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Youngki Yeo, Yoav Sharaby, Nirmal Roy, Noam Raab, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Moshe Ben Shalom

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This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1038/s41586-024-08380-2.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Polytype switching by super-lubricant van der Waals cavity arrays](https://mdr.nims.go.jp/datasets/05f3d7ac-1f37-4be8-a9a9-5786fb0f723e)

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Polytype switching by super lubricant van der Waals cavity arrays  Youngki Yeo1, Yoav Sharaby1, Nirmal Roy1, Noam Raab1, Kenji Watanabe2, Takashi Taniguchi3, Moshe Ben Shalom1*1School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel2Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan3Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan*School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel. e-mail: moshebs@tauex.tau.ac.ilExpanding the performance of field effect devices is a key challenge of the ever-growing chip industry at the core of current technologies1. Nonvolatile multiferroic transistors that control atomic movements rather than purely electronic distribution are highly desired2. Recently, a field effect control over structural transitions was achieved in commensurate stacking configurations of honeycomb van der Waals (vdW) polytypes by sliding boundary strips between oppositely polarized domains3–6. This ferroelectric hysteretic response, however, relied on preexisting dislocation strips between relatively large micron-scale domains, severely limiting practical implementations3,7,8.Here, we report the robust electric switching of single-domain polytypes in nm-scale islands embedded in super lubricant vdW arrays. We etch cavities into a thin layered spacer and then encapsulate it with functional flakes. The flakes above/under the lattice-mismatched spacer sag and touch at each cavity to form islands of commensurate and metastable polytype configurations. By imaging the polytypes' polarization, we observe nucleation and annihilation of boundary strips and geometry-adaptable ferroelectric hysteresis loops. Using mechanical stress, we further control the position of boundary strips, modify marginal twist angles, and nucleate patterns of polar domain. This Super Lubricant Arrays of Polytype (SLAP) concept suggests “slideTronics” device applications such as elastic-coupled neuromorphic memory cells, and non-volatile multi-ferroic tunneling transistors and programmable response by designing the size, shape, and symmetry of the islands and of the arrays9.MainUnlike electronic transitions, crystalline structural transitions are challenging to control due to considerable energy barriers associated with breaking solid bonds at ambient conditions, away from the lattice melting temperature. Nevertheless, some materials may exhibit practical transitions between amorphous and crystalline orders in response to external stimuli like optical or electric pulses10. Switching the discrete periodic symmetries in these "phase-change" materials directly impacts their collective lattice excitations and numerous subsequent properties. Thus, electric control of structural transitions enables, in principle, switching of intrinsic responses such as light emission, conductivity, and magnetic order in so-called multiferroic devices11.Exceptional electric field switching between vdW polytypes with discrete commensurate stacking configurations that break inversion and mirror symmetry was recently demonstrated 12–14. Owing to relatively weak interlayer adhesion and high planar stiffnesses, partial dislocations strips between domains with opposite structural and polar orientations elongate and slide3 to expand better-stable configurations of co-aligned polarization Pz. These stacking-fault dislocation strips in polytypes of honeycomb graphene15, hexagonal boron nitride16 (h-BN), or transition metal dichalcogenides17 (TMDs), are ~ 30 atoms wide as determined by the Burgers vector in the partial dislocation (one bond length), the potential well energy in the commensurate state (~one meV per atom), and the planar elastic modulus18 (~1 TPa). The energy cost of these dislocation strips due to the extra layers' separation and planar strain is ~1 eV per nm length16. Thus, electric nucleation of a boundary strip that crosses the system, an essential step for structural transition, is restricted at room temperature (below the turbostratic transition19), even if cutting the structure into small nanoscale islands and applying the external field locally3. Apparently, the open dangling bonds at the physical edges of the layers tend to zip the layers together and restrict interlayer motions7. As a result, previous electric hysteresis measurements have relied on preexisting dislocations in micrometer-size structures3,7,8,20,21. Additional challenges arising in mechanically assembled interfaces are uncontrollable twists and stiff moiré networks that suppress the sliding motion and restrict local switching. Moreover, after removing the external field, the rigid strip network pulls the moiré pattern back to its initial dimensions and hence eliminates the desired hysteretic memory response7,22. The Super Lubricant Arrays of Polytypes (SLAP) concept reported here overcomes these challenges by embedding tiny commensurate islands in an incommensurate super lubricant medium. It enables electrical domain nucleation and subsequent switching of nanoscale single-polytype islands. Given the polytype-dependent electronic phases reported to date such as cumulative polarizations23–25, superconductivity26, spin27, orbital28, and topological orders29, the structural switching of SLAP islands by electric field offers appealing multiferroic control mechanisms for subsequent electronic responses9.Superlubricity-mediated slidingThe main idea behind our SLAP devices is to 1) Squeeze the active polytype interface into small cavity islands with loower dislocation nucleation energy costs, but without physically cutting the functional layers and introducing open edge bonds (see Figure 1). 2) Use lattice mismatched or considerably twisted layered spacers to enable super-lubricant motion outside the active islands that further support dislocation nucleation. These "not-active" incommensurate regions between the cavities eliminate the stiff topological networks of boundary dislocations between commensurate domains that suppress the sliding and prevent switching9,15. Moreover, these regions facilitate exceptionally high sliding lubricity with record low ~10-5 friction coefficients30–32 and hence mediate long-range elastic interactions between the cavities, which are typically restricted by any pinning barrier. For example, the commensurate pining barrier that prevents super lubricity ~1meV/atomic area  confines the planar strain relaxation range to a few nm wide boundary strip only. This range (or strip width)  ~7 nm 15,33 is determined by minimizing the planar elastic energy ~  ( ~150 N/m the shear stiffness,  nm the bond length) and the misalignment energy cost ~ . Therefore, planar stress fields emerging in layers which are part of a super lubricant interface with residual pining much below  may extend substantially beyond  and elastically couple adjacent islands9. Figure 1 illustrates cross-sectional and top views of the superlubricant array concept using a graphene spacer and functional h-BN flakes. We etch circular cavities into a graphene bilayer (BLG, see the identical carbon spheres in Fig.1a) using the electrode-free local anodic oxidation (LAO) method34 (see Methods). Then, we encapsulate the BLG with h-BN layers (blue and yellow spheres, respectively) that sag to touch at the cavity position, forming aligned commensurate AB or BA interfaces (dark/bright brown shaded). These stable polytype configurations break inversion and mirror symmetry as shown by the unit cells line-cuts along the armchair direction (see rectangular frames), inducing vertical polarization at this active interface. Outside the cavity, on the other hand, the h-BN/graphene interfaces are incommensurate owing to lattice mismatch and finite twist angle (blue-shaded interfaces). Fig.1b shows a top view of a cavity array design with various cavity diameters and inter-cavity spaces. Outside the blue-shaded spacer (top right side), triangular domains of AB and BA configuration form, with opposite structural orientations and internal polarizations Pz (noted by bright/dark colors)3. Islands of non-polar AA' and AB1' polytypes that preserve inversion symmetry (also illustrated) appear in regions of antiparallel functional layers as expected for an extra (rotated) interfacial layer14 (dashed-dotted line frame, top view).Imaging switching by surface potentialTo monitor the cavity polytypes, as a ferroelectric-case study, we use flakes of h-BN or WSe2 as the functional encapsulating crystals (see Device 1-3 details in Methods and Extended Data Table 1, Extended Data Fig. 1). A parallel commensurate stacking of these binary compounds spreads the electrons unequally between the top and bottom layers, inducing interfacial-confined polarization Pz. Each interfacial shift by a single inter-atomic distance switches the untwisted AB stacking to BA and vice versa, which is equivalent to switching the interface and Pz upside down12 (see rectangular frames in Fig. 1a). Hence, monitoring Pz is an exceptional sensor for minute interfacial shear motions, with opposite Pz orientation in adjacent AB/BA modifying the electric surface potential by ∆𝑉~240, 120 mV for h-BN and WSe2, respectively3,5,14, allowing us to distinguish each polytype configuration. Figure 1c presents an atomic force microscope (AFM) topography map of the device structure illustrated in Fig.1a,b. We cut the graphene spacer with straight borders, punctured 300, 200, 100, and 20 nm cavity diameters, and used 2 nm thick flakes of functional h-BN (see darker circles, and further details in Methods and Extended Data Fig. 2).The surface potential map, measured by Kelvin Probe Force Microscopy (KPFM, see methods), is presented in Fig. 1d. Outside the spacer, at the top and right sides of the map, bright/dark domains differing by 240 mV potential steps confirm the formation of polar AB and BA interfaces. Notably, the same bright/dark circles at the cavity's location reveal uniform single-domain polytypes embedded in uniform spacer potential. A similar response is observed in Device 2 with a monolayer graphene spacer (Fig. 2, Extended Data Figs. 1, 3-7) and Device 3 with a trilayer graphene spacer and WSe2 monolayers as the functional flakes (Fig. 3, Extended Data Fig. 1). We note that all cavities above the dashed dark line in Fig.1d appear either bright or dark. Conversely, below this line, the potential at the cavities and outside the spacer is measured to be the average potential as expected for non-polar antiparallel interfaces. The topography map in this section confirms an additional h-BN layer in the bottom flake (7/6, 7/5 layers in the top/bottom flake below/above the dashed line, respectively) and the formation of mirror symmetric AA' or AB1' interfaces3,14 (as in the naturally grown 2H flakes, see framed illustration in Fig. 1b). Altogether, the topography and potential maps confirm commensurate interface formations in pristine cavity arrays spanning many µm2 regions, released from external contaminations, even at the circular edges of the spacer. Dislocation nucleation and annihilationTo explore the cavities switching dynamics, we applied external displacement fields between the AFM tip and a bottom graphite electrode using bias contact scanning mode (see Methods). A set of poling and then imaging maps are taken above representative cavities with different diameters (Fig. 2a). Figure 2b shows surface potential maps of a 150 nm wide cavity after increasing/decreasing the poling bias by 0.3 V steps, corresponding to electric displacement field steps of 0.05 V/nm. Notably, a new dislocation strip nucleates at ~ 0.3 V/nm and then slides at a coercive field Ec ~ 0.6 V/nm to entirely switch the cavity between uniform single-domains of up/down polarization. While previously reporting smaller coercive fields of ~ 0.3 V/nm, we note that these former experiments3 could only slide preexisting dislocation strips without nucleating new strips up to displacement fields as high as 1.5 V/nm and dielectric breakdown.To analyze the hysteresis loop and the intermediate polarization states, we plot the relative coverage of up (bright) domains, . A complete set of maps is shown in Methods and Extended Data Fig. 3 and was repeated over five switching cycles. The hysteresis loops of three additional cavities marked in dashed frames in Fig. 2a are presented in Methods and Extended Data Fig. 4. While the 150 and 250 nm cavities show similar hysteresis windows, we could only switch the 350 nm cavity partially under electric displacements as high as 1 V/nm (before the sample is damaged). In all cavities, the center of the hysteresis loop shifts to positive or negative potentials with no apparent sign preference. Since vertical electric fields from the asymmetric tip/graphite electrodes or flexoelectric effects should show sign preference35, we attribute the random shifts to elastic coupling with adjacent cavities and remote pinning by nearby contaminants. We also find strip elongations aligning with the smaller width axes of the oval-shaped cavities (see the two bottom left cavities in Fig.2a). Such tendency to shrink the strip length and to snap many cavities into single domains (see Fig.1d) testifies that releasing the strain to the lubricant interfaces is energetically favorable. Occasionally, we find intermediate triangular domains snapping into 120- or 180-degree head angles rather than straight boundary strips (see the Illustration in Fig. 2c, Methods, and Extended Data Fig. 5).Mechanical switching and twistsMechanical nucleation and reconfiguration of domain boundaries were previously observed under vertical loads as low as 600 nN in oxide ferroelectric films36, and 400 nN in case of preexisting dislocation strips between non-polar graphitic polytypes (ref.37). Dislocation nucleation and domain switching required more intensive mechanical loads exceeding 40 µN (ref.38). Even greater nucleation challenges appear in twisted interfaces due to the rigid moiré network and topologically defined number of alternating domains for a given global twist angle15. Once the planar relaxation clicks the layers into commensurate domains, the external stress impact becomes irreversible39,40.To assess the mechanical switching dynamics in SLAP devices, we scanned the arrays in AFM contact mode while applying vertical pressures of 50 to 300 nN and keeping the slow axis scan direction parallel to the underlining armchair direction (see Methods). Figure 3a presents three surface potential maps of Device 3 (with WSe2 as active layers) measured before and after applying a vertical pressure of 300 nN at times – t1, t2, t3. Notably, the domain patterns modify between the scans in nearly all cavities. The red/blue rectangles mark relatively large cavities in which triangular domains are tuned to a single/double domain pattern and back, respectively, as illustrated in Fig.3b. We find a threshold load for domain nucleation and motion of ~200 nN (Fig. 3), corresponding to a pressure of ~161MPa (see Methods and Extended Data Fig. 6)  on a ~1000 nm2 effective tip diameter, and a planar shear force of ~30 nN measured by the horizontal deflections of the tip (as measured by the horizontal deflections of the tip, Extended Data Fig. 8). We note the 100 nm triangular domains appearing in Device 3 due to a twist angle of ~0.1 between the active layers while Device 1,2 show more uniform islands. We attribute the triangular domains in this device (rather than snapping into uniform islands) to a larger residual pinning potential in addition to the twist angle. This domain pattern further depends on the cavity dimensions, and the distance to nearby cavities that also pin down the moiré network. In some cases, we could push and pin down the dislocation strip within the cavity by scanning the fast axes along the strip axes. Fig. 3c shows such a strip that precisely follows the end position of the scanning pattern.Conclusions and outlookWhile the reported SLAP devices behave as exceptionally sensitive strain detector, with any mechanical shift by one atomic spacing changing the cavity color in the potential map, we find the electric switching of uniform polytypes within each island to be the main observation reported here. The electric nucleation of boundary strips that slide spontaneously to annihilate at the island boundary and switch uniform polytype configurations implies efficient device concepts that were practically out of reach to date. Moreover, coercive switching fields that depend on the island dimensions and the long-range elastic coupling to adjacent cavities in the array, suggest novel tools to design the overall switching dynamics and response. 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Mechanical writing of ferroelectric polarization. Science 335, 59–61 (2012).37. Tsuji, T., Irihama, H. & Yamanaka, K. Observation of anomalous dislocation behavior in graphite using ultrasonic atomic force microscopy. Jpn. J. Appl. Phys. 41, 832–835 (2002).38. Jiang, L. et al. Manipulation of domain-wall solitons in bi- and trilayer graphene. Nat. Nanotechnol. 13, 204–208 (2018).39. Ribeiro-Palau, R. et al. Twistable Electronics with Dynamically Rotatable Heterostructures. Science 361, 690-693 (2018).40. Yang, Y. et al. In Situ Manipulation of van Der Waals Heterostructures for Twistronics. Sci. Adv. 6, eabd3655 (2020).41. Gilbert, S. M. et al. Alternative stacking sequences in hexagonal boron nitride. 2D Mater. 6, 021006 (2019). Main figure legendsFig. 1: Super-Lubricant Array of vdW Polytypes (SLAP). a,b, Sideview, and Top view device illustrations. The line cut shows a pair of cavities etched in a bilayer graphene spacer (identical carbon spheres) and encapsulated by two parallel h-BN layers (yellow and blue spheres). Commensurate h-BN interfaces of AB/BA polytype configurations at the cavities are shaded with dark/bright brown color for down/up internal polarizations. Lubricant incommensurate interfaces with the spacer are cyan-shaded. The right-side cavity island shows mixed BA/AB domains separated by a w-wide partial dislocation strip. The dashed-dotted line borders a region of antiparallel AA' and AB1' polytypes41 islands marked by dark blue/bright blue colors, respectively. c, Topographic image of Device 1 with two nm thick parallel h-BN flakes. Note the brighter (one layer thicker) surface below the dashed-dotted line. d, Corresponding electric surface potential map by Kelvin probe force microscopy (KPFM).Fig. 2: Electric field-induced dislocation nucleation and annihilation. a, AFM topography and surface potential maps of Device 2 before electric field poling. b, The relative bright domain area () in the 150 nm cavity marked by a solid line frame in a, as a function of the tip bias during the electric poling scan before imaging. The coercive switching fields are indicated by bright/dark bars. Full hysteresis loop maps of all marked cavities are shown in Extended Data Figs. 3,4. c, Illustration of intermediate domain structures observed in the experiments (see Extended Data Fig. 5). Fig. 3: Mechanical nucleation and reconfiguration of confined domain patterns. a, Surface potential maps of Device 3 with functional WSe2 monolayers before and after contact mode scans at a tip force of 300 nN. Black arrows show the orientation of the slow and fast contact scanning axes before the non-contact imaging. b, Schematic illustration of the cavity topologies observed, including single, two, and multi-domains of twisted moiré patterns. c, Surface potential maps taken after pressure scanning the regions marked in dashed lines. Scanning the fast axes perpendicular to the boundary strip in the forward direction only (straight arrows) does not change the final pattern, while back and forward scanning of the fast axes along the strip (armchair) direction (curved arrows) controls the boundary position accurately and reversibly. MethodsSample preparation: Our vdW cavity arrays include (top to bottom): h-BN / top functional layer / graphene spacer / bottom functional layer / graphite gate electrode / SiO2 substrate assembled using dry polymer stamping method with either monolayers WSe2 or few layers h-BN as the functional layers.Device characterizationIn the main text we present data from three selected devices. Device 1, (Figure 1) with a 4.3 nm thick h-BN flake used to pick up active 2.3 nm and 2 nm active h-BN flakes, and a bilayer graphene spacer. In device 2 (Figure 2) we used 2.5 nm thick h-BN to pick up trilayer h-BN (1 nm), monolayer graphene spacer, and trilayer h-BN. In device 3 (Figure 3) we used a 4.5 nm h-BN to pick up monolayer WSe2, graphene spacer and monolayer WSe2. Thicknesses of the Flakes are summarized in Extended Data Table 1, and an optical microscope image of each device is shown in Extended Data Fig. 1. Pick-up h-BN, top layer, graphene spacer, bottom layer are outlined with red, green, blue, and orange lines respectively.Graphene spacer lithographyThe quality of the cavity edges is crucial to minimizing the pinning of dislocation boundary strips. Our best results were obtained using the electrode free local anodic oxidation (LAO) lithography method34. Step-by-step procedures are summarized as follows, a. Choose the wrinkle- and tape-residue free graphene monolayer with optical microscope.b. Pt-coated AFM tip (Mikromasch HQ:NSC35/Pt Tip C) was used to clean 1010  lithographic area in advance for removing dirt which is not captured by optical microscopy. Relative humidity (RH) was maintained 60-80 % to boost chemical reaction between tip and graphene with commercial humidifier.c. Tip was retracted from the graphene surface to form water bubbles on the tip edge. 10 VAC, 40 kHz were applied in PFM mode (NX10, Parksystem inc.).d. Using the lithographic option in NX10, a predesigned bitmap image was used to make various shapes. 100 nN setpoint was used for each pixel approach. We avoid higher setpoint results in breaking and flipping graphene edge.e. After lithography, any remaining oxidized residue and dirts was removed by cleaning the surface using HQ:CSC38/Al BS tip B from MikroMasch. The outer spacer dimensions were cut to ~ 10  10 μm2 using high-intensity pulsed laser light (1064 nm, in a WITEC alpha300 Apyron confocal microscope setup).A typical AFM topography map and an optical microscopy image of a trilayer graphene spacer are shown in Extended Data Fig. 2a, b. The cavity diameter is reduced down to ~20 nm which is related to the tip apex dimensions (see AFM map) and remains free of oxidation residues. In contrast, cutting the spacer with high-intensity pulsed laser light resulted in substantial oxidation rings (see bright rings in Extended Data Fig. 2c) that damaged the device performance. We note that various laser exposure times and beam intensities always resulted in oxidized layers and topographic eruptions at the edges, extending by approximately 1 µm from the center of the heated area. These oxide layers are not visible in optical microscopy (Extended Data Fig. 2d).KPFM: KPFM images were acquired under an inert nitrogen environment using a Park NX10 Hivac system in sideband mode3. HQ:NSC35/Pt tip C with ~150 kHz resonant frequency, 5.4 N/m spring constant or B doped diamond tip HQ:DMD-XSC11 tip B with ~110 kHz resonant frequency, 6.5 N/m spring constant were used for KPFM measurements. For sideband measurements, the resonant frequency of the tip was calibrated and then set 2.5 kHz away. The tip was excited by 2 VAC with 9 nm – 15 nm setpoints for all measurements. Dislocation control by electric fields: To maintain a large contact area between the tip and the surface, we used contact scanning with 160 nN on HQ:NSC35/Pt tip C (apex radius below 30 nm), 1 Hz scan speed, and pixel sizes under 5 nm at all specified DC voltage. Alternatively, for HQ:DMD-XSC11 tip B, (apex radius 100-250 nm), we used 90 nN. The same scan direction was used in all scans.Size dependence of coercive switching fieldsSwitching a uniform single-domain cavity into a full oppositely-polarized state involves intermediate domain patterns that govern the system response. To reveal the intermediate state pattern, we imaged the cavity’s surface potential evolution after each increment of the external electric field. Extended Data Fig. 3 shows a selected set of images for a 150 nm cavity (see the hysteresis loop of this cavity in Fig. 2 main text). In this case, we used bias increments of ~0.3 V, corresponding to displacement field steps of 0.06 V/nm, and measured repeatable hysteresis loops for 5 times. The first two maps show a fully-polarized cavity after polling beyond the positive/negative coercive fields (as indicated). Starting with a uniform up (bright) polarization in Fig. 2b in the main text, the following image (1 V, at time t3) shows the first bias in which a boundary wall nucleates and a dark domain covering ~1/2 of the cavity area appears. This domain pattern remains the same up to a 3 V bias, where the cavity switches to a fully down-polarized state. The following maps show reversible switching along hysteresis loops with a coercive field between -2.1 Vtip and -2.4 Vtip for up-polarization and a coercive field between 2.7 Vtip and 3.0 Vtip for down-polarization.Extended Data Fig. 4 presents hysteresis loop measurements of the three additional cavities marked by dashed frame in Fig. 2a of the main text. The additional 150 nm-size cavity and the 250 nm-size cavities exhibit a switching bias window of 5 V, while the 350 nm-size cavity does not switch completely in a window of 8 V. We could switch up-polarization at 4 V but could not achieve complete down-polarization even at 4.5 V. We note that higher field values were avoided due to finite damage observed (in other cavities). We also note an asymmetry in positive and negative coercive fields in different cavities, while the overall window remains the same. Since the center of the switching window shifts from positive to negative potential in different cavities and seems to be smaller for cavities that are further separated from neighbors and pining contaminants, we attribute this anisotropy to elastic coupling of the cavity to its environment, rather than vertical electric fields arising by flexoelectric response35.Intermediate switching statesHere, a cavity of 250 nm diameter is scanned with a sharp tip (< 30 nm apex diameter) in Extended Data Fig. 5, allowing better spatial resolution and a more local polling electric field. A biased scan of the single domain map (dark uniform potential, panel b) first opens a 120 triangle domain (bright, panel c), which then extends by 60 to a straight dislocation strip (boundary of dark/bright, panel d). We note that the tip force and bias affect the stability of the intermediate state and that so far we were not able to robustly control the triangular intermediate states. We call for further experiments to establish the intermediate domain pattern as a function of the cavity dimensions, shape, and elastics coupling to adjacent cavities.Dislocation control by tip pressing: Twisted angle control can be performed by various methods. For example, nm to µm size cantilever were used to apply external stress to control twisted layer in the other works40,42–44. In this paper, we used commercial HQ:NSC35/Pt tip C (MikroMasch inc.) with 50 – 600 nN forces, 1 Hz scan speed, and pixel size under 20 nm. The spring constant was calibrated using Sader methods, which is recommended above 100 kHz resonant frequency, and optical lever sensitivity was calibrated using a single-layer graphene on SiO2.Threshold force for boundary strip slidingTo test the threshold pressure for dislocation nucleation and movement, we conducted dragging experiments with unbiased tip. Extended Data Fig. 6 shows the potential maps of cavity arrays after applying increasingly growing forces to a narrow tip of less than 30 nm apex radius. The first map showing any domain wall motion appears after applying a 200 nN force (marked by blue rectangular frames). Note that variations in the cavity matrix potential are extremely sensitive to any deformation in the array. Contact scanning with 200 nN in the opposite direction reverts the domain pattern in a reversible manner, while higher force levels moved the strips in additional cavities and to larger extent (see 250 nN maps). The latter indicates different threshold values in different cavities as naturally expected. Applying forces below the 200 nN threshold value and after doing dragging experiments, did not change the potential pattern as expected (see bottom two maps).We used HQ:NSC35/Pt – Tip C for these experiments, with typical spring constant value of 5.4 N/m. Assuming that 20 nm tip apex curvature, threshold pressure is approximately 161 MPa.Sagging of active layers in pristine cavitiesOccasionally, the stamping process resulted in commensurate layers sagging and the appearance of clear polar polytypes only in part of the array. In Extended Data Fig. 7, for example, the topography and surface potential maps show that cavities from the top part of the array are commensurate and polar (see darker cavity color in topography and bright/dark potential domains). Conversely, the bottom part of the array remains non-polar and exhibits flat topography of suspended cavity membranes or pockets of aggregated contaminations (bright topography regions). In this case, we scanned the array in contact mode with a finite pressure of 300 nN, pushing the active layers to dwell into the vdW adhesion and to push away the self-cleaning contamination pockets. Imaging the array after the several pressured scans confirms clean and commensurate cavities everywhere (see Extended Data Fig. 7c,d). Hence, we note that the surface potential signal is sensitive to the vertical adhesion and the planar interlayer motion. Effect of shear/friction force around the cavityA few hundreds of MPa shear force is known to switching graphene polytypes45. To understand detailed impact of mechanical switching of dislocations inside the cavities, it is essential to compare the shear forces applied at the edges and within the cavity. The friction force induces tortional movement of the tip which is reflected in difference between forward and backward lateral photodiode signals (V). We calibrated conversion factor (nN/V) of lateral force by SiO2 substrate where the friction coefficient is known as 0.08 (ref.46). Our estimated h-BN friction coefficient is 0.055 derived from the conversion factor which is also reported in AFM friction experiment on h-BN47Friction to normal load conversion curve measured on atomically flat h-BN flakes is presented in Extended Data Fig. 8a. A topographic and friction force maps are shown in panel b,c respectively taken around a cavity at a 300 nN loading force. The brighter signal in c indicates that the lateral friction forces are higher at the edge of cavity, reaching ~30 nN compared ~15 nN in the flat regions. Both values are much below the values reported in previous experiments of mechanical domain nucleation in uniform crystalline flakes (with loading forces exceeding µN (Ref.38)). Methods References42. Wu, H. et al. Direct Visualization and Manipulation of Stacking Orders in Few-Layer Graphene by Dynamic Atomic Force Microscopy. J. Phys. Chem. Lett. 12, 7328–7334 (2021).43. Inbar, A. et al. The quantum twisting microscope. Nature 614, 682–687 (2023).44. Tang, H. et al. On-chip multi-degree-of-freedom control of two-dimensional materials. Nature 632, 1038-1044 (2024).45. Nery, J. P., Calandra, M. & Mauri, F. Long-Range Rhombohedral-Stacked Graphene through Shear. Nano Lett. 20, 5017–5023 (2020).46. Bosse, J. L., Lee, S., Andersen, A. S., Sutherland, D. S. & Huey, B. D. High speed friction microscopy and nanoscale friction coefficient mapping.  Meas. Sci. Technol.  25, 115401 (2014).47. Zhang, X., Yu, K., Lang, H., Huang, Y. & Peng, Y. Friction reduction of suspended multilayer h-BN based on electrostrain. Appl. Surf. Sci. 611, 155312 (2023).AcknowledgementsWe thank Neta Ravid and Itzhak Malker for laboratory support. K. W. and T. T. acknowledge support from the JSPS KAKENHI (Grant Numbers 21H05233 and 23H02052) and World Premier International Research Center Initiative (WPI), MEXT, Japan. M.B.S. acknowledges funding by the European Research Council under the European Union’s Horizon 2024 research and innovation program ("SlideTronics", consolidator grant agreement no. 101126257) and the Israel Science Foundation under grant nos. 319/22 and 3623/21. We further acknowledge the Centre for Nanoscience and Nanotechnology of Tel Aviv University. Author informationAuthors and AffiliationsSchool of Physics and Astronomy, Tel Aviv University, Tel Aviv, IsraelYoungki Yeo, Yoav Sharaby, Nirmal Roy, Noam Raab & Moshe Ben ShalomResearch Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, JapanKenji WatanabeResearch Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, JapanTakashi TaniguchiContributionY.Y. performed the experiments, supported by Y.S., N.R. and N.R. and supervised by M.B.S. K.W., T.T. provided the h-BN crystals. All authors contributed to the writing of the manuscript. Competing InterestsRamot at Tel Aviv University Ltd. has applied for a patent (US application no. 63/676,819) on some of the technology and materials discussed here, on which Y.Y., Y.S., N.R. and M.B.S. are listed as co-inventors.Corresponding authorMoshe Ben Shalom, School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel. e-mail: moshebs@tauex.tau.ac.il Data availabilityAll the data in the experiments and analysis that support the findings of this study are included main paper and Methods. Any other relaevant data are available at https://doi.org/10.5281/zenodo.14011946.Extended data figure legendsExtended Data Table 1 | Flakes thickness of three devices presented in the main text.Extended Data Figure 1 | Optical device images. a,b,c, Optical microscope image of devices 1,2,3 presented in figures 1,2,3 in the main text respectively. Scale bars indicate 25 μm.Extended Data Figure 2 | Comparison of spacer lithography methods. a,b, AFM and optical microscope image of local anodic oxidation lithography with cavity diameter down to ~20 nm. c,d, AFM and optical image of laser pulse lithography.Extended Data Figure 3 | Imaging ferroelectric hysteresis loop for a 150 nm cavity (Device 2, see Fig.2 main text). Domain pattern imaged by KPFM after bias scans at the voltage and time indicated on each map.Extended Data Figure 4 | Additional ferroelectric hysteresis measurements (Device 2). a, Topographic and KPFM maps of the cavity array. b, c, d, Hysteresis loops of the cavities marked in a, with diameters 150, 250, 350 nm respectively. Bright and Dark column stands for the switching to complete up and down polarization.Extended Data Figure 5 | Triangular intermediate transition states (Device 2). a, Topographic image of a 250 nm cavity. b,c,d, KPFM image measured before and after applying bias scans as indicated in each map.Extended Data Figure 6 | Determination of threshold pressure for dislocation movement. a, Topographic AFM image of the measured array. b, KPFM signals before tip pressing. c, Successive pressing experiments. Scanning illustration and applied force indicate the contact mode scan parameters before the KPFM image.Extended Data Figure 7 | Imaging sagging of active layers (Device 2). a.b, Topography and surface potential maps of as-fabricated cavity array. c,d, Topographic and KPFM maps after AFM contact mode scans at a pressure of 300 nN. Scale bars are 1 μm.Extended Data Figure 8 | Friction force measurement around the cavity. a, Friction force calibration curve measured in atomically flat h-BN. b, Topographic image of cavity in Device 3 measured in 300 nN loading force. c, Corresponding friction force mapping at 300 nN normal force applied.