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Stefano Chiodini, Giacomo Venturi, James Kerfoot, Jincan Zhang, Evgeny M. Alexeev, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Andrea C. Ferrari, Antonio Ambrosio

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[Electromechanical Response of Saddle Points in Twisted hBN Moiré Superlattices](https://mdr.nims.go.jp/datasets/1de76584-8d39-44f6-a860-7fef9dff3aad)

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Electromechanical Response of Saddle Points in Twisted hBN Moiré SuperlatticesElectromechanical Response of Saddle Pointsin Twisted hBN Moire ́ SuperlatticesStefano Chiodini,* Giacomo Venturi, James Kerfoot, Jincan Zhang, Evgeny M. Alexeev,Takashi Taniguchi, Kenji Watanabe, Andrea C. Ferrari, and Antonio Ambrosio*Cite This: ACS Nano 2025, 19, 16297−16306 Read OnlineACCESS Metrics & More Article Recommendations *sı Supporting InformationABSTRACT: In twisted layered materials (t-LMs), an interlayerrotation can break inversion symmetry and create an interfacial arrayof staggered out-of-plane polarization due to AB/BA stackingregistries. This symmetry breaking can also trigger the formation ofedge in-plane polarizations localized along the perimeter of AB/BAregions (i.e., saddle point domains). However, a comprehensiveexperimental investigation of these features is still lacking. Here, weuse piezo force microscopy to probe the electromechanical behaviorof twisted hexagonal boron nitride (t-hBN). For parallel stackingalignment of t-hBN, we reveal very narrow (width ∼ 10 nm) saddlepoint in-plane polarizations, which we also measure in the antiparallel configuration. These localized polarizations can still befound on a multiply stacked t-hBN structure, determining the formation of a double moire.́ Our findings imply thatpolarizations in t-hBN do not only point in the out-of-plane direction but also show an in-plane component, giving rise to amuch more complex 3D polarization field.KEYWORDS: moire ́ superlattices, hexagonal boron nitride, piezo force microscopy, electromechanics, saddle pointsThe detection and manipulation of electric,1 magnetic2and valley polarizations3 are key for device perform-ance optimizations.4 As Moore’s law approaches itsphysical limits,4 the need for miniaturized nanoelectronics,5involving high-density integrated circuits and low powerconsumption6 has triggered research into layered materials(LMs),7,8 in order to reduce polarization domains from the100 nm2 scale down to the atomic scale.5 Room temperatureout-of-plane ferroelectricity offers a wide range of technologicalapplications, such as ultrathin nonvolatile memories9 and high-permittivity dielectrics.9,10 However, only few suitable ferro-electric LMs have been identified so far, like CuInP2S6,11In2Se3,12,13 MoTe214 and WTe215 in their 1T phase.In other widely studied LMs, such as hexagonal boronnitride (hBN) and 2H-type transition metal dichalcogenides(TMDs), vertical polarizations cancel out,16 due to thecentrosymmetric lattice structure, which makes these crystalsunpolarized. A possible way to engineer polarization in theseLMs is to break the inversion symmetry by introducing a twistangle, θTW, between top and bottom layers,16−18 determining aperiodic modulation of the interlayer atomic registry, i.e., amoire ́ superlattice. In twisted hBN (t-hBN) structures theinterfacial vertical alignment of the N and B atoms distorts thebonding 2pz N electronic orbital,17 locally creating an electricdipole moment that leads to a moire ́ superlattice characterizedby adjacent domains with out-of-plane (OOP) polarizationspointing in opposite directions.16−19 Refs 18, 20, and 21predicted that in-plane (IP) polarizations can also appear at themoire ́ domains’ edges of t-hBN (with clockwise or anticlock-wise orientation), resulting into three dimensional (3D)vectorial patterns with rich topological structures. Topologyplays a key role in LMs, ranging from band theory toskyrmions in magnetic samples.20 Topological domains inferroelectrics22−24 received much attention, owing to theirnovel functionalities, such as negative capacitance25 and high-density information processing.26 However, experimentalproofs of the IP polarizations in t-LMs are limited to irregulart-hBN moire ́ patterns,27 or twisted double bilayer graphenesamples.28Here, we use piezo force microscopy (PFM) to reveal edgeIP polarizations in t-hBN moire ́ superlattices for parallel andantiparallel stacking. We find very sharp (width ∼ 10 nm)polarizations localized at the edges between different domainsof the moire ́ pattern, called saddle points (SPs), not seen byReceived: September 3, 2024Revised: March 18, 2025Accepted: March 19, 2025Published: April 23, 2025Articlewww.acsnano.org© 2025 The Authors. Published byAmerican Chemical Society16297https://doi.org/10.1021/acsnano.4c12315ACS Nano 2025, 19, 16297−16306This article is licensed under CC-BY 4.0Downloaded via NATL INST FOR MATLS SCIENCE (NIMS) on May 7, 2025 at 07:57:32 (UTC).See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Stefano+Chiodini"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Giacomo+Venturi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="James+Kerfoot"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Jincan+Zhang"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Evgeny+M.+Alexeev"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Takashi+Taniguchi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Takashi+Taniguchi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kenji+Watanabe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Andrea+C.+Ferrari"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Antonio+Ambrosio"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/showCitFormats?doi=10.1021/acsnano.4c12315&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?goto=articleMetrics&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?goto=recommendations&?ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?goto=supporting-info&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?fig=tgr1&ref=pdfhttps://pubs.acs.org/toc/ancac3/19/17?ref=pdfhttps://pubs.acs.org/toc/ancac3/19/17?ref=pdfhttps://pubs.acs.org/toc/ancac3/19/17?ref=pdfhttps://pubs.acs.org/toc/ancac3/19/17?ref=pdfwww.acsnano.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://doi.org/10.1021/acsnano.4c12315?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://www.acsnano.org?ref=pdfhttps://www.acsnano.org?ref=pdfhttps://acsopenscience.org/researchers/open-access/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/other scanning probe microscopy (SPM) techniques, such aselectrostatic force microscopy (EFM),18,29 amplitude-modu-lation kelvin probe force microscopy (AM-KPFM),18 andtapping mode phase imaging.30 We prove the universality ofthese SP features by systematically probing them forsuperlattices corresponding to different in the range 0.04−0.18°. We also explore samples consisting of three hBN stacks(i.e., two twisted interfaces).31 The superposition of SPpolarizations arising at the two interfaces is still measurableby PFM, showing a double moire.́ The possibility of interfacingmultiple layer polarizations could pave the way for unconven-tional properties, such as modulations of moire ́ ferroelectricbehaviors.RESULTS AND DISCUSSIONParallel Stacking Alignment in t-hBN. When two hBNlayers are stacked together and twisted, the misalignment ofthe rotated atoms results in a periodic array of local stackingdomains, i.e., a moire ́ superlattice.18 To rationalize thegeometry of t-hBN stacking domains and their 3D polarizationnetwork (IP and OOP), the hBN unit cell has to beconsidered. For t-hBN, two stacking alignments are possible,i.e., parallel and antiparallel.18,21,33 For parallel stacking, 4different domains can be identified: AA, AB, BA, SP. Theirspecific atomic registry is reported in Figure 1a. The AAconfiguration is characterized by a full overlap between N (B)atoms of one layer and N (B) atoms of the twisted layer. In AB(BA) registry, the B (N) atoms in the top layer sit above the N(B) atoms in the bottom layer, while the N (B) atoms in theupper layer lay above the empty site at the center of thehexagonal cell of the lower layer. SP regions are betweendifferent domains, where the atomic registry changes from onedomain to another.The alternation of these 4 stacking regions forms the parallelmoire ́ superlattice (where “parallel” refers to the stackingalignment) of t-hBN (Figure 1b), according to a geometrywhich is set by a -dependent balance16 between interlayerinteractions and intralayer elasticity of the lattice, i.e., theatomic relaxation. This is the driving force shaping the moire ́domains’ geometry (triangular or hexagonal), mainly at θTW <1°, where atomic relaxation is more pronounced).16−18,34According to simulations,32 AB and BA regions areenergetically equivalent with a corresponding stacking energy(calculated with respect to the natural AA’ stackingconfiguration)32 Δε∼ 1 meV (Figure 1a) and, mostimportantly, energetically favorable with respect to the AAdomain (Δε∼ 20 meV), since the latter has pairs of N atomsatop of each other, resulting in an increased steric repulsion.16Hence, as shown in Figure 1b, for parallel alignment at θTW <1°, AB/BA regions cover the majority of the moire ́ superlattice,with a triangular geometry,18,21,33 while unfavorable AAdomains are reduced to a smaller hexagonal coverage (Figure3f).21,27,35,36In Supporting Information (SI), Section 1, we extend thedescription of the stacking domains to the t-hBN antiparallelalignment.PFM of t-hBN Parallel Moire ́ Superlattices. We firstconsider a 2 nm thick top hBN (∼5 layers) on an 8 nm bottomhBN (>10 layers) on Si + 285 nm SiO2. The two flakes arealigned at θTW ∼ 0°. This sample is characterized by PFM,where a conductive tip is in contact with the surface, while anoscillating electrical bias is applied via the tip itself. ThroughPFM, the electromechanical (EM) response can be meas-ured.37 We define the EM coupling as any effect that producesan electric field across the material in response to a surface orvolume deformation and vice versa (i.e., piezoelectric andinverse-piezoelectric effects,37 respectively). Due to the inversepiezoelectric effect, an electromechanically active sampledeforms under a bias, and this distortion couples with thecantilever motion, whose deflection is measured by thecantilever detection system (i.e., the standard AFM opticallever system - such as for our microscope - or the morepowerful interferometric displacement sensor).37 More detailsin SI, Section 2. The origin of this EM sample deformation canarise from two main effects, piezoelectricity (PZ) orflexoelectricity (FLX).38 PZ allows conversion of mechanicalstrain into electric fields (and vice versa) and it arises only innoncentrosymmetric samples, i.e., when a broken inversionsymmetry is present.39 FLX, instead, allows a material topolarize in response to a strain gradient (i.e., mechanicalbending), and, conversely, to bend in response to an electricfield. Despite half a century of history, the latter has been lessFigure 1. t-hBN parallel stacking configurations. (a) Atomic registries corresponding to the 4 domains (AA, AB, BA, SP) typical of parallelstacking in a t-hBN interface (for the SP region we illustrate the average atomic registry). For AA, AB, BA configurations, the correspondingstacking energy per atom, Δε, relative to the naturally occurring AA’ registry,32 is reported. B and N atoms of top (smaller circles) andbottom (larger circles) layers are sketched in maroon and blue, respectively. (b) Representation of two hBN atomic layers, red and blue,(rigidly) stacked and twisted by a small θTW < 1° . The superimposed internal drawing represents the typical 6 triangular shapes obtainedafter atomic relaxation, defining the moire ́ superlattice. The position of each of the 4 domains (AA, AB, BA, SP) is shown.ACS Nano www.acsnano.org Articlehttps://doi.org/10.1021/acsnano.4c12315ACS Nano 2025, 19, 16297−1630616298https://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?fig=fig1&ref=pdfwww.acsnano.org?ref=pdfhttps://doi.org/10.1021/acsnano.4c12315?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asconsidered because of its expected weak strength at themacroscale.38 However, at the nanoscale, FLX can competewith PZ, or be bigger.38 FLX is a universal property of allmaterials, without any symmetry constraint.40Figure 2a,b shows two representative PFM amplitude andphase images obtained on our t-hBN sample (topographyreported in SI, Section 3). The moire ́ domains arecharacterized by narrow features at the edge of the triangularAB/BA regions (width ∼ 10 nm, inset of Figure 2b), whichlook the same in both trace and retrace maps (see SI, Section3). This observation points toward the reliability of the PFMsignals even if artifacts could still affect this mapping,37 (SI,Section 3). Figure 2c is a zoom of a (representative) triangulardomain from the PFM amplitude map (Figure 2a), where the 3Figure 2. IP polarizations measurement via vertical PFM in t-hBN. (a, b) PFM amplitude and phase images of t-hBN. The inset of (b) is aPFM phase line profile highlighting a feature localized in a width ∼ 10 nm. (c) Zoom of a representative triangular domain in (a). The 3triangle sides are labeled (a−c) following an anticlockwise orientation. (d) PFM average amplitude as a function of an angle, α, between thetriangle side (a−c) and the x-axis (panel (e)). Data and error bars are obtained averaging over 7 triangular domains. Red line: best fit withsinusoid: A = y0 + a · sin α (y0, a: fitting parameters). In SI, Section 5 we report similar measurements with 9 experimental points, obtainedby repeating the same PFM measurements for 3 different sample orientations. (e) Vectorial decomposition of each polarization involved inthe triangular shape in (c). (Blue, pink, gold): polarization vectors Pi . Gray: P( )i ycomponents along the y-axis (main cantilever axis) with i =a, b, c. α measured with respect to the positive direction of the x-axis. All polarizations are oriented anticlockwise.ACS Nano www.acsnano.org Articlehttps://doi.org/10.1021/acsnano.4c12315ACS Nano 2025, 19, 16297−1630616299https://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?fig=fig2&ref=pdfwww.acsnano.org?ref=pdfhttps://doi.org/10.1021/acsnano.4c12315?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asedges of the triangle (a, b, c) are highlighted. Since we measurethe EM response of the sample via vertical PFM, one couldexpect these features to emerge from OOP polarizations.However, IP polarizations detection through standard verticalPFM is also possible, due to the buckling effect.41,42 This stemsfrom cantilever buckling oscillations occurring when domainswith IP polarization are aligned parallel to the long axis of thecantilever (see SI, Section 4). Based on this, we now prove theobserved features to emerge from an IP contribution to thesample EM response. The experimental proof is provided in V-PFM (Figure 2) and L-PFM (SI, Section 5), going beyond pastliterature that, for t-hBN, only focused on L-PFM,27 atechnique not always available on AFM microscopes.If the buckling effect is relevant, the measured PFMamplitude should emerge from the vectorial coupling betweenthe cantilever main axis and the projection of the IPpolarization along this very axis. Hence, we expect an angle-dependent PFM amplitude (A) signal,27 i.e., A ∼ Pi · sin α =P( )i y, where Pi is the IP polarization vector, the label i = a, b, crefers to one of the sides of a triangle (Figure 2c,e), and α isthe angle between the cantilever x-axis and the triangle sideunder consideration (Figure 2e). In Figure 2e, the polar-izations Pi are in blue, pink and gold, while their y-componentin gray.To corroborate this hypothesis, we report in Figure 2d theaverage (over seven triangles sides) of the PFM amplitudesmeasured along the triangular edges as a function of α. Thethree data points nicely fit a sinusoidal function, i.e., A = y0 + a ·sin α, with y0 and a as fitting parameters, representing theglobal background of the PFM image and the amplitude of theoscillation, respectively. This can be considered the fingerprintof the IP nature of such polarizations localized along the SPs ofthe triangular moire ́ domains.27 In SI, Section 5 we increaseFigure 3. Parallel stacking domains evolution with increasing θTW. (a−e) 5 moire ́ patterns characterized by a different moire ́ period (Λm)corresponding to an increasing θTW between top and bottom hBN. At the bottom of each image, the scan size is reported. The big blue andred arrows show the evolution of Λm and θTW, respectively. For the determination of θTW, see the SI, Section 6, while Λm is experimentallydetermined as the average distance between AA domains.47 Amplitude scale bar: (a) 2.7−6.6 mV, (b) 1.3−2.3 mV, (c) 6.3 - 9.9 mV, (d) 8.5−14.5 mV, (e) 19−24 mV. (a, b) are for a t-hBN with top flake thickness ∼ 2 nm, bottom flake thickness ∼ 8 nm, θTW ∼ 0°. (c−e) are for adifferent t-hBN with top layer thickness ∼ 4.5 nm, bottom flake thickness ∼40 nm, θTW ∼ 0.2°. (f) PFM amplitude map (equivalent to Figure3d), with all stacking domains identified on the surface (AB/BA, AA, SP). The white dashed line represents the moire ́ superhexagonal shapeused in the relative stacking area quantification of (g). (g) Relative (%) stacking area evolution with increasing θTW for AA (red), SP (black)and AB/BA (blue) regions. Following the SP trend, 2 regions can be highlighted: a first one (yellow), for θTW < ∼ 0.1°, where the SPrelative area is increasing with θTW, and a second (blue) where this trend saturates reaching a plateau for θTW > 0.1°. The last point on theright of the plot (θTW ∼ 0.25°) is obtained on the additional PFM image in Figure 5b, corresponding to Λm ∼ 55 nm.ACS Nano www.acsnano.org Articlehttps://doi.org/10.1021/acsnano.4c12315ACS Nano 2025, 19, 16297−1630616300https://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?fig=fig3&ref=pdfwww.acsnano.org?ref=pdfhttps://doi.org/10.1021/acsnano.4c12315?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asthe statistics of Figure 2d from 3 to 9 points. As shown inFigure S4j, this extended set of data is fitted by a sinusoidal,further supporting our interpretation of the IP nature of theseedge polarizations.Notably, such IP polarizations can also couple with thetorsional motion of the cantilever probed in lateral PFM. As anadditional confirmation of the IP nature of these SPpolarizations, in SI, Section 5, we provide lateral PFM imagesof a t-hBN moire ́ pattern.Figure 2a,b show that the internal area of the triangulardomains does not offer any EM contrast between adjacenttriangular regions (AB/BA domains). Refs 17 and 43 reportedthat nearby triangular AB/BA domains provide a PFM contrastin the internal area. In our case, the different samplethicknesses could play a role. Indeed, while we work with a2 nm-thick top hBN flake, refs 17 and 44 used monolayer (1L)top hBN. Due to a vertical PFM sensitivity necessarilydependent on the top layer thickness, as a result of our largerflakes thicknesses, the vertical EM contrast between AB andBA polarizations is not measurable. This is confirmed byperforming the same measurements on a different t-hBNsample with a 0.8 nm-thick top layer (with a bottom flake of5.7 nm on Si + 285 nm SiO2). We report the corresponding V-PFM amplitude and phase channels in Section 11 of the SI,where the contrast between AB/BA domains can beappreciated in Figure S12b,c.The EM origin of these IP polarizations (PZ and/or FLX) isstill under debate.27,45 However, the inset of Figure 2b shows aphase profile with two opposite peaks (with respect to thecommon background of ∼16°), pointing toward the presenceFigure 4. t-hBN parallel and antiparallel stacking domains measured with different SPM techniques. (a−e): Parallel to antiparallel alignmenttransition induced by a 1L topographical step ∼ 0.3 nm on a t-hBN sample with top flake thickness ∼ 4.5 nm, bottom flake thickness ∼ 40nm, θTW ∼ 0.2°. (a) AFM topography of 1L step. (b−d) PFM phase, AM-KPFM, and phase-imaging maps in the same region of (a). (e)Schematic sample structure corresponding to Figure 4a−d. On the top part a possible stacking transition is shown from parallel AB toantiparallel BA’ lattice registry. (f−j): Parallel to parallel alignment transition due to a 2L-hBN topographical step ∼ 0.6 nm. (f) AFMtopography of 2L-hBN step. (g−i) corresponding PFM phase, AM-KPFM, and phase-imaging channels. (j) Schematic sample structurecorresponding to Figure 4f−i. The top part of panel (j) sketches a parallel stacking domain (AB) on both sides of the 2L-hBN step. Thethicknesses of the flakes and steps are not to scale.ACS Nano www.acsnano.org Articlehttps://doi.org/10.1021/acsnano.4c12315ACS Nano 2025, 19, 16297−1630616301https://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?fig=fig4&ref=pdfwww.acsnano.org?ref=pdfhttps://doi.org/10.1021/acsnano.4c12315?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asof opposite IP polarizations across the SP. Following theinvestigations on twisted bilayer graphene of ref 45. (Figure4b), this could be in line with a major FLX contribution to theEM response of our sample. Nevertheless, we cannot excludethe presence of PZ effects. According to ref 45, the sample EMresponse is thickness dependent and, for our specific case ofmultilayer hBN, it can also have contributions of PZphenomena.45We now extend the analysis of SP polarizations to moire ́patterns arising from different. In order to consider them ageneral feature of such superlattices, they have to be presentindependently of θTW. The fact that θTW may vary on a givensample is a consequence of the fabrication procedure, whichdoes not allow for deterministic control of θTW. Defects andfabrication residuals with unknown distribution over thesample areas can locally alter the twisted structure causingheterogeneous strain distributions and variations of θTW.Hence, when dealing with a t-LM at a specific θTW, we expectlocal deviations around the target value, which will also tunethe moire ́ superlattice to a different periodicity (Λm, see Figure3b). According to the theory of moire ́ superlattices, an inverserelation exists between Λm and i.e., Λm = (a/2)/sin(θTW/2),28,46 with a corresponding to the hBN lattice constant of0.25 nm.47 This formula is valid under two assumptions: thehBN layers are treated as rigid (i.e., atomic relaxation isneglected, see SI, Section 6 for more information), and theyare unaffected by strain. The latter constraint can be relaxed byconsidering the presence of strain, as in ref 46, and SI, Section6. In our case, the θTW variation with respect to an unstrainedcase is calculated to be only ∼5%.Figure 3a−e plot the PFM amplitude images obtained ondifferent sample regions characterized by a decreasing(parallel) moire ́ pattern period. Λm ranges from ∼350 to∼80 nm, corresponding to an increasing estimated θTW from∼0.04 to ∼0.18°. For each image, sharp features are present atthe evolving SP regions, revealing the universality of thislocalized EM response of t-hBN.Figure 3a−e also allow us to evaluate the shape evolution ofall atomic registries with θTW. Their identification, from AB/BA domains (in blue) to AA (in red) and SP (in black) ispresented in Figure 3f. This image proves AA domains to havea hexagonal shape, as theoretically expected,21,36 but, thus far,not observed experimentally, to the best of our knowledge.Going from Figure 3a−e, there is a decreasing coverage oftriangular AB/BA regions, in favor of AA hexagonal domains,progressively growing in size. To quantify this evolution, wefirst need to define a superhexagon for each PFM image ofFigure 3a−e. This acts as an effective “unit-cell” for the moire ́superlattice and encloses 3 AB and 3 BA triangular domains.E.g., the superhexagon corresponding to Figure 3d ishighlighted by the white dashed line in Figure 3f. Second,for each PFM amplitude image, we can obtain the arealcoverage48 for AA, AB/BA, SP regions confined inside thecorresponding superhexagon. These areas can be normalizeddividing by the total coverage of the superhexagon itself,defining what we have called in Figure 3g “relative stackingarea”. The θTW-dependent evolution of the relative stackingarea for AA, AB/BA, SP regions is illustrated in Figure 3g.Different trends are observed: while the AA relative coverageincreases with θTW (red data), the AB/BA behavior (blue data)decreases. This is consistent with a θTW -dependent atomicrelaxation, progressively decreasing the relative area covered byAB/BA triangular domains at larger angles, favoring AAregions.36There is a point where the relative coverages of AB/BA andAA domains balance, marking the boundary between tworeconstruction regimes where energetically unfavorabledomains take over. This happens at θTW = ∼ 0.10°, furtherconfirmed by following the SP relative area evolution (blackdata). For θ < we observe a linear SP trend, which thenreaches a plateau for θ > . A similar trend was reported for t-BLG,35 where assumes a higher relevance as it marks theappearance of flat bands, via 4D-scanning transmissionelectron microscopy (4D-STEM).35 Hence, we believe PFMcould be employed for the identification of correlatedelectronic states in t-LMs.The analogous evolution of the EM response of moire ́superlattices for the antiparallel alignment probed at twodifferent θTW is presented in the SI, Section 7.PFM of t-hBN Antiparallel Moire ́ Superlattices. Wefurther generalize the relevance of SP polarizations byexperimentally revealing their presence also for t-hBNantiparallel stacking alignments. To access this interfacialalignment, we exploit the topography of a t-hBN sampleoffering a 1L step underneath the top flake, Figure 4a (seeFigure 4e for a sketch of the sample structure). Sincemultilayer hBN (ML-hBN) such as the bottom flake, has anatural AA’ stacking,18 the addition of a 1L step, wouldproduce a rotation of 180° with respect to the underlyingstructure, determining a parallel to antiparallel stackingtransition (Figure 4e).18 Figure 4a confirms the step tocorrespond to 1L of hBN, ∼0.3 nm.18 Figure 4b plots therelated PFM phase (see SI, Section 8, for the correspondingamplitude map). While triangular AB/BA domains are visibleon the top-right part of these three images (parallel interfacialstacking), the bottom-left region, corresponding to the 1L-hBN addition, shows hexagonal structures typical of anti-parallel stacking, with features localized at the SP domains (seealso Figure S8d). Figure 4c,d show the corresponding AM-KPFM and phase-imaging maps of the same region. While allthree SPM techniques allow the visualization of AB/BAtriangular domains, PFM is the only approach capable ofvisualizing antiparallel stacking. The reason for this can onlystem from the different imaging mechanisms. Indeed, whilePFM relies on the EM coupling between tip and sample, AM-KPFM and phase-imaging are noncontact AFM techniquesprobing their electrostatic interaction.To validate this further, we focus on a different region of thesame sample offering a topographical 2L-hBN step ∼ 0.6 nm(see Figure 4f for the topography and Figure 4j for the samplestructure). If a 1L-hBN step is responsible for a 180° rotation,it follows that a 2L-hBN step does not induce any parallel toantiparallel stacking transition. Figure 4g−i shows the PFMphase (PFM amplitude image shown in the SI, Section 8), AM-KPFM, and phase-imaging maps of the same region,addressing a parallel stacking on both sides of the 2L-hBN step.Double-Moire.́ There is an increasing interest in t-2L-LMsand t-ML-LMs, due to their emerging superconducting49−51and correlated insulating behaviors,52−54 and in t-ML-TMDwhere cumulative polarizations have been measured.31 Weconsider a specific region of our t-hBN where an additionallayer is present with an uncontrolled orientation relative to theunderlaying hBN. This turns the area into a t-ML-hBN sample.Figure 5a is a PFM amplitude map obtained in this zone,ACS Nano www.acsnano.org Articlehttps://doi.org/10.1021/acsnano.4c12315ACS Nano 2025, 19, 16297−1630616302https://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfwww.acsnano.org?ref=pdfhttps://doi.org/10.1021/acsnano.4c12315?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asrelated to a topographical step (∼4 nm, see Figure 5c),separating 2 different regions. The top-left part of the imageinvolves a moire ́ superlattice made of big (Λm ∼ 300 nm)triangular AB/BA domains. The bottom-right part has twooverlapped textures: a first superlattice that follows thepreviously discussed pattern, plus a second finer superlatticewhose tiny details can be visualized through a high-resolutionPFM amplitude map, see Figure 5b. Figure 5d is an AM-KPFMmap of the same region of Figure 5a. Only the first superlatticecan be distinguished, probably due to a weaker IP signal and/or a limited spatial resolution of AM-KPFM.55From Figure 5b, we derive Λm ∼ 50 nm, smaller than thetypical dimension of the first superlattice (Λm ∼ 300 nm).There is a different geometry of the fine pattern, mainlycharacterized by hexagonal structures, corresponding to centralAA stacking domains. The rounded areas surrounding AAregions may be SP domains, with AB/BA regions limited tovery small (but still visible) triangular domains. Consideringthe ML-hBN structure in this region (schematic in the SI,Section 9), we ascribe this PFM experimental observation tothe presence of a double-moire ́ (in the bottom-right part ofFigure 5a), emerging from three t-hBN stacks.CONCLUSIONSWe used PFM to probe the local electromechanical propertiesof t-hBN, showing the formation of in-plane polarizations atthe edges of the stacking domains (saddle points) of bothparallel and antiparallel moire ́ superlattices. We explained theorigin of these saddle point polarizations, proving theiruniversality by evaluating moire ́ superlattices for a range oftwist angles. The relevance of these saddle point polarizationswas extended by measuring them also in a double-moire ́emerging from the relative twisting of three hBN stacksinvolving two interfaces.Our work unveils a richer polarization (in- and out-of-plane)network in t-hBN, whose spatial distribution can be tuned bythe twist angle, a behavior not found in conventional bulkferroelectric materials,17 where the polarization domains aredetermined by the fixed crystal structure. This complex 3Dvectorial polarization pattern could trigger interesting topo-logical investigations,20 related to negative capacitance,25 orhigh-density information processing,26 but also provides newinsights for exploring unconventional behaviors in t-LMs. Inthis context, the experimental observation of a double-moire ́ isimportant, due to the properties observed in t-ML-graphene,where superconducting49−51 and correlated insulating proper-ties53,54 have been found, and in t-ML-TMD, wherecumulative polarizations were measured.31 Similarly, theemergence of a double-moire ́ in t-hBN involving both IPand OOP polarizations, could pave the way for moire ́ferroelectricity modulations via multistacking.56The ability of PFM to image both parallel and antiparallel t-hBN alignments, with high spatial resolution (about 10 nm),not possible with other SPM techniques, confirms it as a verypowerful technique to study moire ́ superlattices in t-LMs.METHODSSample Fabrication. t-hBN samples are prepared by exfoliatingbulk hBN crystals, grown at high pressure and temperature,57 onto Si+ 90 nm SiO2 by micromechanical cleavage (MC). In order to controlθTW, either large flakes (>50 μm) selectively torn during transfer58 orneighboring hBN flakes cleaved from the same bulk crystal duringMC18 are identified by studying the orientation of their faceted edgesusing optical microscopy.59 t-hBN samples with controlled interlayerrotation are then fabricated using polycarbonate (PC) stamps.60 First,a PC film on polydimethylsiloxane (PDMS) is brought into contactwith the substrate with hBN flakes at 40 °C using a micromanipulator,so that the contact front between stamp and substrate covers part ofone flake or one of two adjacent flakes exfoliated from the same flakeon the tape. Stamps are then retracted, and the material in contactwith the PC is picked up from the substrate. After picking up the firstflake, a controlled θTW (±0.01°), as determined by the resolution andwobble of the rotation stage, can be applied by rotating the samplestage, before the flake on PC is aligned to the second one and broughtinto contact at 40 °C. The stamp is then retracted and the resulting t-hBN is picked up by PC. t-hBN is then transferred onto Si + 285 nmSiO2 at 180 °C, before the PC residue is removed by immersion inchloroform and then ethanol for 30 min. While Si + 90 nm SiO2 isused to facilitate the identification of hBN flakes,61 n-doped Si + 285nm SiO2 is chosen for further characterization, such as gate dependentelectrical measurements. Characterizations via Raman spectroscopy isdiscussed in ref 30, as well as in Section 10 of the SI.Scanning Probe Microscopy. AFM measurements are per-formed at about 25 °C (RH ∼ 40%), in air, using a Multimode 8(Bruker) AFM microscope. For PFM images we used ASYELEC.01-R2 cantilevers (Asylum Research, k ∼ 2.8 N·m−1, f ∼ 75 kHz). Thedeflection sensitivity is obtained by performing 10 force−distancecurves on mica (without changing the laser spot position onto thecantilever) and calculating the average inverse slope in the contactregion. An average value of 68 nm·V−1 is found. The nominal tipradius is 25 nm. For an applied force F = k · d ∼ 15 nN we calculate,from standard Hertz contact mechanics62 and assuming an effectivehBN Young modulus ∼35 GPa,63 a contact radius rc ∼ 2 nm.Considering that the hBN lattice constant is ∼ 0.25 nm,47 this contactradius implies a statistical amount of atoms (∼500) involved in thetip−sample interaction, therefore justifying the use of macroscopicparameters, such as polarization and piezoelectric coefficient, also inline with refs 27 and 28.Figure 5. Double-moire ́ in multiply stacked t-hBN measured viaPFM. (a) PFM amplitude map showing a double-moire ́ in thebottom-right corner. (b) Zoom of red square in (a). (c) Heightprofile across the 4 nm step highlighted in panel (a). (d) AM-KPFM map of the same area of Figure 5a.ACS Nano www.acsnano.org Articlehttps://doi.org/10.1021/acsnano.4c12315ACS Nano 2025, 19, 16297−1630616303https://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acsnano.4c12315/suppl_file/nn4c12315_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnano.4c12315?fig=fig5&ref=pdfwww.acsnano.org?ref=pdfhttps://doi.org/10.1021/acsnano.4c12315?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asSCANASYST FLUID cantilevers (Bruker, k ∼ 0.7 N·m−1, f ∼ 150kHz) are used for phase-imaging, while ASYELEC.01-R2 cantilevers(Asylum Research, k ∼ 2.8 N·m−1, f ∼ 75 kHz) for all the PFM andAM-KPFM images. The phase-imaging typical parameters are freeamplitude A0 ∼ 8 nm, set-point ∼7 nm. The attractive phase values inthis work are reported following the Asylum Research convention.21For vertical and lateral PFM, we use a set-point ∼5 nm, with typicalcontact resonance f CR ∼ 330 kHz, and an AC sample bias amplitudeVac = 2 V (Vdc = 0, referring to eq S1). Vertical and lateral PFMmeasurements for Figure S4 are performed on a Dimension Icon(Bruker) AFM microscope. In AM-KPFM, the images are acquiredwith A0 ∼ 20 nm, set-point ∼ 5 nm, lift height ∼ 2 nm, lift drivingvoltage ∼ 2 V. All AFM images are obtained at a typical scan rate of0.8 Hz and analyzed in Gwyddion.48 AM-KPFM maps are flattenedtogether with a second order polynomial correction to enhance themoire ́ contrast between AB and BA triangular domains.ASSOCIATED CONTENT*sı Supporting InformationThe Supporting Information is available free of charge athttps://pubs.acs.org/doi/10.1021/acsnano.4c12315.Antiparallel stacking alignments in t-hBN; resonance-enhanced vertical PFM; Figure 2 full set of data;buckling effect; lateral PFM measurements of IPpolarizations in t-hBN moire ́ superlattice; twist angleextraction from PFM images; shape evolution of twoantiparallel stacking moire ́ superlattices; PFM amplitudeimages for Figure 4; schematic of sample showing adouble-moire ́ in Figure 5a; Raman characterization ofthe t-hBN sample; and V-PFM images for a 0.8 nm/5.7nm t-hBN sample (PDF)AUTHOR INFORMATIONCorresponding AuthorsStefano Chiodini − Center for Nano Science and Technology,Fondazione Istituto Italiano di Tecnologia, 20134 Milan,Italy; Email: stefano.chiodini@iit.itAntonio Ambrosio − Center for Nano Science andTechnology, Fondazione Istituto Italiano di Tecnologia,20134 Milan, Italy; orcid.org/0000-0002-8519-3862;Email: antonio.ambrosio@iit.itAuthorsGiacomo Venturi − Center for Nano Science and Technology,Fondazione Istituto Italiano di Tecnologia, 20134 Milan,ItalyJames Kerfoot − Cambridge Graphene Centre, University ofCambridge, CB3 0FA Cambridge, United Kingdom;orcid.org/0000-0002-6041-4833Jincan Zhang − Cambridge Graphene Centre, University ofCambridge, CB3 0FA Cambridge, United KingdomEvgeny M. Alexeev − Cambridge Graphene Centre, Universityof Cambridge, CB3 0FA Cambridge, United Kingdom;orcid.org/0000-0002-8149-6364Takashi Taniguchi − Center for Materials Nanoarchitectonics,National Institute for Materials Science, Tsukuba 305-0044,Japan; orcid.org/0000-0002-1467-3105Kenji Watanabe − Research Center for Functional Materials,National Institute for Materials Science, Tsukuba 305-0044,Japan; orcid.org/0000-0003-3701-8119Andrea C. Ferrari − Cambridge Graphene Centre, Universityof Cambridge, CB3 0FA Cambridge, United Kingdom;orcid.org/0000-0003-0907-9993Complete contact information is available at:https://pubs.acs.org/10.1021/acsnano.4c12315Author ContributionsS.C. developed the investigation approach and performed andanalyzed the AFM measurements. G.V. performed the angleextraction from the PFM data. J.Z., E.M.A., and A.C.F.prepared and characterized all the samples. T.T. and K.W.provided the bulk crystals. 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