Introduction

The in-plane sliding of one two-dimensional (2D) material over another in vdW stacked layers of a non-centrosymmetric configuration can switch the out-of-plane ferroelectricity due to incomplete compensation of interlayer electric dipoles, known as sliding ferroelectrics1,2,3,4,5,6,7,8. This unique rationale enables mechanically robust ferroelectrics by leveraging the intralayer stiffness and interlayer slipperiness of 2D materials, while also ensuring electrical reliability through decoupling of electric polarization and in-plane conductivity1,3,8,9,10,11. Structurally different from conventional oxide ferroelectrics with enhanced depolarization during scaling down12, sliding ferroelectrics showcase strikingly stable and switchable electric dipoles down to few and bilayer limit. Therefore, a visionary goal of sliding ferroelectrics is to serve in future high-density memory technology, but with the preconditions of sufficiently large polarization and thermal stability under practical operations13,14,15.

The sliding ferroelectrics emerge typically in rhombohedral-stacked bilayers that are assembled in a parallel lattice orientation, for instance, parallel-stacked 2D transition metal dichalcogenides including WSe2, MoSe2, WS2, MoS2 and WTe2, where each layer is offset by one third of a unit cell6,7,8,9,10,11. The broken inversion symmetry and polar stacking order in such bilayer architecture further enable the engineering of sliding ferroelectrics even based on several constituents that are non-ferroelectric or non-polar in bulk, for example, hexagonal boron nitride (hBN)4,5. Further encapsulation of bilayer graphene by two hBN flakes at certain crystallographic alignment triggers unconventional ferroelectricities but with inadequate polarization value at room temperature16,17,18. In addition, the finite uncompensated charge density and limited superlattice size in aforementioned bilayers, restrict the upper limit of ferroelectric polarization and corresponding robustness3,19,20.

In this Article, we propose a rhombohedral-like three-layer that consists top hBN layer, central graphene and bottom hBN layer for achieving robust room-temperature ferroelectricity, termed as oblique-stacked heterostructure (OSH) (Fig. 1a) in which boron atom, carbon atom and the empty site of hexagonal center from three individual layers are vertically aligned (B-C-h stacking, left panel in Fig. 1a). In this configuration, the inversion and mirror reflection symmetries are broken, resulting in a positive polarization P+ in this domain5. Microscopically, the unequal pz orbital couplings at two graphene flanks, the distorted C orbital binding with B orbital gives rise to an out-of-plane polarization. The third hBN layer that vertically aligns its hexagon lattice center sequentially with C and B atoms is of great importance to stabilize the stacking order. Stimulated by a moderate electric field, both graphene and top hBN layer synergistically slides to form reversely polarized h-C-B stacking (right panel in Fig. 1a). Figure 1b shows the proposed co-sliding path from ab initio calculations (see Fig. S1-S3 for detailed discussions). The polar domains expand (shrink) with the applied electric fields to reach the minimum energy, resulting in net out-of-plane polarizations. Compared to the traditional bilayer ferroelectrics, the superlubric graphene/hBN hetero-interface with minor lattice mismatch21 and enlarged moiré superlattice size22 leads to strong polarizations with ultralow coercive fields11, while the relatively higher barrier of co-sliding motion here assures the out-of-plane polarization persisting up at and beyond room temperature.

Fig. 1: Electric hysteresis of the OSH device 1.
figure 1

a Atomic structure of the OSHs at two metastable states. b Structural evolution of the OSHs under co-sliding motions of graphene and hBN. White, gray and green spheres denote N, C and B atoms, respectively. Pink background marks the stationary bottom hBN layer while graphene and top hBN layers co-slide during ferroelectric switch. Brown and green arrows mark the sliding direction of graphene and hBN, respectively. c An optical image of one OSH stack. Scale bar: 10 μm. The zigzag edges of top and bottom hBN flakes are marked by red and yellow dashed lines, respectively. d Band structure of graphene/hBN heterolayer with zero twist angle. In the OSH device 1, the graphene electronic band is folded by graphene/hBN moiré superlattice potential, which clones the Dirac point (DP) at the superlattice band edges, termed as secondary Dirac points DP1 and DP2, respectively (below and above the main DP, Fig. 1d)23. e Top: four-probe longitudinal resistance Rxx of OSH device 1 during forward (blue) and backward (red) sweeps of back-gate voltages, at T = 1.5 K. Bottom: Hall resistance Rxy hysteresis at B = 0.05 T.

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Results and discussion

To precisely achieve the OSHs, we developed a flip and reflection transfer method (see Supplementary Fig. S4), which actualizes the parallel alignment of B(N)-terminated zigzag edge of one hBN, graphene zigzag edge and B(N)-terminated zigzag edge of other hBN (Fig. 1c). Figure 1e displays the measured longitudinal resistance Rxx against the bottom electric field Vb/db during the forward and backward sweeps of back-gate voltage Vb. Upon forward sweep, the Fermi level shifts upward from a position below a secondary Dirac point DP1, the main Dirac point DP to a position above another secondary Dirac point DP2 (Fig. 1d)23. Three resistance peaks are sequentially observed at Vb/db = –0.235, –0.220, and –0.205 V/nm when the Fermi level crosses the DP1, DP and DP2, respectively; whereas during the backward sweep they shift to 0.221, 0.206, and 0.014 V/nm, respectively. The sharp peaks during the unidirectional gate sweep indicate a single domain configuration for charge polarization with a sample-wide homogeneity. The pronounced electrical hysteresis is a hallmark of intrinsic ferroelectricity, which is re-confirmed by the measured Rxy whose sign depends on the charge polarity (Fig. 1e, bottom). In addition, the hysteresis features are robust after ramping the temperature up to 300 K (see Supplementary Fig. S5–S10).

The oblique-stacking configuration is central to realize and stabilize the ferroelectricity in such three-layer heterostructure. For verifications, we further fabricated extra hBN/graphene/hBN three-layer devices in different stacking configurations (Table S1): (i) two parallel-aligned hBN flakes but with graphene twisted by ~2° (device 2) (see Supplementary Fig. S11–S15), (ii) two anti-parallel aligned hBN flakes (flip without reflection) but with graphene aligned (device 3) (see Supplementary Fig. S16-S17) and (iii) completely misaligned hBN/graphene/hBN stack (device 4) (see Supplementary Fig. S18). The ferroelectricity vanishes in non-OSH device 3 and device 4, revealing the necessity of oblique-stacking in generating ferroelectricity in hBN/graphene/hBN systems. Considering two variable stacking surfaces (A and A’) of AA’-stacked bulk hBN, two options for hBN’s principal edges (armchair and zigzag), and two options for zigzag edges, the possibility of realizing OSHs in the occasionally aligned hBN/graphene/hBN stack for inducing ferroelectricity is only 1/8. This may explain why no ferroelectricity has been reported previously in such a simple system. By developing a new transfer method that involves controllable flip and reflection of hBN multilayers, we have achieved 100% productivity of OSHs demonstrating similar ferroelectric hysteresis behavior.

Negative capacitance and unconventional ferroelectric loop

To understand the ferroelectric hysteresis, we conducted magneto-transport measurements of the OSH device 1 by applying a vertical magnetic field B. Figure 2a presents the mapping of measured Rxx versus B and Vb/db under the forward sweep. The magnetic field-induced quantum Hall effect in graphene is manifested as linear Landau fans that follow the Streda formula dn/dB = ve/h (where n is the carrier density in graphene, e the elementary charge, h the Planck constant, and v the filling factor)24. The slope dVb/dB for each Landau state should be a constant at a given v, as described by a parallel capacitor model under a gate voltage. By contrast, we observe an abrupt change of slope dVb/dB at Vb/db = –0.20 V/nm for each Landau state. The change in slope also arises at Vb/db = 0.20 V/nm during the backward sweep (Fig. 2b). As the quantum Hall oscillation depends only on n and B, these results suggest an abrupt change in the total capacitance Ctot that dictates how efficient Vb is to modulate n in graphene, differentiating from reported bilayer graphene/hBN devices18. As such, one could divide the gate-voltage modulation of Rxx into two regions, which are temporarily assigned as the high-capacitance and low-capacitance regions.

Fig. 2: Ferroelectric capacitance of the OSH device 1.
figure 2

The four-probe resistance Rxx as functions of applied electric field (Vb/db) and magnetic field (B) during forward (a) and backward (b) sweeps of Vb. The inset illustrates the series-connected ferroelectric and geometric capacitances, i.e., Cf and Cg. n = Ctot (Vb - Vb0) and Cg = ϵϵ0/db, Vb0 is the Vb required to shift the Fermi level to the DP, ϵ0 is the permittivity of vacuum, and ϵ = 4 represents the relative permittivity. The extracted ferroelectric capacitances during forward (c) and backward (d) sweeps. Light gray-colored backgrounds highlight the negative capacitance regions. e The obtained polarization hysteresis loop. Arrows indicate the scanning directions of Vb/db. The inset sketches the mutual action of ferroelectric polarization PF and electric field E.

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The abrupt change in capacitance reflects the reversal of ferroelectric polarization during the sweep of Vb. To shed light on this point, we modify the parallel capacitor model by considering a series connection of a capacitance Cf induced by the ferroelectricity and a common geometric capacitance of back-gate Cg (Fig. 2a, inset). The total capacitance Ctot reads as (Cg -1 + Cf -1)-1, we can isolate the contribution of Cf from Ctot based on the observed Landau fans. Cf turns out to be –12.3 nF/cm2 in the high-capacitance region and 10.7 nF/cm2 in the low-capacitance region for the forward sweep (Fig. 2c); the corresponding values are –12.3 and 11.3 nF/cm2 for the backward sweep, respectively (Fig. 2d). The negative Cf results in a 16-fold increase of Ctot with respect to Cg alone. As a result, the back-gate modulation to carrier density n is efficient in negative Cf region yet highly sluggish in the region of positive Cf. This phenomenon is also supported by the results shown in Fig. 1d, where three Rxx peaks (in the region of negative Cf) exhibit a full-width at half maximum of only 0.004 V/nm in forward sweep while that of the DP1 peak (in the region of positive Cf) is broadened to 0.085 V/nm in backward sweep. The negative capacitance further verifies the ferroelectricity in the sandwiched graphene heterostructure, as has been used for proving ferroelectricity in Pb(Zr0.2Ti0.8)O325 and Hf0.5Zr0.5O226.

The out-of-plane ferroelectric polarization PF can be determined based on the carrier density n in graphene through D = PF + E= ne, where D represents the displacement field comprising PF and electric field E (Fig. 2e, inset). According to the n derived from the Landau fan diagram, we obtain the electric field-dependent PF that forms a unique parallelogram-shaped hysteresis loop (Fig. 2e). When Vb/db is swept forward from -0.25 V/nm, PF linearly increases from a reversely saturated -0.8 μC/cm2 and reaches a saturated value of +1.76 μC/cm2 at –0.20 V/nm, significantly larger than all reported values in previous sliding ferroelectrics. The inequivalent positive and negative polarizations support our theory of co-sliding ferroelectric (see Supplementary Fig. S1). The electric field-dependent PF evolves vice versa for the backward sweep and constitutes a closed hysteresis loop. Moreover, the linear dependence of PF on Vb/db distinctly differs from the nonlinear behavior typically observed in conventional ferroelectrics27, enabling a precise control over polarization-based electric properties.

Electric-field-dependent hysteresis behavior

To further disclose the unconventional ferroelectric loop, we conducted extensive measurements of Rxx against Vb/db sweeps from different, initial back-gate voltages Vbini. During the forward sweep (Fig. 3a), three resistance peaks (DP1, DP, and DP2) were evenly spaced by 0.015 V/nm independent of Vbini, indicating that the negative Cf is involved in sensitively modulating n. However, as PF is completely reversed, Cf becomes positive and the Fermi level turns to slowly shift with the applied Vb/db. As a result, the DP1 peak is not only significantly broadened but also located at a nearly fixed position of 0.014 V/nm. When Vbini is below 20 V, PF cannot be completely reversed even when the Fermi level starts to cross the DP1, such that the negative Cf remains active in modulating n therein, leading to partial sharpening of the DP1 peak on the right-hand side. As Vbini decreases further, the region influenced by negative Cf extends towards zero field since PF gets farther from complete reversal, making the DP1 peak increasingly sharpened (Fig. 3b). Our theoretical calculations suggest that such hysteresis behavior may stems from the ferroelectric lattice dynamics in hBN/Gr/hBN stacks (see Supplementary Fig. S19 for detailed description).

Fig. 3: Gate-dependent ferroelectric switch.
figure 3

The four-probe resistance Rxx as a function of Vb/db during the forward (a) and backward (b) sweeps from different initial back-gate voltage Vbini. The Dirac point of each curve is marked and aligned by a pink dashed line. c Rxx under applied periodic electric pulses. The pulse interval is 0.5 min, respectively. Top: evolution of Vb with time. Middle: the responses of Rxx to the electric pulses of Vb = 15 V. Bottom: the responses of Rxx to the electric pulses with positive Vb of 20 V. The negative Vb is fixed at −10 V. d Electric polarization and coercive field of our OSH devices, compared to previous 2D ferroelectrics.

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We then demonstrate the nonvolatile memory function by subjecting OSH device to a periodic pulse of Vb (Fig. 3c, top panel) and monitoring the corresponding variation in Rxx. Upon applying an electric pulse of Vb = 20 V, Rxx promptly transitions from its intrinsic value of approximately 3 Ω to 3 kΩ (Fig. 3c, bottom panel), dominated by the DP1 peak (Fig. 3b). Periodic applications of positive and negative pulses robustly switch the OSH device between high and low resistance states for twenty consecutive cycles (see Supplementary Fig. S7), validating the inherent ferroelectric nature of OSHs. After reducing the electric pulse to Vb = 15 V, however, no sustainable high resistance state is achieved since this voltage does not sufficiently saturate PF for forming a stable polar state. The threshold Vb/db for switching the electric transport is taken as the coercive field of PF, which is respectively determined to be 0.067 and -0.033 V/nm for positive and negative coercive fields (see Supplementary Fig. S8). These coercive fields are several times lower than the value of ~0.2 V/nm in rhombohedral stacked bilayer TMDs9 and 0.08-0.20 V/nm in doped HfO2 films28,29.

Figure 3d compares the PF and coercive field of our OSH devices with those of previously reported sliding ferroelectrics. Our determined PF of ~12 pC/m (1.76 μC/cm2 × 0.68 nm, by taking the spacing of 0.68 nm between two hBN layers as the dipole separation) is significantly larger than the values in all sliding ferroelectrics, e.g., 2.25 pC/m in stacked hBN bilayers4, 0.6 pC/m in marginally twisted MoS28, 0.12 pC/m in bilayer graphene superlattice16. Notably, this value lies in the same order of magnitude as the remanent polarization ranging from 1-10 μC/cm2 in Si-doped HfO2 nanofilms30. In addition, our OSH device exhibits lower coercive fields only secondary to that of semi-metallic 1 T’-WTe2 bilayers10.

Layer-dependent polarizations and corresponding robustness

To re-validate this robust vdW ferroelelctric, we further fabricated two multilayer OSHs by replacing monolayer graphene with Bernal bilayer and trilayer graphene. Figure 4a shows the Hall carrier density [nHall = B/(eRxy)] of OSH device 5 with bilayer graphene under forward/backward back-gate scans. The parallelogram-shaped loop with two capacitance regions is clearly observed during each unidirectional scan. After converting nHall to PF (Fig. 4b), the positive (negative) ferroelectric polarization PF is determined to be 0.81 μC/cm2 (-0.55 μC/cm2), one half of the values of monolayer-graphene-basis OSHs. In this B-C-C-h stacking order (Fig. 4c), unlike the B-C-h stacking case where the inversion symmetry is completely broken, opposite charge polarization occurs at dual graphene/hBN interfaces (see Supplementary Fig. S20–S21), resulting in a reduced and reversed net polarization. The directions of polarizations are determined by calculating the electrostatic energy profile of each stacking configuration (see Supplementary Fig. S1).

Fig. 4: Robust hysteresis and ferroelectric switching in multilayer OSH devices with Bernal bilayer and trilayer graphene.
figure 4

a nHall as a function of Vb/db during forward (blue) and backward (red) sweeps in OSH device 5. b The extracted polarization hysteresis loop of OSH device 5. c Atomic illustration of OSH device 5 showing the parallel-orientation of bilayer graphene and top/bottom hBN layers. The local registry with vertical B-C-C-h alignment possesses a negative polarization. d The nHall vs Vb/db loop of OSH device 6 with trilayer graphene. e The polarization hysteresis loop of device 6. f The atomic arrangement of the OSHs based on trilayer graphene with vertical B-C-C-C-h alignment. g Structural evolution of the OSHs under co-sliding motions of Bernal stacked multilayer graphene and hBN. Pink background marks the stationary bottom hBN layer. Brown and green arrows mark the sliding direction of graphene and hBN, respectively. h nHall hysteresis loops of OSH device 6 under different Vbini at T = 300 K. i The Rxy response of OSH device 6 under 50,000 electric pulses (Vb = +20/−20 V) at T = 300 K & B = 1 T. Inset is the close-view of 87 switches within 500 s.

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Interestingly, the ferroelectric polarization of OSH device 6 based on trilayer graphene (Fig. 4d, e) increase up to PF = 1.22 μC/cm2, right in between two values of monolayer- and bilayer-graphene OSH devices. With respect to monolayer-graphene-basis OSHs, two graphene/hBN interfaces (Fig. 4f) are mirrorly asymmetric and their couplings become lower because of wider separation, hence reducing the total polarization. Compared with bilayer graphene OSHs, meanwhile, the inversion symmetry of trilayer graphene breaks (see Supplementary Fig. S22–S24) and leads to a relatively larger polarization.

We finally test the robustness of ferroelectric switching behavior against magnetic field, electrical stimuli and elevated temperature. At T = 300 K and B = 1 T, the nHall with respect to Vb/db (Fig. 4h) maintains a well-defined parallelogram-shaped loop at varying initial back-gate voltages Vbini. The corresponding negative capacitance maintains a constant value of -12.7 nF/cm2 in the temperature ranging from 100 K to 300 K (see Supplementary Fig. S25). The gate-dependent polarization and hysteretic behavior allow us to write and read the polarization in a nonvolatile way. After 50,000 write/read cycles, the hall resistances at two states (Fig. 4i) fully recovery and maintain well-defined square waves. The positively charged state can steadily persist for 24 hours after voltage withdrawal but can be instantaneously switched back to the negatively charged state upon application of a negative pulse (See supplementary Fig. S26). It is recognized that the actual memory devices usually work beyond room temperature (for example, 325 K) because of massive heat dissipations. Interestingly, the switching behavior of our ferroelectric device are well duplicated after tens of consecutive pulses at 325 K (see Supplementary Fig. S27), demonstrating itself a potential building block for miniaturized memory devices.

In summary, we have demonstrated monolayer graphene-basis OSH device that exhibits robust room-temperature ferroelectricity up to ~1.76 μC/cm2, several times higher than the reported values in all sliding ferroelectrics, while the coercive field of ~0.07 V/nm can be three times lower. In contrast to conventional metal-oxide-basis ferroelectrics, the ultrathin ferroelectric system composed of graphene and hBN avoids formation of parasitic SiOx layers and any degradation during classical silicon processing, becoming an good alternatives in densely integrated electronics31. Our experimental clues of odd-even parity may substantially expand 2D ferroelectricity boundaries by constructing alternative graphene and hBN stacks and even tandem OSHs. Moving forward, with the successful growth of wafer-scale and single-crystalline graphene32 and boron nitride33, the trinity of robust hysteresis, remarkable controllability and high mobility in the unconventional ferroelectrics opens a wealthy of opportunities for developing ultrathin devices with superior performance.

Methods

Device fabrications

Graphene and hexagonal boron nitride (hBN) were respectively exfoliated on SiO2 (285 nm)/Si wafer by blue ‘magic’ tapes (ELP BT-150E-KL). The graphene and hBN flakes with sharp and straight edges were localized under optical microscope and the edges were analyzed by Raman spectroscope to determine whether it follows the armchair or zigzag lattice orientation34. After that, graphene and hBN were assembled into the hBN/graphene/hBN heterostructure in argon-filled glovebox via our well-established flip and reflection transfer method (see Supplementary Note S4 for details). The final stacks were thermally annealed at T = 200 °C for 48 h in an ultrahigh vacuum ( ~ 5 × 10–10 mbar) chamber.

Configurations of different devices

(1) For OSH device 1, the hBN/monolayer-graphene/hBN heterostructure was perfectly double-aligned in which the zigzag lattice orientations of both hBN flakes and graphene were precisely aligned.

(2) For device 2, top hBN and bottom hBN were parallel-stacked, but the sandwiched monolayer graphene was slightly twisted by an angle of ~2°.

(3) For non-OSH device 3, the top hBN, graphene and bottom hBN were aligned with zero twist. The device was fabricated via a flip without reflection method, the top and bottom hBN flakes were antiparallel-stacked.

(4) For device 4, monolayer graphene and two hBN flakes were completely misaligned.

(5) For OSH device 5, top hBN, Bernal bilayer graphene and bottom hBN were oblique-stacked that produce a vertical B-C-C-h alignment.

(6) For OSH device 6, top hBN, Bernal trilayer graphene and bottom hBN were oblique-stacked, in which vertical B-C-C-C-h alignment of five layers was formed.

Transport measurement

The transport measurements were conducted in a TeslatronPT system (Oxford Instrument) with a base temperature of ~1.5 K. Four-probe measurement was conducted by using lock-in amplifiers (Stanford Research systems: SR830) with a frequency 13.373 Hz and a constant source-drain current of 100 nA. The pulse measurements were conducted by using Keithley 2400 for voltage supply and Keithley 2000 for voltage measurement.

Tight binding calculation

The moiré bands were calculated using a tight-binding model by considering only the pz orbitals. The Hamiltonian is written as:

$$H=-{\sum}_{i,j}T({R}_{i}-{R}_{j})|{R}_{i}\rangle \langle {R}_{j}|+{\sum}_{i}V({R}_{i})|{R}_{i}\rangle \langle {R}_{j}|,$$
(1)

where Ri represents the lattice point at atom site i. V(Ri) is the on-site energy on site i. we assume VC = 0 for carbon atoms, VB = 3.34 eV for boron atoms and VN = –1.40 eV for nitrogen atoms, respectively. T(Ri-Rj) is the transfer integral between sites i and j and is simply built with the common Slater-Koster-type function:

$$\begin{array}{c}T(R)={V}_{pp\pi }\left[1-{\left(\frac{{R}_{z}}{R}\right)}^{2}\right]+{V}_{pp\sigma }{\left(\frac{{R}_{z}}{R}\right)}^{2},\\ {V}_{pp\pi }={V}_{pp\pi }^{0}\exp \left(-\frac{R-{a}_{0}}{{r}_{0}}\right),\\ {V}_{pp\sigma }={V}_{pp\sigma }^{0}\exp \left(-\frac{R-{d}_{0}}{{r}_{0}}\right).\end{array}$$
(2)

Here, Rz is the z-component of the distance R, a0 ≈ 0.142 nm is the distance of nearest-neighbor atoms in graphene, and d0 is the interlayer spacing of graphene. Vppπ and Vppσ are the transfer integrals between the nearest-neighbor atoms of monolayer graphene and the vertically located atoms on the neighboring layers. We adopt Vppπ ≈ –2.7 eV and Vppσ ≈ 0.48 eV to fit the dispersions of graphene. r0 ≈ 0.45 nm is the decay length of the transfer integral35.

Ab initio calculations

The calculations were conducted employing the density functional theory within the VASP code36,37. The exchange-correlation functional utilized was the Perdew-Burke-Ernzerhof (PBE) functional generalized gradient approximation38. To account for core electrons, the projector augmented wave method was employed39. A vacuum region with a width of 15 Å was introduced to the models to effectively isolate adjacent periodic images. The kinetic cutoff energy for plane-waves was set at 500 eV, and for two-dimensional models, a simple 24 × 24 × 1 k-point mesh was employed for the Brillouin zone. The relaxation of atomic structures was carried out until the force on each atom dropped below 0.01 eV/Å, and energy convergence was aimed at 10-5 eV. To capture dispersive forces, the advanced optB86b-vdW method was integrated40,41, and for crystalline polarization evaluation, the Berry-phase method was adopted42. Differential charge density is calculated using the total charge density of the system subtracting the charge density of each constituent part layer. The ferroelectric switching pathways were calculated by the nudged elastic band (NEB) method43 with a cutoff energy of 500 eV and with the force on each atom being less than 0.2 eV/Å. The other parameters for the NEB calculation were set to default values.