Reversible electromechanical manipulation of domain wall in trilayer graphene via ferroelectric sliding

Abstract

Two-dimensional (2D) homo- and heterojunctions in van der Waals materials exhibit remarkable electrical, mechanical, and optical properties, making them promising for diverse applications. In trilayer graphene, ABA (Bernal) and ABC (rhombohedral) stacking domains naturally form homojunctions at lateral boundaries, enabling in-plane semi-metal/semiconductor p–n junctions under a perpendicular electric field. The domain-wall (DW) soliton, characterized by strained carbon rings, plays a key role in these junctions. Here, we present a low-energy approach to dynamically manipulate DW solitons by integrating electrically tunable ABC/ABA homojunctions combining nanoscale shear strain with low-voltage fields by an atomic force microscope (AFM) tip. By leveraging ferroelectric sliding, this method enables precise control over stacking configurations, allowing flexible repositioning of DW solitons. Our work provides a scalable and efficient strategy for tailoring 1D p–n junctions, opening new avenues for nanoscale physical applications.

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New concepts

This work introduces a novel electromechanical strategy to reversibly manipulate domain-wall (DW) solitons in trilayer graphene through ferroelectric sliding, a previously unexplored mechanism in van der Waals homojunctions. By integrating atomic force microscopy (AFM)-induced shear strain (<50 nN) with low-voltage electric fields (±2 V), we achieve precise and energy-efficient control over DW motion. Unlike conventional approaches requiring high mechanical loads, elevated temperatures or strong electric fields, our method exploits weak ferroelectricity in ABC-stacked domains to lower energy barriers for the soliton migration. Crucially, the manipulated DWs exhibit spontaneous self-recovery over time (e.g. 93% recovery after one month), a phenomenon absent in prior studies where solitons remained pinned. This elasticity stems from the metastable strain and polarization states, enabling cyclic reconfiguration of 1D p–n junctions. The discovery of ABC-stacking-dependent ferroelectric coupling advances the understanding of electromechanical interactions in 2D materials, offering a scalable pathway for reconfigurable nanoelectronics and quantum devices.

Introduction

Two-dimensional (2D) homo- and heterojunctions have expanded the potential applications of van der Waals materials, attracting significant interest due to their exceptional electrical, mechanical and optical properties.^1–6 While vertically stacked configurations have been widely studied for their novel physical phenomena,^7–9 such as twistronics^10,11 and sliding ferroelectricity,^12,13 lateral junctions remain relatively unexplored.¹⁴ In trilayer graphene, natural homojunctions arise at the lateral boundaries between ABA-stacked (Bernal) and ABC-stacked (rhombohedral) domains due to intrinsic structural variations.^15,16 When subjected to a perpendicular electric field, ABC-stacked regions develop a bandgap, forming in-plane metal–semiconductor p–n junctions.^17,18 These stacking-dependent electronic and optoelectronic properties can be characterized using techniques such as Kelvin probe force microscopy (KPFM),¹⁹ Raman spectroscopy^20,21 and near-field infrared spectroscopy.²² At the interface, the domain-wall (DW) soliton—a narrow region with strained carbon rings—plays a crucial role in defining the properties of these lateral junctions. Despite the absence of a moiré superstructure,²³ these one-dimensional (1D) p–n junctions offer a promising platform for further interesting explorations.

Various techniques have been developed to manipulate DW solitons in trilayer graphene. Early methods, such as prolonged heating and laser pulses,¹⁶ enabled transitions between stacking configurations but required high energy input. Mechanical stress, applied using micronewton-level forces via a blunt atomic force microscope (AFM) tip, has also been employed to reposition DWs.²⁴ Additionally, vertical electric fields of tens of volts can induce similar effects, allowing control over ABC/ABA stacking configurations.²⁵ However, these approaches often involve high temperatures, substantial mechanical loads, or elevated voltages, limiting their practicality for energy-efficient applications. In this study, we introduce a novel method for manipulating 1D p–n junctions in trilayer graphene through ferroelectric sliding. By applying nanoscale forces with a standard AFM tip, DW solitons can be precisely repositioned via an electric-mechanical coupling. Notably, the manipulation is reversible over time, depending on the number of operations. This scalable and efficient approach provides a promising pathway for the precise control of atomically thin p–n junctions, advancing their potential for nanoscale electronic and mechanical applications.

Results and discussion

To characterize stacking configurations in trilayer graphene, we conducted atomic force microscopy (AFM) measurements on samples transferred onto a SiO₂/Si substrate using a soft probe (spring constant k ≈ 0.2 N m⁻¹). The AFM topographic image (see Fig. 1(a)) shows a graphene flake with a height of 1.26 nm, consistent with the thickness expected for trilayer graphene in the consideration of the interlayer spacing.²⁶ However, conventional topography does not resolve the lateral domain walls (DWs) between ABC- and ABA-stacked regions. To identify these subtle boundaries, we employed piezoresponse force microscopy (PFM), a reliable technique for distinguishing stacking heterostructures.²⁷ As shown in Fig. 1(b) left, PFM electrostatic responses clearly differentiate ABC and ABA domains, confirming distinct out-of-plane polarizations. When applied with a perpendicular electric field, the ABC-stacked domain transitions to a semiconducting state due to its opened bandgap,^18,20 leading to enhanced charge accumulation from efficient screening effects.²⁸ This increased activity is reflected in the PFM amplitude channel, where ABC regions exhibit stronger responses than ABA regions. Additionally, DW boundaries are also distinguishable in the friction force signal, as shown in Fig. 1(b) right, aligning with previously reported tribological behavior in ferroelectric LiNbO₃ crystal.²⁹ The frictional contrast between domains likely stems from differences in interlayer bonding. The asymmetric ABC stacking disrupts electron–phonon coupling between graphene layers,³⁰ lifting surface puckering and then friction forces.³¹

Fig. 1 Characterization of ABC and ABA stacking domains in trilayer graphene. (a) Topography of trilayer graphene on SiO₂/Si substrate scanned by AFM, with the inset of step height for graphene flake. (b) Polarized amplitude (left) and friction force (right) measured by PFM (V_AC = 2 V, ω = 24 kHz). (c) Compensated potential measured by KPFM, with the normalized histogram of work function difference between ABC and ABA domains shown in (d). Scale bars for (a) and (b): 4 μm, (c): 1 μm.

Kelvin probe force microscopy (KPFM) was used to further characterize the compensated potential difference (CPD) of the trilayer graphene. As shown in Fig. 1(c), the ABC-stacked domains exhibit a higher surface potential than the ABA-stacked domains, with the silicon substrate displaying the lowest potential. In our KPFM setups, an AC modulation voltage combined with a DC bias was applied to the tip, resulting in opposite surface potentials and work functions, as described by the following equation:

where ϕ_s and ϕ_f represent the work functions of the substrate and sample films, respectively. When the AC and DC biases are applied directly to the sample holder, approximate surface potential and work function values can be obtained.^32,33 Using the known work function of SiO₂ as 5.05 eV³⁴ and the measured CPD value of 35 mV^19,35 (see Fig. 1(d)), the work functions of ABC and ABA stacking are calculated to be 4.884 eV and 4.917 eV based on eqn (1), respectively. The lower work function of the ABC-stacked region facilitates easier electron escape, reducing surface charge accumulation and leading to a lower resonant amplitude in PFM when V_AC = 0 V (see Fig. S1, ESI†). Collectively, the differences in friction force, resonant amplitude and surface potential observed through PFM and KPFM highlight the intrinsic electrical and mechanical distinctions of ABC- and ABA-stacked regions along the DW soliton. Domain wall (DW) manipulation in trilayer graphene was performed using friction force microscopy (FFM) under a direct current electric field. As shown in Fig. 2(a), friction-normal force curves were obtained with external loads and voltages ranging from −10 nN to 60 nN and −2 V to 2 V, respectively. The ABC-stacked domains (dashed lines) exhibited higher friction forces than the ABA-stacked domains (solid lines), consistent with their differing interlayer bonding strengths. This behavior aligns with observations in other 2D stacking heterostructures, exhibiting lower work functions and accompanied higher friction forces.^33,36,37 Under an applied DC electric field, the friction-normal force curves at 0 V and ± 1 V remained relatively linear with increasing normal force, while friction increased at higher bias. This increase is attributed to additional electrostatic adhesion forces at the tip-sample interface, which scale with the square of the applied voltage^38,39 (see Fig. S2 and S3, ESI†). These findings highlight the complex interplay between work function differences, interlayer interactions and tip-sample electrostatics in governing frictional behavior during DW manipulation.

Fig. 2 Friction force and DWs manipulation under the applied electric field and normal force: (a) Friction-normal force curves with DC bias of 0 V, ± 1 V and ± 2 V for both ABC and ABA domains. (b)–(f) DWs manipulation by loaded AFM tip under 0 V, ± 1 V and ± 2 V, respectively, with the selected loading force of 10 nN, 30 nN and 50 nN in each figure. The green arrows are the moving directions of DW at ± 2 V. Scale bars: 500 nm.

Frictional images at 0 V and ± 1 V were selected under normal forces of 10 nN, 30 nN and 50 nN, respectively, as shown in Fig. 2(b)–(d). At these external conditions, no significant DW manipulation was observed. However, this stability was disrupted when the voltage was increased to ± 2 V. As shown in Fig. 2(e) and (f), the DW remained unchanged at 10 nN but exhibited clear displacement at 30 nN and 50 nN, shifting from the ABC-stacked (high friction) to the ABA-stacked (low friction) regions. This behavior is consistent with previously reported DW manipulation through the tip dragging along the friction-reduced direction.^24,40

Notably, the friction-normal force curves at ± 2 V in Fig. 2(a) differ from those at lower biases, showing a linear increase up to 30 nN but plateauing beyond that point. This suggests enhanced energy dissipation at higher voltages, facilitating DW manipulation during frictional sliding and reducing friction growth beyond 30 nN. This electro-mechanical coupling mechanism effectively lowers the energy barrier for DW soliton motion, enabling ABC-to-ABA transitions under relatively low DC voltages and moderate normal loads. The energy consumption per unit area for DW manipulation here is speculated to be around 1 J m⁻², where E_mech = F_f·L = 2 × 10⁻¹⁵ J (here friction force F_f = 4 nN, sliding distance L = 500 nm), E_elec = 0.5CU² = 0.5 × 4ε₀r·U² = 4.45 × 10⁻¹⁸ J (here tip radius r = 20 nm, ε₀ = 8.85 × 10⁻³ F nm⁻¹, U = 2 V, ignored in comparison to E_mech) and A_tip = πr² = 1.25 × 10⁻¹⁵ m². Owing to the electromechanical coupling, the order of magnitude is much lower than the laser-induced ∼10⁶ J m⁻² (e.g. pulse width = 5 ns, energy = 1 μJ and spot size = 1 μm²) or thermal ∼10⁴ J m⁻² (e.g. power = 100 mW, time = 10 s and area = 100 μm²) methods.¹⁶

A key feature of DW soliton migration in this study is its reversible self-recovery over time. Unlike previous reports where artificially induced DW structures in trilayer graphene remained stable for months under micronewton forces,²⁴ our experiments reveal that DWs begin to recover shortly after the manipulation. As shown in Fig. 3(a), the intact DW soliton shifts further into the ABA-stacked region after friction measurements, creating two noticeable splits along the initial DW baseline (see the black arrows and dashed line in Fig. 3(b)). By the following day, one of splits fully recovers, while the larger split exhibits more than 50% recovery (see the white arrow in Fig. 3(c)). The DW soliton also moves closer to its original position, as seen by comparing Fig. 3(b) and (d). However, by the third day (see Fig. 3(e)), the recovery speed is decelerated, with only ∼30% of the split healing. This suggests the fatigue occurred during the reciprocal movement and recovery process, rendering the DW soliton increasingly fragile. After repeated friction experiments (see Fig. 3(f)), larger splits emerge, shifting farther from the initial DW baseline. Comparing single and repeated manipulations, the former allows easier recovery to the original soliton position, while the latter induces fatigue, requiring longer relaxation time for the dissipation of stored strain and energy in the metastable DW solitons.

Fig. 3 Friction force maps of DWs manipulation via electro-mechanical coupling from: (a) and (b) Day 1, before and after friction experiments, respectively. (c) and (d) Day 2, with the white and black arrows for recovery and manipulation directions, respectively. (e) and (f) Day 3. (g) Day 4 for only DW recovery without any friction experiments. (h) Day 11 for DW recovery (one week after day 3). (i) Day 33 for DW recovery (one month after day 3). Scale bars: 2 μm.

To investigate the recovery behavior following repeated DW soliton manipulations, we drew an analogy to the cement curing, which progresses over intervals of 3 days, 7 days and 28 days to achieve full hydration and maximum strength.⁴¹ Similarly, after friction experiments shown in Fig. 3(f), the sample was kept untested for intervals of 1 day, 1 week and 1 month to evaluate the DW recovery. As shown in Fig. 3(g)–(i), the DWs gradually reformed, with recovery rates increasing from 15% to 93%. Notably, after one month (see Fig. 3(i)), the DW structure had nearly returned to its original state, comparable to the recovery observed after a single manipulation within just one day (see Fig. 3(c)). The self-restoration behavior originates from elastic relaxation of strain localization. Low-energy input (30–50 nN and ± 2 V) displaces DW solitons into metastable states without triggering plastic deformation. The strain energy gradient drives solitons back to the energy-minimum configuration, with recovery rate obeying: τ⁻¹ = v₀ exp(−E_a/k_BT). This mechanism contrasts with high-force methods²⁴—where μN-level inputs exceed graphene's yield strength—causing permanent bond rupture. Unlike pinned DW solitons that remain trapped following high-load manipulations, the reversible electro-mechanical approach enables elastic displacement, facilitating gradual recovery. The extent and rate of this recovery depend on the manipulation frequency, with longer resting intervals allowing greater relaxation and energy dissipation within the metastable soliton structure. Previous studies have shown that manipulating DW solitons between ABC and ABA domains using high force or strain usually results in permanent pinning.^24,42 Similar effects have been observed under high gate voltages exceeding tens of volts.²⁵ However, in our study, the observed self-recovery of DW solitons suggests that mechanical loading alone does not solely determine their stability. This raises the question of how the electric field contributes to the electro-mechanical coupling process during DW manipulation. While high-voltage fields enhance conductivity differences between the ungapped ABA and gapped ABC-stacked trilayer graphene,¹⁸ low-voltage fields (below ± 5 V) have minimal influence on the ABC domain's bandgap. Considering the critical displacement field theory,¹⁸ it established that bandgap opening in ABC-stacked trilayer graphene requires a critical perpendicular displacement field (D_c). For trilayer graphene, D_c ≈ 0.25 V nm⁻¹ is necessary to break layer degeneracy and open a bandgap. On a standard d = 285 nm SiO₂ dielectric (κ = 3.9), this translates to a gate voltage threshold as V_c = D_c·d·e/ε₀/κ ≈ 18 V, indicating a theoretical minimum for bandgap modulation in trilayer graphene. Similarly in the Raman response modeling,²¹ it predicted that bandgap-induced phonon softening in ABC domains produces a measurable G-band redshift (Δω_G > 2 cm⁻¹) only when |V_g| > 15 V. At low electric fields (|V_g| < 10 V), electron–phonon coupling remains unperturbed, leaving ω_G unchanged. Overall, these evidences suggest an alternative mechanism driving DW soliton manipulation under electro-mechanical conditions, distinct from the effects of high-voltage fields or mechanical force alone.

Sliding ferroelectricity is a potential mechanism driving the electrical responses that facilitate DW soliton manipulation. This phenomenon has been widely observed in monolayers of In₂Se₃ and CuInP₂S₆, as well as in parallel-stacked multilayers of h-BN and transition-metal dichalcogenides (TMDs).^13,27 In the case of ABC-stacked domain, the introduction of asymmetry by the third layer suggests a similar effect. To investigate this, we performed PFM measurements on trilayer graphene to measure the ferroelectric hysteresis. Fig. 4(a) presents the amplitude and phase mappings of ABC- and ABA-stacked regions. Under polarization testing conditions (V_AC = 4 V and ω = 32 kHz), amplitude and phase curves were recorded for both domains. In the ABA-stacked region (see Fig. 4(b)), the amplitude curves overlap significantly, with a minimum value around ∼0.828 V, corresponding to the CPD between the tip and sample (see Fig. 1(d)). At this point, the amplitude approaches almost zero, and the phase curve flips, forming a distinct hysteresis loop with pronounced oscillations.

Fig. 4 Characterization of ferroelectric hysteresis loop. (a) Amplitude and phase of ABA and ABC domains, with the testing points marked in the circles. (b) and (c) Hysteresis behaviors measured at V_AC = 4 V for ABA and ABC domains, respectively. Scale bar: 1 μm.

In contrast, the polarization curves of the ABC-stacked region exhibit distinct behavior, as shown in Fig. 4(c) (with full tip bias details provided in Fig. S4, ESI†). The forward and backward amplitude curves forms a double butterfly shape, which correspond to a hysteresis area highlighted by the phase curves. It indicates the observation of ferroelectricity in the ABC domain, though significantly weaker compared to conventional ferroelectric materials like perovskites.^29,43 While ABA domains show negligible hysteresis, it excludes substrate-induced artifacts, as both domains share the same SiO₂/Si substrate. Although PFM hysteresis may arise from non-ferroelectric effects (e.g. charge injection⁴⁴), the domain-specific response in ABC regions, the correlation with DW motion voltage, and consistency with rhombohedral graphene literature^45,46 collectively point to sliding ferroelectricity as the most plausible origin. Thirdly, in ABC stacking, polarization reversal occurs via interlayer slip,^12,13 not ionic displacement. Applied ± 2 V biases induce identical slip directions (e.g. top-layer sliding to rightward in Fig. 2(e) and (f)), displacing DWs toward ABA regions regardless of voltage polarity. This contrasts with traditional ferroelectrics (e.g. LiNbO₃) where polarization direction dictates motion.²⁹ Furthermore, the coercive voltage in PFM (±1.5 V, see Fig. 4(c)) aligns with the threshold for DW motion (±2 V), confirming coupling between ferroelectric switching and soliton dynamics. Both phenomena are voltage-symmetric (occur identically at +V and −V), inconsistent with unidirectional effects like ionic drift. Rather than a bandgap opening, the observed ferroelectric activation in the ABC domain facilitates the electro-mechanical coupling responsible for driving DW soliton motion toward the ABA-stacked region. Deterministic DW positioning gates carrier transport between metallic (ABA) and semiconducting (ABC) regions, exploiting the intrinsic work function difference (see Fig. 1(c)) for gate-free switching. This achieves ultralow switching energy, outperforming phase-change devices by orders of magnitude. Crucially, DW recovery to >90% of its original state after 1 month (see Fig. 3(i)) ensures long-term stability absent in filamentary memristors, enabling energy-efficient memory. Furthermore, sub-5-nm DW solitons (see Fig. 1(b)) act as tunable barriers for valley-polarized electrons, facilitating atomic-scale control of quantum interference. Integration with h-BN encapsulation—a standard van der Waals fabrication process—ensures scalability without degradation. These features bypass high-voltage or mechanical inputs, utilizing instead the weak ferroelectric response of ABC domains for deterministic and low-energy control.

Conclusions

We demonstrate a reversible and energy-efficient approach to domain-wall (DW) soliton manipulation in trilayer graphene using ferroelectric sliding. Unlike conventional methods requiring high force or strong electric fields, our electro-mechanical strategy enables controlled DW motion with low-voltage fields and nanoscale forces. Our findings reveal that DW solitons self-recover over time, with recovery rates dependent on manipulation frequency and relaxation intervals. It reveals an elastic self-recovery mechanism (recovery rate >90%) that fundamentally differs from irreversible pinning dominated by mechanical forces, establishing a new pathway for reconfigurable devices. Additionally, weak ferroelectricity in the ABC-stacked domain facilitates DW motion, driven by electro-mechanical interactions rather than bandgap modulation. While electrostatic contributions to PFM hysteresis cannot be fully excluded, the synergy of (i) domain-specific ferroelectric signatures, (ii) voltage-symmetric DW manipulation, and (iii) interfacial built-in fields collectively support sliding ferroelectricity as the dominant mechanism. It provides a scalable method for tuning stacking domains in trilayer graphene, offering insights into gate-tunable DWs serving as atomic-scale channels in field-effect transistors, while reversible electromechanical switching aligns with memristor functionality for neuromorphic computing. This approach may further facilitate quantum devices (e.g. valley filters) by tailoring spin-polarized edge states along DWs.

Author contributions

Z. L. conceived the original idea and the experiments. Z. L., Y. Y. W. and W. O. wrote the manuscript; Z. L., J. Y. Z. and F. L. acquired the research funding. All authors discussed the results and revised the manuscript.

Conflicts of interest

The authors declare no competing interests.

Data availability

Data required to evaluate the conclusions here presented is fully provided both in the main manuscript and the ESI.†

Acknowledgements

We gratefully acknowledge the financial support by the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB0470101), the National Key Research and Development Program of China (2021YFA1601004), as well as the National Natural Science Foundation of China (52405228, 12472099 and U2441207).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5mh00921a

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