Stabilizing Phosphorene‐Like Group IV–VI Compounds via van der Waals Imprinting for Multistate Ferroelectricity and Tunable Spin Transport

Layered group IV–VI compounds (i.e., SnSe, SnS, GeSe, and GeS) in the puckered structure resembling black‐phosphorene (BlackP) have attracted increasing interest because of their intriguing ferroic orders and outstanding thermoelectric properties. By invoking the guiding principles of isovalency and isomorphism for promoting van der Waals epitaxy, and based on comprehensive first‐principles calculations, here it is shown that the typically metastable BlackP‐like GeTe can be readily stabilized on the (001) surface of isostructural SnSe. Importantly, the ferroelectricity of such a BlackP‐like GeTe monolayer can be substantially enhanced compared to the freestanding state, due to the substrate enlarged in‐plane polar displacements. The GeTe/SnSe heterobilayer exhibits multiple ferroelectric/ferrielectric polarization states, which can be exploited for high‐density memory devices. These mutually switchable polarization states are also shown to be internally locked with the spin polarization of the valence/conduction bands with pronounced Rashba spin‐orbit splitting and Berry curvature dipole. These findings highlight the intuitive yet enabling power of van der Waals imprinting in growing novel 2D materials for enriched functionalities.


Introduction
Ever since the exfoliation of graphene, [1] 2D materials have been extensively studied because of their exceptional properties beyond bulk counterparts and vast technological DOI: 10.1002/aelm.202300822applications. [2]A wealth of 2D crystals discovered in the past two decades, such as silicene, [3] black phosphorene (BlackP), [4] borophene, [5] stanene, [6] bismuthene, [7] tellurene, [8] hexagonal boron nitride, [9] and transition metal dichalcogenides (TMDs), [10] have greatly expanded the family of 2D materials.Among them, BlackP is a unique member, whose puckered honeycomb structure [11] endows it with rich anisotropic electronic, [11d] optical, [12] and mechanical [13] properties.More compellingly, possessing an appropriate band gap and high carrier mobility desired for charge transport, BlackP has been integrated into nano-sized high-performance field effect transistors. [14]More intriguingly, some BlackP-structured single-element materials have been found to exhibit unusual intrinsic ferroelectricity. [15]ecently, another class of compounds, which also possess BlackP-like layered structure but are composed of binary group IV and VI elements (e. g.SnSe, SnS, GeSe, and GeS), have attracted broad interest. [16]16f,20] On the other hand, when the heavier chalcogen element Te takes the place of S/Se, the BlackP-like structure is no longer the ground state.For example, stable GeTe has a rhombohedral structure consisting of exfoliatable buckled honeycomb layers, [21] featured by the hitherto-reported largest Rashba splitting [22] and room-temperature out-of-plane ferroelectricity; [23] the ground state structure of SnTe is also rhombohedral, but its metastable rock-salt allotrope is more widely known as the first identified topological crystalline insulator [24] and exhibits unprecedented in-plane ferroelectricity at the one-unit-cell limit. [25]Inspired by the fascinating and outstanding properties exhibited in available group IV-VI compounds with various compositions and structures, it is highly desirable to seek for alternative viable routes to synthesize those not yet realized metastable polymorphs, which may harbor distinct yet promising features.To this end, epitaxial growth has been demonstrated as a powerful technique.As a prime example, blue phosphorene (BlueP) had been predicted as a metastable monolayer allotrope of BlackP, which lacks bulk counterparts for exfoliation, [26] but was eventually grown epitaxially thanks to the identification of fertile proper substrates. [27]Recently, our theoretical and experimental efforts have demonstrated the isovalency and isomorphism rules as powerful guiding principles for identifying fertile substrates and promoting high-quality epitaxial growth of BlackP-like group V compounds. [28]n this work, we invoke such principles to predict the epitaxial growth of two typically metastable phases of group IV-VI compounds, namely, BlackP-like GeTe and BlueP-like SnSe monolayers, and reveal improved and enriched functionalities of the as-grown heterostructures using the former as an example.We first show that the typically metastable BlackP-like GeTe can be readily stabilized on the (001) surface of isostructural SnSe, and so as the BlueP-like SnSe on BlueP-like GeTe (111).Importantly, it is revealed that in the BlackP-like GeTe/SnSe heterosystem, the ferroelectric substrate can significantly enhance the ferroelectricity of the epilayer via enlarging the in-plane polar displacements.Going beyond the concept of bistability in most monolayer ferroelectric systems, we uncover multiple polarization states within a BlackP-like GeTe/SnSe heterobilayer, including two stable ferroelectric states and two metastable ferrielectric states originating from uncompensated polarizations of the two constituent layers, offering an appealing platform for developing high-density FE memory devices.These mutually switch-able polarization states are also shown to be internally locked with the spin polarization of valence/conduction bands with giant Rashba-splitting and Berry curvature dipoles, thereby can be implemented to intriguing polarization-tunable transport phenomena such as coherent spin transport and nonlinear Hall effect.These findings highlight the intuitive yet enabling power of van der Waals (vdW) imprinting and further demonstrate promising potentials of the as-grown heterostructures in harboring enriched functionalities and tunable properties for various device applications.

Computational Details
First-principles calculations based on density functional theory (DFT) were performed using the projector-augmented wave method, [29] implemented in the Vienna ab initio simulation package (VASP), [30] with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional. [31]The kinetic energy cutoff of the plane-wave basis was chosen to be 450 eV.To account for the vdW interactions between the overlayer and substrate, the semi-empirical dispersion-corrected DFT-D2 method [32] was employed.The Brillouin zone was sampled by Monkhorst-Pack kmesh with a density of 2 × 0.02 Å −1 .The convergences of force for geometry optimization and total energy for electron wavefunction self-consistency were set to be 0.02 eV Å −1 and 10 −5 eV, respectively.
The spontaneous polarization was calculated using the Berryphase approach, [33] incorporating both ionic and electronic contributions, Here, e is the elementary charge, S is the area of the unit cell, Z ion i is the effective charge and r i denotes the atomic displacement.While k is the wavevector in reciprocal space, integrated over the Brillouin Zone, |u n (k)〉 is the periodic part of the electronic Bloch wavefunction for band n and ⟨u n (k)| u n (k) k i ⟩ is the Berry connection, which characterizes the geometric phase associated with the adiabatic transport of the electronic states as k varies.Technically, to estimate the polarization of the Black-GeTe layer supported on SnSe(001), we displaced the Te atoms with respect to the Ge atoms (y i ) to achieve +P y and -P y FE states while keeping the ferroelectric substrate unchanged, as displayed in Figure 3a.The polarization of the epilayer was obtained by subtracting the contribution from the substrate.
For 2D materials, the Berry curvature dipole (BCD) behaves as a pseudo-vector, with the -component ( = x, y) given by where f n is the Fermi-Dirac function and the Berry curvature Ω z (k)can be calculated by using the Kubo formula, with Ψ n (k) and E n (k) respectively the Block wavefunction and energy of the n-th band at the momentum k, and v x(y) the velocity operator.To compute the Berry curvature, the maximally localized Wannier functions were constructed using the WANNIER90 code [34] in conjunction with the WannierTools package. [35]The Wannierberri code [36] was employed to compute the Berry curvature dipole.
To mimic a semi-infinite substrate, a four-layer slab model was constructed, with the bottom layer fixed at their bulk  [16a,37] The in-plane lattice constants of these bulk materials are adopted for the slab models, and the epitaxial monolayer is adjusted to match them, which reflects the realistic growth process.The eligibility of the four-layer slab model is further validated by comparing the band structures of the epilayerslab heterosystem and the bulk structure of the substrate, which indicates that the finite-size effect does not qualitatively alter the results (see Figure S7, Supporting Information).The finite displacement method was implemented to calculate the phonon dispersion, with the aid of the Phonopy code. [38]Ab initio molecular dynamics (AIMD) simulations were performed to verify the thermal stability, with the bottom two layers of the four-layer slab fixed at their bulk positions to mimic the semi-infinite substrate.The canonical ensemble was adopted by using the Nosé thermostat, [39] and the time step for integration is 1 fs.

Isomorphism-Isovalency-Promoted Epitaxial Growth
Similar to the elementary phosphorene, [26] binary group IV-VI 2D compounds can have BlackP-like and BlueP-like phases, as shown in Figure 1.Without ambiguity and for simplicity, we hereafter refer to the puckered and buckled structures of these binary compounds as the "Black" and "Blue" phases, following phosphorene.Their relative stability can be measured by the cohesive energy defined as E c = E IV-VI − E IV − E VI , with E IV-VI and E IV (E VI ) being the total energies of the group IV-VI monolayer and a single group IV (VI) atom respectively.As summarized in Table 1, Black-SnSe is the ground-state phase, while Blue-SnSe is metastable; in contrast, Blue-GeTe is more stable than its BlackP-like allotrope.The ground-state phases, namely Blue-GeTe and Black-SnSe, have been exfoliated from their corresponding parental layered bulk structure; [18b,c,40] yet the two metastable phases, namely Black-GeTe and Blue-SnSe, remain unrealized due to the lack of exfoliatable bulk counterpart.The rapidly developed bottom-up approaches provide alternative routes to access such metastable phases, among which the epitaxial growth is a powerful technique but critically relies on the choice of matched substrate.Inspired by our recent successful practice of vdW epitaxy empowered by structural similarity and isovalency, [28] we here choose available isostructural ground-state group IV-VI compounds as the substrates to achieve such a goal.
The growth geometries are schematically illustrated in Figure 1c,f.We deposit the Black-GeTe and Blue-SnSe monolayers on the Black-SnSe (001) and Blue-GeTe (111) surfaces, respectively.The lattice constants of the freestanding monolayers, as well as the mismatches upon deposition, are summarized in Table 1.The mismatches are within a reasonable range to grow defect-free vdW epilayers. [41]Our structure optimizations further reveal slight structural deformations in the grown 2D monolayers compared to the corresponding freestanding state, which can be attributed to their interaction with the substrate.Specifically, in the Black-GeTe, the Ge─Te bonds along the in-plane directions contract from 2.86 to 2.82 Å, while those along the out-of-plane directions elongate from 2.71 to 2.73 Å.Such slight deformations, as will be elaborated later, are highly desirable for achieving enhanced electric polarization.

Energetics and Stabilities
To assess the energetic viability of depositing Black-GeTe and Blue-SnSe monolayers on corresponding isostructural substrates, we calculate the binding energy E b = E total − E sub − E mono , with E total , E sub , and E mono the total energies of the substratesupported 2D system, the substrate, and the freestanding monolayer, respectively.The calculated binding energies are −35.19 and −35.81 meV Å −2 for the Black-GeTe/SnSe (001) and Blue-SnSe/GeTe (111) heterosystems, respectively, in the same order of magnitude as that of other vdW heterostructures. [42]e thereby envision that the proposed isomorphism-promoted growth is energetically feasible, and the heterostructures can be stabilized once formed.The dynamical stabilities of the proposed heterosystems are also examined by calculating the phonon spectra.As shown in Figure 2a,c, the frequencies of all phonon modes are real, indicating that both systems are dynamically stable.Furthermore, our AIMD simulations reveal that the geometries of both heterosystems remain intact after heated for more than 5 ps at 300 K, with the total potential energies almost invariant throughout the simulated heating process (Figure 2b,d).Based on these analyses, we confirm that epitaxial vdW imprinting of Black-GeTe monolayer on Black-SnSe (001) and Blue-SnSe monolayer on GeTe(111) are both energetically viable, and the as-grown heterostructures are dynamically and thermally stable.Thus, these typically metastable group IV-VI monolayers are highly probable to be grown and stabilized on the proposed isostructural substrates.

Substrate Enhanced Ferroelectricity of the Black-GeTe/SnSe (001) Heterosystem
The Black-GeTe and Blue-SnSe monolayers grown on isostructural semiconducting substrates naturally form heterostructures, allowing us to explore their potential applications without extra transfer operation.The Black-GeTe monolayer has been demonstrated to exhibit sizeable in-plane ferroelectricity in the freestanding state. [43]In this work, we further exploit its interplay with the substrate as an epilayer and potential enhancement of polarization by the isostructural substrate which is also ferroelectric.16f] When the high-temperature centrosymmetric paraelectric (PE) phase with zero polarization is cooled down to T C , the group-IV atoms displace along the x(y)-direction with respect to the chalcogen atoms, breaking the structural inversion symmetry.Consequently, depending on the polarization displacements, spontaneous polarization can be induced along different orientations, either −x/+x or −y/+y, as illustrated in Figure S1a-d (Supporting Information).The reversal of polarization (e.g. from +P y to −P y ) can be realized by electric switching which displaces the chalcogen atoms along the kinetic path +P y →PE→−P y .Our calculated spontaneous polarization (P s ) of freestanding Black-GeTe monolayer is 0.30 nC m −1 , larger than that of isostructural SnSe (0.18 nC m −1 ) [20b,44] , which can be attributed primarily to its larger polarization displacement (y as illustrated in the inset of Figure 3b and the values listed in Table 1).When deposited on SnSe (001), structure optimization reveals that the polar displacements can be further enhanced to y = 0.32 Å through interfacial interactions, surpassing the value in the freestanding state.Accordingly, we naturally expect that the ferroelectricity in Black-GeTe would be enhanced when grown on the SnSe (001) surface.
To confirm this conjecture, we calculate the spontaneous electric polarization of Black-GeTe in supported states, yielding P s = ∼ 0.39 nC m −1 , ∼30% higher than that of the freestanding state.The evolutions of polarizations along the minimumenergy path of ferroelectric switching are mapped in Figure 3b, for both the freestanding and supported cases.Symmetric features are observed in both curves, namely, the polarization enhancements are achieved in both +P y and −P y states for the supported case, indicating that the polarization displacements can be strengthened regardless of the polarization of the ferroelectric substrate.The influence of interlayer coupling can be further characterized via comparing the polarization of the epilayer with different heights above the substrate (Figure S5, Supporting Information).Furthermore, as there is a strong correlation between the magnitude of polarization and the relative displacement between the Ge and Te atoms, this characteristic aligns with the behavior expected in displacive-type ferroelectrics. [45]These results not only highlight the crucial role of vdW interface engineering in achieving enhanced ferroelectricity but also reveal coexisting electric dipoles in the epilayer and substrate with moderate interlayer coupling, which may pave the way to develop new multistate ferroelectric devices.

Multi-State Ferroelectricity of the Black-GeTe/SnSe Heterobilayer
Noting that Black-SnSe, the substrate invoked for vdW epitaxial growth, has also been demonstrated to be ferroelectric even in the monolayer limit, [46] here we explore the interplay between the BlackP-like GeTe and SnSe both in monolayer regime, which may give rise to enriched functionalities.In doing so, we consider a Black-GeTe/SnSe vdW heterobilayer, with possible geometric configurations and the corresponding layer-resolved inplane polarizations sketched in Figure 4a.Our total energy calculations reveal that the C1 and C4 configurations with the inplane polarizations aligned parallel correspond to the degenerate ground states, while C2 and C3 with antiparallel in-plane polarizations are metastable.Our comprehensive calculations demonstrate that these configurations exhibit both energetic and dynamic stability, as shown in Figure S6 (Supporting Information), and could be synthesized under suitable experimental conditions.As presented in Figure 4b, the calculated P s values for C1 and C2 states are respectively −0.62 and 0.16 nC m −1 , while C4 and C3 exhibit net polarizations the same as C1 and C2 respectively in magnitude but with an opposite sign.The C2 and C3 states holding uncompensated polarizations can be regarded as ferrielectric (FIE), similar to polarization states discovered in PbZrO 3 [47] and BaFe 2 Se 3 . [48]Here in the heterobilayer, it is worth mentioning that the sign of the P s in C2 or C3 is dictated by the Black-GeTe monolayer with a larger magnitude of polarization.In contrast, in homobilayers, electric polarizations are fully compensated and the systems are antiferroelectric with zero net polarization (see, for example, for the Black-GeTe bilayer, Figure S1e,f, Supporting Information).In the context of thickness-dependent FE properties of Black GeTe, it is reasonable to presume that, owing to the same crystal structure, it may exhibit a similar thickness-dependent FE behavior as Black SnTe, i.e., initially increasing and then decreasing with increasing film thickness. [49]urthermore, we demonstrate that strain engineering is an efficient approach for tuning ferroelectricity in group IV-VI compounds (see Figure S8, Supporting Information).
To facilitate the application of the heterobilayer for building multistate ferroelectric devices, it is important to study the kinetics of electric switching.The kinetic pathways for the Black-GeTe/SnSe heterobilayer to transform between different polarization states, are calculated using the climbing-image nudged elastic band (CI-NEB) method. [50]As confirmed in Figure 4c, each polarization state corresponds to a stable local minimum protected by an energy barrier.The barrier for directly transforming the heterobilayer FE-I to FE-II amounts to 128 meV (Figure S2, Supporting Information).However, we identify two kinetically more favored, indirect pathways for such transformation, namely, FE-I→FIE-I→FE-II (Path A) and FE-I→FIE-II→FE-II (Path B).Along Path A, the polarization state of the GeTe layer is reversed first, transforming the heterobilayer from FE-I to FIE-I, then the SnSe layer is switched, bringing the system to the FE-II state; the maximum energy barrier to overcome corresponds to the first-step transition, which is 102 meV (Figure 4c, bottom left).Along Path B, the polarization state of the SnSe layer is switched first, and the intermediate state is FIE-II, thus the maximum energy barrier to surmount is further lowered to 73.2 meV, which corresponds to the subsequent FIE-II-to-FE-II transition (Figure 4c, bottom right).that in Figure 4a, the energy barrier for switching the heterobilayer between two FIE states has been shown to be 103 meV, also in the same order of magnitude.Based on these results and analyses, we demonstrate that the Black-GeTe/SnSe heterobilayer possesses multiple stable/metastable FE/FIE states with non-zero P s , which are inter-switchable and controllable, thus can be implemented as the building block of new non-volatile ferroelectric memory devices.These salient properties revealed in the vdW imprinting enabled heterobilayer also present an alternative and transferrable route to go beyond convention bistability, which can efficiently complement the rare single-material multistate ferroelectrics. [51]

Tunable Spin/Charge Transport Properties of the GeTe/SnSe Heterobilayer
The multistate ferroelectricity of the Black-GeTe/SnSe heterobilayer with pronounced magnitude and switchable feature, enables us to further exploit electric polarization as a knob for tun-ing other fundamental properties that are interlocked with the built-in electric field.Here we investigated two exemplified properties related to the electronic structures, namely the spin texture and geometric phase; the former is promising for realizing persistent spin transport and related spintronic devices, [52] while the latter is intimately associated with nonlinear charge transport and may find potential photovoltaic applications. [53]Before looking into the heterobilayer, we first calculate the band structures of the freestanding Black-SnSe and GeTe monolayers.As shown in Figure S3a,b (Supporting Information), for both monolayers with −P y electric polarization, near the conduction band minimum (CBM) and valence band maximum (VBM), there are two inequivalent band extrema, respectively located on the Γ-X and Γ-Y paths.Turning on the spin-orbit coupling (SOC), the band extrema on the Γ-Y path (VBM and sub-CBM) remain spindegenerate, while those on the Γ-X path (CBM and sub-VBM) exhibit significant spin splitting.The degeneracy along Γ-Y is due to the preserved mirror symmetry with the reflecting plane parallel to the polarization along -y.The spin splitting on the Γ-X path is due to the built-in electric field from the −P y polarization; the splitting energies for the CBM are found to be 58.3 and 35.4 meV respectively for SnSe and GeTe monolayer, consistent with the previous studies. [54]Importantly, upon constructing the Black-GeTe/SnSe heterobilayer and switching it to the interlayer FE state, not only the splitting of CBM on the Γ-X path is enhanced to 90.2 meV, but a splitting of 41.7 meV is also induced for the originally degenerate VBM on the Γ-Y path, as shown in Figure 5a (zoomed in on the right).We note that such ferroelectricity-induced spin-orbit splitting in the CB is much larger than that in most TMDs, [55] because the polarization effectively induces a built-in electric field which can enhance the splitting in addition to atomic spin-orbit coupling.Given the multistate nature of the heterobilayer, it is necessary to clarify the detailed influence of different polarization states on spin splitting.To elucidate the interlocking between the ferroelectricity and electronic structures, we compute the spin-projected band structures of the two switchable FE states of +P y and −P y .As color-mapped in Figure 5a,b.Although the two polarization states exhibit comparable band slitting, the spin orientation is found to be opposite, especially for the bands on the Γ-X path with out-of-plane spin polarization.Similar band splitting and spin polarization can also be observed in the two metastable FIE states but with subtle differences compared to the FE states (Figure S4, Supporting Information).These findings suggest that the electronic structure directly couples with the spontaneous polarization and thus can be delicately tuned via proper switching fields.
As we know, spintronics utilizes both charge and spin for information encoding and processing. [56]However, strong SOC between these two degrees of freedom usually induces the undesired effect of causing spin decoherence through the Dyakonov-Perel mechanism, [57] adversely affecting the spin lifetime and thereby limiting the performance of spintronic devices.To suppress such spin relaxation, the persistent spin helix (PSH) state, which maintains a unidirectional and momentum-independent spin-orbit field orientation, is esteemed for facilitating coherent spin transport. [58]The prerequisite condition to realize such advantageous states is that the strengths of the Rashba and Dresselhaus spin-orbit couplings should be equal, which is often chal-lenging to achieve in physically realistic materials. [59]In this regard, the Black-GeTe/SnSe heterobilayer, hosting well-separated CBM with giant spin splitting and directional spin polarization along the Γ-X path, can be an ideal platform for exploring PSHlike coherent spin transport.
The modern theory of polarization provides a rigorous definition for spontaneous polarizations of periodic solids in the language of the Berry phase, which also implies the possibility of engineering Berry curvature distributions of electronic states in ferroelectric materials for achieving intriguing transport properties.Recently, it has been proposed that when the inversion symmetry is broken but the time-reversal symmetry is preserved, the Hall effect vanishes in the linear order but can survive in the nonlinear regime, owing to the nonzero dipoles of Berry curvature on the nonequilibrium Fermi surface. [60]To explore potential BCD induced by the polarization displacements and centrosymmetry breaking in the Black-GeTe/SnSe heterobilayer, we calculate the Berry curvature distribution within the first Brillouin zone in the charge-neutral condition and subject to the two FE states.One can observe from Figure 5c hotspots of Berry curvatures with large magnitudes and opposite signs at different momenta, indicating the formation of BCDs.The Berry curvature distributions are approximately mirror-symmetric (asymmetric) along the y (x) direction, indicating that the dipoles are along +x/−x.Moreover, the sign of the Berry curvature reverses when the electric polarization direction is switched from +P y to −P y , suggesting that the Berry curvature distribution is interlocked with electric dipoles and thus is also electrically switchable.Such polarized Berry curvature distribution can effectively induce a dipole moment which contributes to several nonlinear transport phenomena, whose signatures have been recently confirmed experimentally in other 2D materials. [61]The calculated BCDs corresponding to the two inter-switchable FE states are shown in Figure 5d.It can be seen that the BCD is zero in the gap.However, upon moving the chemical potential into the CBM or VBM via moderate doping/gating, a finite BCD emerges.Again, the BCD is found to be reserved in two switchable polarization states.The calculated peak values of BCD can reach up to ∼10 Å for both FE-I and FE-II states within the given energy window [−1,1] eV, significantly larger than those of previously reported T d -WTe 2 (0.1−3 Å), [62] SnTe (0.3 Å), [53] and Nb 2n+1 Si n Te 4n+2 (−1.54 Å), [63] implying that a giant nonlinear Hall conductivity can be harbored.The Black GeTe/SnSe heterobilayer can thus also serve as a physically realistic material platform to explore the intriguing optoelectrical response of the pronounced BCD and electrically-controllable nonlinear Hall transport properties. [64]

Conclusion
Following the intuitive isomorphism and isovalency principles, we have demonstrated that two typically metastable phases of group IV-VI compounds, monolayer Black-GeTe and Blue-SnSe, can be respectively stabilized on the Black-SnSe (001) and Blue-GeTe (111) surfaces, enabling their epitaxial growth by vdW imprinting.Strikingly, we reveal that the Black-SnSe (001) substrate can significantly enhance the ferroelectricity of the grown Black-GeTe monolayer via enlarging its in-plane polar displacements.Furthermore, within the exfoliated Black-GeTe/SnSe heterobilayer, the combination of the two ferroelectric monolayers can give rise to four mutually switchable polarization states, offering an appealing platform for designing high-density FE memory devices.The intrinsic electric polarizations are revealed to be locked with the spin texture and Berry curvature dipole of the conduction/valence bands and thereby can be utilized to achieve exotic transport phenomena.

Figure 1 .
Figure 1.Top and side views of the atomic structures of monolayer a) Black-SnSe, b) Black-GeTe, d) Blue-SnSe, and e) Blue-GeTe, with the corresponding unit cells indicated by the dashed lines.c,f) Schematic side-view illustration of the proposed isostructural-epitaxy approach to growing the metastable phases of monolayer c) Black-GeTe on Black-SnSe (001) and f) Blue-SnSe on Blue-GeTe (111), respectively.

Figure 2 .
Figure 2. a) Phonon spectrum and b) total potential energy evolution during AIMD simulation of the Black-like GeTe monolayer grown on the Black-SnSe (001) surface at 300 K.The insets in (b) display the side-viewed atomic structures at the beginning and end of the simulation.c,d) Same as (a,b), but for Blue-SnSe grown on the Blue-GeTe (111) surface.

Figure 3 .
Figure 3. a) Geometric structures of the two switchable FE states of the Black-GeTe grown on the SnSe (001) surface.The arrows on top indicate the polarization of the GeTe epilayer.b) Calculated polarization of the Black-GeTe monolayer in the freestanding/supported state.Inset: illustration of the polar atomic displacements y i which dictate the spontaneous electric polarization (blue arrow) of the Black-GeTe monolayer.

Figure 4 .
Figure 4. a) Geometric configurations of four possible polarization states of the Black-GeTe/SnSe heterobilayer.Each layer is ferroelectrically polarized with a net dipole moment aligned with the b-axis.The total polarization value of each state is given in (b).c) Kinetic pathways for the switching between various polarization states.

Figure 5 .
Figure 5. a,b) Electronic band structures of the two switchable FE states of the Black-GeTe/SnSe heterobilayer, with the CBM and VBM, zoomed in on the right.c) Berry curvature distributions and d) the xz component of BCD of the two FE states.The Fermi level is set to the band gap center.

Table 1 .
Optimized Defined as Δa = |a sheet − a sub |/a sub , where a sheet and a sub are the cell parameters of the grown 2D monolayer and substrate, respectively.Similar for Δb.