Stacking Ferroelectricity: Interlayer Registry Effects

• Stacking ferroelectricity is defined as the emergence of spontaneous polarization through interlayer registry changes, not by traditional ionic displacement.
• It exploits lateral sliding, rotational twist, or vertical shifts between layers to break inversion symmetry, enabling ferroelectric and multiferroic behavior in nonpolar systems.
• Recent experiments in bilayer h-BN and TMDs reveal measurable switching fields and domain-wall dynamics, offering insights for next-generation nanoelectronic devices.

Stacking ferroelectricity is a form of ferroelectric order in which spontaneous polarization is created by interlayer registry rather than by the intrinsic polar instability of an isolated monolayer or by the conventional bulk displacive mechanism. In this framework, relative translation, rotation, reversed stacking, twist, or more general heterodeformation can remove the symmetries that enforce vanishing dipole moment, so that bilayers, multilayers, moiré superlattices, and even trilayer sandwiches assembled from nonpolar constituents become polar and electrically switchable (Ji et al., 2022, Zhou et al., 2023, Yu et al., 30 Aug 2025). The subject now spans interfacial sliding ferroelectrics in hexagonal boron nitride and rhombohedral transition-metal dichalcogenides, mixed-stacking graphene, vertical trilayer ferroelectrics, stacking-controlled multiferroics, and quasi-one-dimensional van der Waals crystals whose macroscopic polarity is fixed by the stacking of polar subunits (Yasuda et al., 2020, Wang et al., 2021, Garcia-Ruiz et al., 2023, Zhang et al., 2023, Sun et al., 2022).

1. Definition and distinguishing features

The general bilayer formulation treats the second layer as a stacked image of the first,

$S'=\hat t_z \hat O S,$

where $\hat t_z$ is an out-of-plane translation and $\hat O=\{O\mid \mathbf T_O\}$ is the essential stacking operator with rotational part $O$ and in-plane translation $\mathbf T_O$ (Ji et al., 2022). In that sense, stacking ferroelectricity is a symmetry problem posed on the assembled bilayer or multilayer, not on the monolayer alone. The relevant order parameter is therefore a stacking coordinate—most commonly a relative sliding field, but in other realizations a layer flip, a relative rotation, or a vertical off-centering of a sandwiched layer.

This distinguishes stacking ferroelectricity from conventional displacive ferroelectricity. In perovskite-like systems, polarization is associated with ionic off-centering within a three-dimensional unit cell. In stacking ferroelectrics, by contrast, polarization is “rooted in the interlayer charge compensation and the resultant dipole formation between adjacent layers,” and ferroelectric behavior can be created “even from non-ferroelectric monolayers by breaking the inversion symmetry through specific stacking configurations” (Yu et al., 30 Aug 2025). The underlying monolayers may be nonpolar, centrosymmetric, or only weakly polar; what matters is whether the assembled stack retains or destroys the symmetries that forbid a net dipole.

Sliding ferroelectricity is the most prominent realization of this idea, but it is not the whole subject. The general bilayer-stacking-ferroelectricity framework includes pure translation, rotation-related stacking, mirrored or reversed bilayers, twisted bilayers, and combined in-plane and out-of-plane polar states (Ji et al., 2022). A distinct but related branch is vertical stacking ferroelectricity, in which an A/B/A trilayer acquires bistable out-of-plane polarization through the vertical off-centering of the middle layer rather than through in-plane sliding (Zhang et al., 2023).

2. Symmetry principles and microscopic theory

A systematic group-theory analysis over all 80 layer groups classifies monolayers into 15 IP, 13 OP, 4 CP, and 48 NP layer groups and then determines which bilayer stackings can become ferroelectric (Ji et al., 2022). The central symmetry statement is that layer-exchanging operations $R^{-}$, such as inversion, $m_z$, $C_{2\alpha}$, or $S_{nz}$, forbid the corresponding polarization component if they survive in the bilayer. A particularly important rule is that pure sliding cannot break monolayer inversion for a centrosymmetric monolayer; therefore sliding ferroelectricity is impossible in that case unless the stacking operation includes a nontrivial rotational part (Ji et al., 2022). This is why general bilayer stacking ferroelectricity is broader than sliding ferroelectricity.

Beyond symmetry selection rules, a quantum-geometric description has been developed for out-of-plane stacking ferroelectricity in van der Waals bilayers. In that approach, the bilayer at fixed in-plane momentum is mapped to the two-cell limit of an SSH/Rice–Mele chain, so that the vertical polarization is controlled by a Berry phase,

$$P = \frac{e}{2\pi} \oint \langle u_{-}(k)|-i\partial_k|u_{-}(k)\rangle\, dk,$$

with robust polarity when the broken-sublattice-symmetry scale and the asymmetric interlayer hopping are comparable, summarized by the criterion $\hat t_z$0 (Zhou et al., 2023). This framework unifies AB-stacked honeycomb bilayers, 3R bilayer TMDs, and $\hat t_z$1 bilayer TMDs, and it explains why SiC-type bilayers are strongly polar, 3R-TMDs are intermediate, and $\hat t_z$2-TMDs are weak and cancellation-prone (Zhou et al., 2023).

A complementary microscopic route appears in mixed-stacking graphene. There the polarization is computed directly from layer charge redistribution,

$\hat t_z$3

using a self-consistent full hybrid $\hat t_z$4-tight-binding Slonczewski–Weiss–McClure Hamiltonian (Garcia-Ruiz et al., 2023). Structural asymmetry alone is not sufficient: a reduced electron-hole-symmetric model still gives $\hat t_z$5, so a nonzero equilibrium dipole requires both broken inversion and electron-hole-symmetry-breaking terms such as $\hat t_z$6, $\hat t_z$7, $\hat t_z$8, and $\hat t_z$9 (Garcia-Ruiz et al., 2023). Screening is essential; in ABCB tetralayer graphene, the unscreened $\hat O=\{O\mid \mathbf T_O\}$0 is reduced to a screened $\hat O=\{O\mid \mathbf T_O\}$1, and the sign can even reverse (Garcia-Ruiz et al., 2023).

These theories converge on a common picture. Stacking ferroelectricity is produced when stacking lowers symmetry so that layer-resolved charge, orbital hybridization, or effective Wannier-center positions become inequivalent between the two sides of the bilayer. The resulting dipole may be predominantly electronic, mixed ionic-electronic, or coupled to a structural relaxation of the stacking coordinate, depending on the material class.

3. Bilayer and interfacial realizations

Parallel-stacked bilayer h-BN is the canonical sliding-ferroelectric realization. In experimentally assembled $\hat O=\{O\mid \mathbf T_O\}$2 bilayers, the ferroelectric states are AB and BA, while the natural bulk-like $\hat O=\{O\mid \mathbf T_O\}$3 AA′ stacking is nonpolar (Yasuda et al., 2020). Transport measurements with an adjacent graphene sensor yield

$\hat O=\{O\mid \mathbf T_O\}$4

equivalent to

$\hat O=\{O\mid \mathbf T_O\}$5

in good agreement with the Berry-phase value $\hat O=\{O\mid \mathbf T_O\}$6 (Yasuda et al., 2020). The switching fields extracted from dual-gate maps are approximately $\hat O=\{O\mid \mathbf T_O\}$7 for BA $\hat O=\{O\mid \mathbf T_O\}$8 AB and $\hat O=\{O\mid \mathbf T_O\}$9 for AB $O$0 BA, while room-temperature writing is achieved with $O$1 $O$2 and $O$3 $O$4; retention remains essentially unchanged after 14 and 31 days at $O$5 (Yasuda et al., 2020).

A direct interfacial view of the same mechanism was obtained in naturally grown h-BN flakes stacked in a metastable parallel orientation. Kelvin probe force microscopy resolves alternating AB and BA domains with

$O$6

corresponding to

$O$7

and reversible switching occurs by biased-tip-driven domain-wall motion coupled to lateral sliding (Stern et al., 2020). The required relative translation is $O$8, the domain-wall width is about $O$9, and domain-wall motion is observed for fields exceeding approximately $\mathbf T_O$0 (Stern et al., 2020). The microscopic origin was traced to a subtle interplay between charge redistribution and a tiny out-of-plane displacement $\mathbf T_O$1 (Stern et al., 2020).

Rhombohedral-stacked bilayer TMDs extend the same mechanism to semiconducting $\mathbf T_O$2 bilayers. In bilayer WSe$\mathbf T_O$3, MoSe$\mathbf T_O$4, WS$\mathbf T_O$5, and MoS$\mathbf T_O$6, parallel stacking produces two local minima, MX and XM, with opposite out-of-plane dipoles generated by asymmetric interlayer hybridization and charge redistribution (Wang et al., 2021). Nearly parallel stacked bilayers reconstruct into triangular MX/XM moiré ferroelectric domains visualized by PFM, and electric-field-induced domain-wall motion is directly observed (Wang et al., 2021). In graphene-sensor devices, the built-in interlayer potential is about $\mathbf T_O$7–$\mathbf T_O$8 mV across all four TMDs, while a WSe$\mathbf T_O$9 device exhibits a coercive field of about $R^{-}$0 (Wang et al., 2021).

A growth-engineered route was demonstrated in bilayer MoS$R^{-}$1 homoepitaxy with co-existing 3R polytypic domains. Under low-Mo, low-temperature, sulfur-rich two-step CVD, fan-shaped bilayer patterns form with alternating AA, AB, and BA domains separated by partial dislocations (Yang et al., 2022). Since AB and BA correspond to opposite out-of-plane interlayer ferroelectric polarizations, their coexistence provides a structural basis for room-temperature switching. Back-gated FETs with these 3R polytypic domains show repeatable counterclockwise hysteresis, and the memory window exceeds that of compact-shaped 3R bilayer control devices (Yang et al., 2022).

4. Multilayer, moiré, vertical, and elemental variants

Graphene broadened stacking ferroelectricity beyond binary compounds. Mixed-stacking few-layer graphene is predicted to host weak ferroelectricity when the stacking sequence breaks inversion and $R^{-}$2 symmetry, as in ABCB and ABAC tetralayers or in $R^{-}$3ABA$R^{-}$4 films with an asymmetrically placed twin boundary (Garcia-Ruiz et al., 2023). For ABCB tetralayer graphene, the self-consistent screened polarization is $R^{-}$5, and in reconstructed small-angle structures the largest local polarization occurs at domain walls and especially near domain-wall intersections (Garcia-Ruiz et al., 2023). A distinct across-layer mechanism in pure multilayer graphene appears for $R^{-}$6: tetralayer ABAC has $R^{-}$7, five-layer ABABC and ABACB have $R^{-}$8 and $R^{-}$9, and six-layer polar states span approximately $m_z$0 to $m_z$1; the polar and nonpolar states are nearly degenerate, within $m_z$2–$m_z$3, and the switching barriers are below $m_z$4 (Yang et al., 2023).

The same subject has now been accessed experimentally without moiré alignment. Dual-gated, non-aligned ABCB tetralayer graphene encapsulated in hBN exhibits pronounced hysteresis under both top and bottom gate modulation, with

$m_z$5

and an inferred polarization

$m_z$6

persisting up to room temperature (Singh et al., 10 Apr 2025). The proposed microscopic origin is reversible layer-polarized charge reordering driven by gate-induced transitions between ABCB and BCBA-related stackings, without requiring a moiré superlattice (Singh et al., 10 Apr 2025).

A separate extension is vertical stacking ferroelectricity in A/B/A trilayers. In this model, the two outer layers are fixed symmetrically while the middle layer is free to move vertically, so the energy can be written as

$m_z$7

with a single-well centered state for $m_z$8 and a double well of two symmetry-related off-center states for $m_z$9 (Zhang et al., 2023). First-principles calculations give $C_{2\alpha}$0 and a $C_{2\alpha}$1 switching barrier for $C_{2\alpha}$2-BN/$C_{2\alpha}$3-BN/$C_{2\alpha}$4-BN, and $C_{2\alpha}$5 with an $C_{2\alpha}$6 barrier for $C_{2\alpha}$7-BN/graphene/$C_{2\alpha}$8-BN; in both cases the crossover to polar stability occurs around $C_{2\alpha}$9 (Zhang et al., 2023).

Large-heterodeformation h-BN shows that stacking ferroelectricity is not confined to the near-AA moiré limit. Bicrystallography and a DFT-informed BFIM continuum model demonstrate ferroelectricity not only in AA-vicinal systems but also in configurations vicinal to the large-angle $S_{nz}$0 parent at $S_{nz}$1 (Ahmed et al., 1 Oct 2025). In the $S_{nz}$2-vicinal case, the two degenerate GSFE minima carry opposite out-of-plane polarization with

$S_{nz}$3

and the relevant interface dislocations have Burgers vector magnitude $S_{nz}$4, much smaller than in small-twist AA-vicinal h-BN (Ahmed et al., 1 Oct 2025).

Stacking engineering also reaches elemental topological ferroelectrics and polar metals. In buckled-honeycomb Bi films, 2BL ABCA is nonpolar and centrosymmetric, whereas 2BL ABAC is polar with layer group $S_{nz}$5, and CABA is its inversion partner with opposite polarization; the two-bilayer Bi film with a polar stacking sequence is identified as an elemental topological ferroelectric, while 3BL and 4BL polar structures are elemental polar metals with topological nontrivial edge states (Zhang et al., 2023).

5. Domains, switching kinetics, and field control

Because the order parameter is a stacking coordinate, switching commonly proceeds through domain-wall motion rather than coherent uniform reversal. A first-principles and machine-learning study of bilayer h-BN showed that AB and BA carry

$S_{nz}$6

while the saddle-point state along the sliding path has vanishing $S_{nz}$7 and a large in-plane polarization of $S_{nz}$8 (He et al., 2022). The domain walls are unusually wide, with widths of $S_{nz}$9, $$P = \frac{e}{2\pi} \oint \langle u_{-}(k)|-i\partial_k|u_{-}(k)\rangle\, dk,$$0, $$P = \frac{e}{2\pi} \oint \langle u_{-}(k)|-i\partial_k|u_{-}(k)\rangle\, dk,$$1, and $$P = \frac{e}{2\pi} \oint \langle u_{-}(k)|-i\partial_k|u_{-}(k)\rangle\, dk,$$2 nm for $$P = \frac{e}{2\pi} \oint \langle u_{-}(k)|-i\partial_k|u_{-}(k)\rangle\, dk,$$3, $$P = \frac{e}{2\pi} \oint \langle u_{-}(k)|-i\partial_k|u_{-}(k)\rangle\, dk,$$4, $$P = \frac{e}{2\pi} \oint \langle u_{-}(k)|-i\partial_k|u_{-}(k)\rangle\, dk,$$5, and $$P = \frac{e}{2\pi} \oint \langle u_{-}(k)|-i\partial_k|u_{-}(k)\rangle\, dk,$$6 walls, respectively, described by

$$P = \frac{e}{2\pi} \oint \langle u_{-}(k)|-i\partial_k|u_{-}(k)\rangle\, dk,$$7

where $$P = \frac{e}{2\pi} \oint \langle u_{-}(k)|-i\partial_k|u_{-}(k)\rangle\, dk,$$8 is the switching barrier between stacking-polarization states and $$P = \frac{e}{2\pi} \oint \langle u_{-}(k)|-i\partial_k|u_{-}(k)\rangle\, dk,$$9 is the effective in-plane elastic stiffness (He et al., 2022). Coherent monodomain reversal requires $\hat t_z$00 at 100 K and $\hat t_z$01 at 300 K, but domain-wall motion lowers the threshold to $\hat t_z$02 for a $\hat t_z$03 wall and $\hat t_z$04 for a $\hat t_z$05 wall; the predicted wall velocity is about $\hat t_z$06, enabling switching in about $\hat t_z$07–$\hat t_z$08 ps (He et al., 2022). In ideal twisted h-BN, the same analysis yields a field-responsive but nearly reversible state termed super-paraelectric (He et al., 2022).

Continuum theory for moiré superlattices clarifies this distinction. In 3R MoS$\hat t_z$09, local stackings carry local spontaneous polarization $\hat t_z$10, and the relaxed moiré divides into AB and BA domains separated by narrow walls because of the competition between stacking and elastic energies (Bennett et al., 2021). An applied field enters the local energy density through

$\hat t_z$11

with a linear $\hat t_z$12 term that splits AB and BA and a quadratic dielectric term that reduces the stacking energy and softens the domains (Bennett et al., 2021). The resulting net polarization of the moiré superlattice arises from unequal domain areas rather than from flipping the sign of local polarization inside each domain. The authors therefore argue that ideal moiré superlattices governed by this mechanism are generally not truly ferroelectric in the strict zero-field-switchable sense, even though they contain local polar domains and exhibit field-tunable average polarization (Bennett et al., 2021). This is a central terminology dispute in the field.

Photoexcitation adds another control channel. In 3R bilayer MoS$\hat t_z$13, the dark-state polarization is $\hat t_z$14, but constrained-DFT calculations show a non-monotonic photoinduced evolution: $\hat t_z$15 at $\hat t_z$16, $\hat t_z$17 at $\hat t_z$18, and $\hat t_z$19 at $\hat t_z$20, while the sliding barrier remains in the $\hat t_z$21–$\hat t_z$22 range (Gao et al., 2024). At $\hat t_z$23–$\hat t_z$24, the original $\hat t_z$25 structure becomes unstable and reconstructs into a $\hat t_z$26 $\hat t_z$27 phase with $\hat t_z$28 enhanced to about $\hat t_z$29 to $\hat t_z$30 (Gao et al., 2024). This underscores that stacking ferroelectricity is often electronically soft because its origin is interfacial charge transfer rather than a large ionic displacement.

6. Multiferroic extensions, non-bilayer analogues, and open problems

Stacking ferroelectricity has increasingly merged with multiferroicity. In bilayer ScI$\hat t_z$31, aligned AB and BA are polar with opposite out-of-plane polarization

$\hat t_z$32

while AA is nonpolar because it preserves $\hat t_z$33; AB and BA are also the lowest-energy aligned stackings, and sliding between them requires an $\hat t_z$34 barrier (Pan et al., 18 Oct 2025). These same stackings are interlayer ferromagnetic and, with SOC and out-of-plane spin orientation, exhibit spontaneous valley polarization with splitting around $\hat t_z$35 (Pan et al., 18 Oct 2025). In reversed bilayer PtBr$\hat t_z$36, AC′ stacking yields a polar antiferromagnet with

$\hat t_z$37

and a CI-NEB switching barrier of $\hat t_z$38; the ferroelectric polarization controls the spin splitting and the sign of the Kerr signal, enabling electrical writing and magneto-optical readout without net ferromagnetism (Sun et al., 2024). More generally, bilayer stacking-ferroelectricity theory predicts that even centrosymmetric 2D ferromagnets can become multiferroic after appropriate stacking, and that in some cases the out-of-plane polarization is interlocked with an in-plane component, allowing deterministic control of $\hat t_z$39 by an in-plane electric field (Ji et al., 2022).

The stacking principle is not confined to two-dimensional bilayers. In quasi-one-dimensional van der Waals oxyhalides NbOX$\hat t_z$40, the local Nb off-centering creates polar double chains, and different ways of stacking those double chains generate ferroelectric or antiferroelectric bulk phases with meV-scale energy differences (Sun et al., 2022). The reported spontaneous polarizations of the ferroelectric phases range from $\hat t_z$41 to $\hat t_z$42, and $\hat t_z$43 reaches $\hat t_z$44 in monoclinic NbOI$\hat t_z$45 (Sun et al., 2022). This suggests that stacking ferroelectricity is best understood as a broader registry-controlled polarity principle, not solely as a van der Waals bilayer phenomenon.

Several limitations remain. Many proposed systems are still intrinsically theoretical, often based on semilocal DFT with empirical vdW corrections, and frequently omit finite-temperature fluctuations, disorder, realistic contacts, substrate effects, and depolarization screening (Zhang et al., 2023). Even in experimentally established systems, the microscopic switching path is often inferred from transport or PFM rather than directly imaged under bias, and quantitative memory metrics such as coercive field, endurance, or retention remain incomplete in several material families (Yang et al., 2022, Singh et al., 10 Apr 2025). The terminology of “ferroelectricity” in moiré systems also remains contested, because domain-redistribution-induced net polarization can mimic ferroelectric response without satisfying the strict criterion of a switchable spontaneous polarization at zero field (Bennett et al., 2021).

Taken together, the literature defines stacking ferroelectricity as a distinct ferroic paradigm in which interlayer geometry is itself the order parameter. It can be realized by lateral sliding between AB and BA, by across-layer symmetry breaking in multilayer graphene, by vertical off-centering in A/B/A trilayers, by bicrystallographic domain formation in twisted or strained bilayers, or by stacking polar subunits into ferroelectric and antiferroelectric manifolds. The unifying statement is that polarization is created, reversed, or annihilated by changing how layers or chains are registered in space.