note that AA-stacked bulk α-As is unstable with respect to forming the gray arsenic (Fig. S9).\u003c/p\u003e\n\u003cp\u003eTo elucidate the origin of ferroelectric distortion in AA-stacked BL α-As, we studied the electronic structure. For ML α-As, the band structure shown in Fig. 3(a) has the band gap ~1.0 eV. It is also shown that the valence band maximum (VBM) orbital at Γ point has the \u003cem\u003ep\u003c/em\u003e\u003csub\u003ez\u003c/sub\u003e orbital symmetries of bonding type σ and antibonding type π* along the vertical and horizontal directions, respectively. For the conduction band minimum (CBM) orbitals, it is reversed. For BL α-As with AA configuration (Fig. 3(b)), the band structure becomes metallic with the reversed orbital symmetry between VBM and CBM due to the significant interlayer hopping. In other words, the bonding type π at Γ is occupied while the antibonding type π* is empty. This band inversion is attributed to the proximity of atoms between layers, appearing in the AA stacking. As shown in Fig. S4, the first nearest-neighbor interlayer atomic distance in the AA-FE is significantly shorter (3.13 Å) than that in the AB (3.72 Å), leading to a band splitting as large as ~1.5 eV by the interlayer hopping. Charge density difference plot (Fig. S5) confirms that this reorganization of orbital occupation. Furthermore, the π band inversion makes the interatomic bonds within the zigzag chains stronger while simultaneously weakening the vertical intralayer bonds. As a result, the lattice compresses significantly along the armchair direction such as \u003cem\u003eb\u003c/em\u003e = 4.68 Å for ML, reduced to \u003cem\u003eb\u003c/em\u003e = 4.35 Å for AA-FE (see Table 1). It has been reported that the compressive strain along the armchair direction makes the buckled structure stable and induces ferroelectricity in α-P [29]. Consistently, a similar behavior is observed for α-As, as one can see the potential energy curves in Fig. 3(c). ML α-As exhibits a paraelectric or ferroelectric behavior for uncompressed \u003cem\u003eb\u003c/em\u003e = b\u003csub\u003e0\u003c/sub\u003e = 4.68 Å or the compressed lattice (\u003cem\u003eb\u003c/em\u003e\u003cstrong\u003e = \u003c/strong\u003e0.93 b₀), respectively, about the B\u003csub\u003e1u\u003c/sub\u003e distortion.\u003c/p\u003e\n\u003cp\u003eIt is worth noting that the potential energy gain associated with FE distortion reduces as the system is changed from ML to BL. Specifically, while for BL the distortion lowers the potential energy by 5.9 meV/u.c. ~ 0.7 meV/As (AA-FE vs AA in Table 1), for the compressed ML with \u003cem\u003eb\u003c/em\u003e = b\u003csub\u003e0\u003c/sub\u003e it stabilizes by 17 meV/u.c. ~ 4.3 meV/As (Fig. 2(d)). Previous studies have shown that the distortion in the ML arises from degeneracy lifting of the\u003cem\u003e p\u003c/em\u003e\u003csub\u003ez\u003c/sub\u003e orbitals of surface atoms [31]. In the BL, we confirm that the interfacial atoms exhibit a favorable bonding type interaction across the vdW gap (Fig. S5). Hence, the reduced energy gain in AA-FE, as compared to the compressed ML, and resulting suppression of buckling height can be attributed to the diminished surface effect.\u003c/p\u003e\n\u003cp\u003eThe interlayer-hopping induced band inversion is further confirmed by the hybrid functional that is more suitable for quantitatively accurate prediction of band structure. As shown in Fig. S6, our HSE06 calculation for ML α-As exhibits a significantly enlarged band gap of ~1.4 eV at Γ, which is ~0.8 eV larger than that by PBE+D3. Despite this enlarged gap in ML, AA-FE still exhibits a pronounced band inversion with the energy difference of ~0.9 eV at Γ, exceeding the value (~0.8 eV) by PBE+D3. This result indicates that the band inversion behavior for BL would not originate from shortcoming of DFT method used, and reinforces the robustness of the proposed FE mechanism related to the remarkable interlayer interaction.\u003c/p\u003e\n\u003cp\u003eTo assess the thermal stability of ferroelectricity in AA-FE, molecular dynamics were conducted using machine-learned interatomic potential (see Section 2 in Supplemental Material for details [43]). Five independent trajectories with each 20 ps long are generated with varying the temperature from 10 K up to 300 K by 25 K step, and statistical analysis was performed on the final 15 ps with 15,000 snapshots for each trajectory. The ferroelectricity is characterized by measuring the buckling height of the zigzag chains. Since calculation of electric polarization for many snapshots in a trajectory is computationally demanding, we first confirmed monotonically increasing behavior of electric polarization with the buckling height (Fig. S8). Then, for every trajectory, we extracted a distribution of the bucking heights whose non-zero mean value indicates a finite polarization value. \u003c/p\u003e\n\u003cp\u003eIn Fig. 4(a), the mean buckling height is plotted as a function of temperature. At low temperatures, the average buckling height exceeds 0.15 Å in the magnitude, corresponding to a polarization predicted to be greater than 0.63 × 10⁻¹⁰ C/m from Fig. 2(c). With increasing the temperature, gradual reduction in the mean buckling height is observed, indicating a gradual decrease in polarization density. This behavior reflects the thermal destabilization of the buckled structure, suggesting that the ferroelectric order becomes increasingly suppressed with raising temperature, where the polarization essentially vanishes at 125 K due to dynamical switching between positive and negative values (Fig. S10). From our simulations, the critical temperature of BL α-As is ~100 K. To show potential ferroelectricity at room temperature, additional molecular dynamics were performed at 300 K with a uniaxial compressive strain along the armchair axis from 0% to -5% whose equivalent lattice parameters are \u003cem\u003eb\u003c/em\u003e = 4.35 Å to 4.13 Å, respectively. In consistency with strain-enhanced ferroelectric transition barrier (Fig. S12), our result in Fig. 4(b) shows room temperature ferroelectric phase beyond 4% compression.\u003c/p\u003e\n\u003cp\u003eIt is insightful to compare the electronic structure of α-As with those of other group-V elements (Fig. S13). For α-P monolayer, there is strong hybridization between \u003cem\u003es \u003c/em\u003eand\u003cem\u003e p\u003c/em\u003e orbitals [42], suppressing the need for \u003cem\u003ep\u003c/em\u003e\u003csub\u003ez\u003c/sub\u003e degeneracy lifting via buckling distortion. In contrast, for heavier pnictogens such as antimony and bismuth, \u003cem\u003es\u003c/em\u003e and \u003cem\u003ep\u003c/em\u003e orbitals are largely decoupled with the pronouncing inert pair effect. This decoupling makes the \u003cem\u003ep\u003c/em\u003e\u003csub\u003ez\u003c/sub\u003e electrons with dangling bonds unstable with respect to the ferroelectric distortion. Positioned between these two extremes in the periodic table, arsenic exhibits an intermediate behavior; its monolayer remains flat, similar to phosphorus. However, in the bilayer configuration, the interlayer electron hopping induces the symmetry breaking as observed in heavier elements. This highlights the unique characteristics of As, which bridges the behavior of lighter and heavier group-V elements.\u003c/p\u003e\n\u003cp\u003eIn summary, we have demonstrated the emergence of a novel ferroelectric phase in bilayer α-As that is absent in its monolayer counterpart. Through systematic DFT calculations, we identified the AA-FE configuration as the most stable structure, exhibiting spontaneous polarization due to ferroelectric buckling. This ferroelectric state deviates from the conventional sliding ferroelectricity mechanism and is instead driven by significant interlayer electron hopping that leads to significant lattice compression. Our findings highlight the crucial role of interlayer interactions in generating novel ferroelectric states in 2D materials. \u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eACKNOWLEDGMENTS\u003c/h2\u003e\u003cp\u003eThis work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (Grants No. RS-2023\u0026ndash;00257666, No. RS-2025-00522876, No. RS-2024-00508578, and No. NRF-2021M3H4A1A02055684). Computation resources were supported by KISTI (Grants No. KSC-2024-CRE-0201 and No. KSC-2024-CRE-0482).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eJ. Wang, J. B. Neaton, H. Zheng, V. Nagarajan, S. B. Ogale, B. Liu, D. Viehland, V. Vaithyanathan, D. G. Schlom, U. V. Waghmare \u003cem\u003eet al.\u003c/em\u003e, Epitaxial BiFeO\u003csub\u003e3\u003c/sub\u003e multiferroic thin film heterostructures, Science \u003cstrong\u003e299\u003c/strong\u003e, 1719 (2003).\u003c/li\u003e\n\u003cli\u003eS. Horiuchi and Y. Tokura, Organic ferroelectrics, Nat. Mater. \u003cstrong\u003e7\u003c/strong\u003e, 357 (2008).\u003c/li\u003e\n\u003cli\u003eA. J. Lovinger, Ferroelectric polymers, Science \u003cstrong\u003e220\u003c/strong\u003e, 4602 (1983).\u003c/li\u003e\n\u003cli\u003eA. K. Tripathi, A. J. J. M. Van Breemen, J. Shen, Q. Gao, M. G. Ivan, K. Reimann, E. R. Meinders, and G. H. Gelinck, Multilevel information storage in ferroelectric polymer memories, Adv. Mater. \u003cstrong\u003e23\u003c/strong\u003e, 4146 (2011).\u003c/li\u003e\n\u003cli\u003eL. Chen, M. E. Pam, S. Li, and K.-W. Ang, Ferroelectric memory based on two-dimensional materials for neuromorphic computing, Neuromorph. Comput. Eng. \u003cstrong\u003e2\u003c/strong\u003e, 022001 (2022).\u003c/li\u003e\n\u003cli\u003eD. Ielmini and S. Ambrogio, Emerging neuromorphic devices, Nanotechnology \u003cstrong\u003e31\u003c/strong\u003e, 092001 (2019).\u003c/li\u003e\n\u003cli\u003eJ. F. Scott, Application of modern ferroelectrics, Science \u003cstrong\u003e315\u003c/strong\u003e, 5814 (2007).\u003c/li\u003e\n\u003cli\u003eC. Cui, F. Xue, W. J. Hu, and L. J. Li, Two-dimensional materials with piezoelectric and ferroelectric functionalities, npj 2D Mater. Appl. \u003cstrong\u003e2\u003c/strong\u003e, 18 (2018).\u003c/li\u003e\n\u003cli\u003eJ. Junquera and P. Ghosez, Critical thickness for ferroelectricity in perovskite ultrathin films, Nature \u003cstrong\u003e422\u003c/strong\u003e, 506 (2003).\u003c/li\u003e\n\u003cli\u003eP. Gao, Z. Zhang, M. Li, R. Ishikawa, B. Feng, H.-J. Liu, Y.-L. Huang, N. Shibata, X. Ma, S. Chen \u003cem\u003eet al.,\u003c/em\u003e Possible absence of critical thickness and size effect in ultrathin perovskite ferroelectric films, Nat. Commun. \u003cstrong\u003e8\u003c/strong\u003e, 15549 (2017).\u003c/li\u003e\n\u003cli\u003eY. Kim, D. Kim, J. Kim, Y. Chang, T. Noh, J. Kong, K. Char, Y. Park, S. Bu, J. Yoon and J. Chung, Critical thickness of ultrathin ferroelectric BaTiO\u003csub\u003e3\u003c/sub\u003e films, Appl. Phys. Lett. \u003cstrong\u003e86\u003c/strong\u003e, 1 (2005).\u003c/li\u003e\n\u003cli\u003eW. Xu, L. Wang, D. C. M. Yang, A. Hajibabaei, Y. Lee, C. Park, T. W. Lee, and K. S. Kim, Supra-binary polarization in a ferroelectric nanowire, Adv. Mater. \u003cstrong\u003e33\u003c/strong\u003e, 2101981 (2021).\u003c/li\u003e\n\u003cli\u003eW. Z. Wu, L. Wang, Y. L. Li, F. Zhang, L. Lin, S, M. Niu, D. Chenet, X. Zhang, Y. F. Hao, T. F. Heinz, J. Hone, Z. L. Wang, Piezoelectricity of single-atomic-layer MoS\u003csub\u003e2\u003c/sub\u003e for energy conversion and piezotronics, Nature \u003cstrong\u003e514\u003c/strong\u003e, 470 (2014).\u003c/li\u003e\n\u003cli\u003eS. Wang, L. Liu, L. Gan, H. Chen, X. Hou, Y. Ding, S. Ma, D. W. Zhang, P. Zhou, Two-dimensional ferroelectric channel transistors integrating ultra-fast memory and neural computing, Nat. Commun. \u003cstrong\u003e12\u003c/strong\u003e, 1 (2021).\u003c/li\u003e\n\u003cli\u003eA. Belianinov, Q. He, A. Dziaugys, P. Maksymovych, E. Eliseev, A. Borisevich, A. Morozovska, J. Banys, Y. Vysochanskii, and S. V. Kalinin, CuInP\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e6\u003c/sub\u003e room temperature layered ferroelectric, Nano Lett. \u003cstrong\u003e15\u003c/strong\u003e, 3808 (2015).\u003c/li\u003e\n\u003cli\u003eW. Ding, J. Zhu, Z. Wang, Y. Gao, D. Xiao, Y. Gu, Z. Zhang, and W. Zhu, Prediction of intrinsic two-dimensional ferroelectrics in In\u003csub\u003e2\u003c/sub\u003eSe\u003csub\u003e3\u003c/sub\u003e and other III\u003csub\u003e2\u003c/sub\u003e-VI\u003csub\u003e3\u003c/sub\u003e van der Waals materials, Nat. Commun. \u003cstrong\u003e8\u003c/strong\u003e, 1 (2017).\u003c/li\u003e\n\u003cli\u003eL. Chen, B. Liu, Z. Guo, X. Duan, G. Fang, Y. F. Zheng, H. Fang, and Y. Y. Zhang, DFSE: Inverse design of ferroelectrics from spatial symmetry breaking evolution, J. Chem. Theory Comput. \u003cstrong\u003e21\u003c/strong\u003e, 5346 (2025).\u003c/li\u003e\n\u003cli\u003eR. Xu, S. Liu, I. Grinberg, J. Karthik, A. R. Damodaran, A. M. Rappe, and L. W. Martin, Ferroelectric polarization reversal via successive ferroelastic transitions, Nat. Mater. \u003cstrong\u003e14\u003c/strong\u003e, 79 (2015).\u003c/li\u003e\n\u003cli\u003eJ. H. Haeni, P, Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W. Tian, M. E. Hawley, B. Craigo \u003cem\u003eet al.\u003c/em\u003e, Room-temperature ferroelectricity in strained SrTiO\u003csub\u003e3\u003c/sub\u003e, Nature \u003cstrong\u003e430\u003c/strong\u003e, 758 (2004).\u003c/li\u003e\n\u003cli\u003eF. Sui, Y. Yu, J. Chen, R. Qi, R. Ge, Y. Zheng, B. Liu, R. Jin, S. Gong, F. Yue, Unconventional (anti)ferroelectricity in van der Waals group-IV monochalcogenides, Nat. Commun. \u003cstrong\u003e16\u003c/strong\u003e, 1 (2025).\u003c/li\u003e\n\u003cli\u003eL. Li and M. Wu, Binary compound bilayer and multilayer with vertical polarizations: Two-dimensional ferroelectrics, multiferroics, and nanogenerators, ACS Nano \u003cstrong\u003e11\u003c/strong\u003e, 6382 (2017).\u003c/li\u003e\n\u003cli\u003eM. V. Stern, Y. Waschitz, W. Cao, I. Nevo, K. Watanabe, T. Taniguchi, E. Sela, M. Urbakh, O. Hod, and M. B. Shalom, Interfacial ferroelectricity by van der Waals sliding, Science \u003cstrong\u003e372\u003c/strong\u003e, 142 (2021).\u003c/li\u003e\n\u003cli\u003eZ. Fei, W. Zhao, T. A. Palomaki, B. Sun, M. K. Miller, Z. Zhao, J. Yan, X. Xu, and D. H. Cobden, Ferroelectric switching of a two-dimensional metal, Nature \u003cstrong\u003e560\u003c/strong\u003e, 336 (2018).\u003c/li\u003e\n\u003cli\u003eZ. Zheng, Q. Ma, Z. Bi, S. de la Barrera, M. H. Liu, N. Mao, Y. Zhang, N. Kiper, K. Watanabe, T. Taniguchi \u003cem\u003eet al., \u003c/em\u003eUnconventional ferroelectricity in Moir\u0026eacute; heterostructures, Nature \u003cstrong\u003e588\u003c/strong\u003e, 71 (2020).\u003c/li\u003e\n\u003cli\u003eA. Weston, E. G. Castanon, V. Enaldiev, F. Ferreira, S. Bhattacharjee, S. Xu, H. Corte-Le\u0026oacute;n, Z. Wu, N. Clark, A. Summerfield \u003cem\u003eet al.\u003c/em\u003e, Interfacial ferroelectricity in marginally twisted 2D semiconductors, Nat. Nanotechnol. \u003cstrong\u003e17\u003c/strong\u003e, 390 (2022).\u003c/li\u003e\n\u003cli\u003eH. Liu, A. T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tom\u0026aacute;nek, and P. D. Ye, Phosphorene: An unexplored 2D semiconductor with a high hole mobility, ACS Nano \u003cstrong\u003e8\u003c/strong\u003e, 4033 (2014).\u003c/li\u003e\n\u003cli\u003eY. Xu, Z. Shi, X. Shi, K. Zhang, and H. Zhang, Recent progress in black phosphorus and black-phosphorus-analogue materials: properties, synthesis and applications, Nanoscale \u003cstrong\u003e11\u003c/strong\u003e, 14491 (2019).\u003c/li\u003e\n\u003cli\u003eW. Ma, J. Lu, B. Wan, D. Peng, Q. Xu, G. Hu, Y. Peng, C. Pan, and Z. L. Wang, Piezoelectricity in multilayer black phosphorus for piezotronics and nanogenerators, Adv. Mater. \u003cstrong\u003e32\u003c/strong\u003e, 1905795 (2020).\u003c/li\u003e\n\u003cli\u003eW. Xu, J. D. Zheng, W. Y. Tong, J. L. Wang, Y. P. Shao, Y. K. Zhang, Y. F. Tan, and C. G. Duan, Strain-induced ferroelectric phase transition in group-V monolayer black phosphorus, Adv. Quantum Technol. \u003cstrong\u003e6\u003c/strong\u003e, 2200169 (2023).\u003c/li\u003e\n\u003cli\u003eW. Shen, J. Shen, F. Wang, and Y. Lu, Emergence of multiple ferroelectric states in multilayer black phosphorus, Phys. Rev. B \u003cstrong\u003e111\u003c/strong\u003e, 115429 (2025).\u003c/li\u003e\n\u003cli\u003eC. Xiao, F. Wang, S. A. Yang, Y. Lu, Y. Feng, and S. Zhang, Elemental ferroelectricity and antiferroelectricity in group-V monolayer, Adv. Funct. Mater. \u003cstrong\u003e28\u003c/strong\u003e, 1707383 (2018).\u003c/li\u003e\n\u003cli\u003eJ. Gou, H. Bai, X. Zhang, Y. L. Huang, S. Duan, A. Ariando, S. A. Yang, L. Chen, Y. Lu, and A. T. S. Wee, Two-dimensional ferroelectricity in a single-element bismuth monolayer, Nature (London) \u003cstrong\u003e617\u003c/strong\u003e, 67 (2023).\u003c/li\u003e\n\u003cli\u003eV. Tran, R. Soklaski, Y. Liang, and L. Yang, Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus, Phys. Rev. B \u003cstrong\u003e89\u003c/strong\u003e, 235319 (2014).\u003c/li\u003e\n\u003cli\u003eX. Luo, X. Lu, G. K. W. Koon, A. H. Castro Neto, B. \u0026Ouml;zyilmaz, Q. Xiong, and S. Y. Quek, Large frequency change with thickness in interlayer breathing mode - Significant interlayer interactions in few layer black phosphorus, Nano Lett. \u003cstrong\u003e15\u003c/strong\u003e, 3931 (2015).\u003c/li\u003e\n\u003cli\u003eN. Zhao, Y. F. Zhu, and Q. Jiang, Thickness-dependent surface energies of few-layered arsenene and antimonene films in \u0026alpha; and \u0026beta; phases, Phys. E Low-Dimens. Syst. Nanostructures \u003cstrong\u003e101\u003c/strong\u003e, 38 (2018).\u003c/li\u003e\n\u003cli\u003eR. Fei, W. Kang, and L. Yang, Ferroelectricity and phase transitions in monolayer group-IV monochalcogenides, Phys. Rev. Lett. \u003cstrong\u003e117\u003c/strong\u003e, 097601 (2016).\u003c/li\u003e\n\u003cli\u003eX. Liu, Y. Yang, T. Hu, G. Zhao, C. Chen, and W. Ren, Vertical ferroelectric switching by in-plane sliding of two-dimensional bilayer WTe\u003csub\u003e2\u003c/sub\u003e, Nanoscale \u003cstrong\u003e11\u003c/strong\u003e, 18575 (2019).\u003c/li\u003e\n\u003cli\u003eK. Mi, J. Xie, M. S. Si, and C. X. Gao, Layer-stacking effect on electronic structures of bilayer arsenene, Europhys. Lett. 117, 27002 (2017).\u003c/li\u003e\n\u003cli\u003eD. Kecik, E. Durgun, and S. Ciraci, Stability of single-layer and multilayer arsenene and their mechanical and electronic properties, Phys. Rev. B \u003cstrong\u003e94\u003c/strong\u003e, 205409 (2016).\u003c/li\u003e\n\u003cli\u003eY. Kadioglu, J. A. Santana, H. D. \u0026Ouml;zaydin, F. Ersan, O. \u0026Uuml;. Akt\u0026uuml;rk, E. Akt\u0026uuml;rk, and F. A. Reboredo, Diffusion quantum Monte Carlo and density functional calculations of the structural stability of bilayer arsenene, J. Chem. Phys. \u003cstrong\u003e148\u003c/strong\u003e, 214706 (2018).\u003c/li\u003e\n\u003cli\u003eS. Zhou, J. Han, S. Dai, J. Sun, and D. J. Srolovitz, Van der Waals bilayer energetics: Generalized stacking-fault energy of graphene, boron nitride, and graphene/boron nitride bilayers, Phys. Rev. B \u003cstrong\u003e92\u003c/strong\u003e, 155438 (2015).\u003c/li\u003e\n\u003cli\u003eY. Kim, I. K. Park, D. C. M. Yang, D. Y. Kim, G. Lee, and N. Kim, Synchrotron x-ray diffraction study of inversion symmetry breaking in bulk black phosphorus, Phys. Rev. B \u003cstrong\u003e111\u003c/strong\u003e, L161407 (2025).\u003c/li\u003e\n\u003cli\u003eSee Supplemental Material for DFT calculation methods and machine-learned potential molecular dynamics.\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Tables","content":"\u003cp\u003e\u003cstrong\u003eTable 1.\u003c/strong\u003e Optimized lattice parameters and relative total energies by PBE+D3 for monolayer (ML) and bilayer (BL) \u0026alpha;-As. For BL, different stacking registries such as AA, AB, AC, AD were considered, where AA-FE refers to AA-stacked ferroelectric. \u0026Delta;\u003cem\u003eE\u003c/em\u003e means the total energy per unit cell relative to the most stable AA-FE.\u0026nbsp;\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"2\" valign=\"top\" style=\"width: 123px;\"\u003e\n \u003cp\u003e\u0026alpha;-As structure\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 159px;\"\u003e\n \u003cp\u003e\u003cem\u003ea\u003c/em\u003e (\u0026Aring;)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 159px;\"\u003e\n \u003cp\u003e\u003cem\u003eb\u003c/em\u003e (\u0026Aring;)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 159px;\"\u003e\n \u003cp\u003e\u0026Delta;\u003cem\u003eE\u003c/em\u003e (meV/u.c.)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"2\" valign=\"top\" style=\"width: 123px;\"\u003e\n \u003cp\u003eML\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 159px;\"\u003e\n \u003cp\u003e3.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 159px;\"\u003e\n \u003cp\u003e4.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 159px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"5\" valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp\u003eBL\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003eAA-FE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 159px;\"\u003e\n \u003cp\u003e3.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 159px;\"\u003e\n \u003cp\u003e4.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 159px;\"\u003e\n \u003cp\u003e0.0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003eAA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 159px;\"\u003e\n \u003cp\u003e3.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 159px;\"\u003e\n \u003cp\u003e4.39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 159px;\"\u003e\n \u003cp\u003e5.9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003eAB\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 159px;\"\u003e\n \u003cp\u003e3.71\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 159px;\"\u003e\n \u003cp\u003e4.61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 159px;\"\u003e\n \u003cp\u003e20.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003eAC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 159px;\"\u003e\n \u003cp\u003e3.72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 159px;\"\u003e\n \u003cp\u003e4.54\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 159px;\"\u003e\n \u003cp\u003e183.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 66px;\"\u003e\n \u003cp\u003eAD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 159px;\"\u003e\n \u003cp\u003e3.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 159px;\"\u003e\n \u003cp\u003e4.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 159px;\"\u003e\n \u003cp\u003e86.9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Department of Chemistry, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulsan 44919, Republic of Korea","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"2d ferroelectrics, DFT modeling","lastPublishedDoi":"10.21203/rs.3.rs-7653762/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7653762/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eFerroelectric (FE) instability in the puckered lattice of arsenic (α-As) is investigated using density functional theory (DFT) calculations. A bilayer (BL) structure with the most stable AA-stacked configuration is found to exhibit spontaneous ferroelectric polarization arising from an intralayer distortion analogous to that observed in α-Bi monolayers. Unlike conventional two-dimensional (2D) ferroelectricity, which is typically driven by sliding-induced charge transfer, the observed polarization in α-As primarily originates from a lattice contraction along the armchair direction caused by inverted band occupation facilitated through interlayer electron hopping. The calculated polarization reaches 0.63 × 10\u003csup\u003e-10 \u003c/sup\u003eC/m with the associated transition barrier 5.4 meV/u.c., and our molecular dynamics simulations using machine-learned interatomic potential shows the FE ordering persisting up to ~100 K or 300 K under a uniaxial compression of 0% or -4%, respectively. These results provide new insight into distinct mechanism of 2D ferroelectricity governed by interlayer electronic coupling.\u003c/p\u003e","manuscriptTitle":"Interlayer Coupling Induced Ferroelectricity in Bilayer α-As","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-23 07:59:31","doi":"10.21203/rs.3.rs-7653762/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"8e3accd0-2d72-4a41-b6bc-97b7d9976a47","owner":[],"postedDate":"September 23rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":54979092,"name":"Hard Condensed-matter Physics"}],"tags":[],"updatedAt":"2025-09-23T07:59:31+00:00","versionOfRecord":[],"versionCreatedAt":"2025-09-23 07:59:31","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7653762","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7653762","identity":"rs-7653762","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}