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Andrew Z. Barabas, Ian Sequeira, Yuhui Yang, Aaron H. Barajas-Aguilar, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Javier D. Sanchez-Yamagishi

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[Mechanically reconfigurable van der Waals devices via low-friction gold sliding](https://mdr.nims.go.jp/datasets/134a8a81-a2cc-4362-8cde-614b44406688)

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Mechanically reconfigurable van der Waals devices via low-friction gold slidingCONDENSED MATTER PHYS ICSMechanically reconfigurable van der Waals devices vialow-friction gold slidingAndrew Z. Barabas1†, Ian Sequeira1†, Yuhui Yang1, Aaron H. Barajas-Aguilar1, Takashi Taniguchi2,Kenji Watanabe2, Javier D. Sanchez-Yamagishi1*Interfaces of van der Waals (vdW) materials, such as graphite and hexagonal boron nitride (hBN), exhibit low-friction sliding due to their atomically flat surfaces and weak vdW bonding. We demonstrate that microfabri-cated gold also slides with low friction on hBN. This enables the arbitrary post-fabrication repositioning ofdevice features both at ambient conditions and in situ to a measurement cryostat. We demonstrate mechani-cally reconfigurable vdW devices where device geometry and position are continuously tunable parameters. Byfabricating slidable top gates on a graphene-hBN device, we produce a mechanically tunable quantum pointcontact where electron confinement and edge-state coupling can be continuously modified. Moreover, wecombine in situ sliding with simultaneous electronic measurements to create new types of scanning probe ex-periments, where gate electrodes and even entire vdW heterostructure devices can be spatially scanned bysliding across a target.Copyright © 2023 TheAuthors, somerights reserved;exclusive licenseeAmerican Associationfor the Advancementof Science. No claim tooriginal U.S. GovernmentWorks. Distributedunder a CreativeCommons AttributionNonCommercialLicense 4.0 (CC BY-NC).INTRODUCTIONNanoscale electronic devices are typically static, with the materialstructure and device geometry set during the fabrication process.Exploring the full parameter space requires fabricating multipledevices with varying geometries and material structures. Ideally, adevice’s material structure and geometry would be reconfigurable insitu, allowing for post-fabrication modification while simultane-ously measuring its properties. Microelectromechanical systemsenable a limited range of mechanical reconfigurability at the costof complex suspended device structures (1). For conventional non-suspended devices, mechanical modification of the device structureis typically not possible because of high friction forces at allinterfaces.An exception to this is van der Waals (vdW) layered materials,which exhibit low interfacial friction due toweak vdW bonds, atom-ically flat layers, and lattice incommensurability (2–8). Recently, thisproperty has been exploited to perform twist angle–dependentstudies of graphite and graphene-based heterostructures bysliding vdW flakes with an atomic force microscope (AFM) (9–12). This approach is powerful, but currently limited by difficultiesin fabricating complex vdW heterostructures, as well as the need toperform experiments in ambient conditions.Here, we show that microfabricated gold exhibits low-frictionsliding on hexagonal boron nitride (hBN), a vdW material, atboth ambient conditions and cryogenic temperatures (7.6 K). Thelow-friction gold-hBN interface enables us to produce a wide rangeof slidable structures to form mechanically reconfigurable vdWdevices, including a tunable graphene quantum point contact(QPC) and sliding-based scanning probe devices. These devicescan be modified ex situ in an AFM or in situ in a measurementcryostat.RESULTSLow-friction gold on hBNWe create reconfigurable structures by depositing gold microstruc-tures directly onto hBN flakes using electron beam lithography(EBL) and electron beam evaporation (see the “Friction measure-ments” section in Materials and Methods for fabrication details).By pushing laterally with an AFM tip, we can slide microscale, poly-crystalline gold features as large as 35 μm2 across the hBN surface.The low-friction sliding enables arbitrary repositioning of depositedfeatures (Fig. 1, A and B). We observe that small features can even bemoved by scanning an AFM tip in tapping mode. The motions arenondestructive, with no change to either the gold or hBN observ-able in AFM except for the cleaning of contaminants on the hBNsurface, which are swept away by the sliding gold (Fig. 1C).To characterize the friction, we slide gold squares of differentsizes on hBN using an AFM tip and determine the interfacial fric-tion from AFM deflection measurements, similar to previous vdWtribological studies (4–6, 8, 13, 14). Figure 1D illustrates the frictionmeasurement scheme. First, the tip is moved laterally at a fixed z-piezo extension elevated above the hBN surface (left). Once the tipmakes contact with the edge of the stationary gold square, it deflectslaterally, resulting in a voltage signal on the AFM photodiode(middle). The lateral deflection increases until the static frictionof the gold-hBN interface is overcome, after which it drops to aconstant value corresponding to the kinetic friction as the goldslides on the hBN (right). These regions are highlighted in anexample deflection trace in Fig. 1E, where the peak (static) voltageand constant (kinetic) voltage are indicated.To determine the scaling of friction with interface size, we repeatthese measurements multiple times each for 0.5- to 3-μm-wide goldsquares and observe a linear scaling of deflection voltages versusarea, with slopes of 82 ± 6 mV/μm2 (static) and 24.4 ± 0.6 mV/μm2 (kinetic). Assuming that force is directly proportional to de-flection voltage, our data show that interface friction scales linearlywith area, which is expected for polycrystalline interfaces (14). Bycontrast, atomically flat and lattice incommensurate interfaces, in-cluding single-crystal gold nanoparticles on graphite, can exhibit1Department of Physics and Astronomy, University of California, Irvine, Irvine, CA,USA. 2Research Center for Functional Materials, National Institute for MaterialsScience, 1-1 Namiki, Tsukuba, Japan.†These authors contributed equally to this work.*Corresponding author. Email: javier.sanchezyamagishi@uci.eduBarabas et al., Sci. Adv. 9, eadf9558 (2023) 7 April 2023 1 of 8SC I ENCE ADVANCES | R E S EARCH ART I C L EDownloaded from https://www.science.org at National Institute for Materials Science on April 14, 2023http://crossmark.crossref.org/dialog/?doi=10.1126%2Fsciadv.adf9558&domain=pdf&date_stamp=2023-04-07sublinear scaling versus area (3, 4, 8, 14). This suggests that increas-ing the grain size of our gold will decrease interface friction. To testthis, we vacuum-annealed our samples at 350°C for 30 min and ob-served that the deflection voltages decrease by 50%. The annealingprocess also caused the average gold grain size to increase from ~20to ~80 nm, suggesting a connection, although the removal of con-taminants from the Au-hBN interface by heat annealing likely playsa role as well.We convert the AFM deflection voltage to a lateral force using alinear model that requires both the AFM tip’s lateral spring constantand the AFM’s lateral sensitivity. The spring constant is the ratio oflateral force applied to the tip and lateral displacement, which wedetermine by simulating our tip in COMSOL Multiphysics. In ad-dition, the sensitivity is the ratio of lateral tip displacement andlateral deflection voltage measured on the AFM photodiode. Tomeasure the lateral sensitivity, we use the slope of the staticregion of our deflection linetraces (see the “Friction measurements”section in Materials and Methods for more details).Converting the deflection voltages yields forces of 6 μN (static)and 2 μN (kinetic) for a 9-μm2 gold square on hBN. Applying theconversion to the linear fits results in a friction force per unit area.For the unannealed Au-hBN interface, the friction values are 800nN/μm2 (static) and 230 nN/μm2 (kinetic), and after annealing,they decrease to 400 and 100 nN/μm2, respectively. These forcevalues have uncertainties of 30%, dominated by uncertainty in thesensitivity, and should be considered upper bounds due to the cal-ibration method and limitations of the linear model (see the “Fric-tion measurements” section in Materials and Methods). Theseinterfacial friction values are comparable to prior tribologystudies of gold on graphite, which measured 50 to 430 nN/μm2(kinetic) for ~60- to ~100-nm-wide, single-crystal, gold nanoparti-cles (13). For additional comparison, the previously reported kineticfriction of unaligned graphite on hBN is smaller, at 15 nN/μm2 (5).We have also made friction measurements of gold with a 3-nm Crsticking layer on hBN, and initial tests show that it exhibits roughlyan order of magnitude higher friction than annealed gold on hBNwithout a sticking layer (see fig. S3).Mechanically tunable QPCThe low friction between Au-hBN enables studies of vdW quantumdevices in which reconfigurable gold gates are used to mechanicallymodify electron confinement. Gate-defined QPC and quantum dotsare of particular interest as they are integral for making graphene-based qubits (15–17) and for studying non-Abelian quasiparticles(18, 19).We apply this unique confinement control capability to make areconfigurable QPC defined by movable gold-only top gates on anhBN-encapsulated graphene device (Fig. 2A). The top gates confineelectrons by depleting the graphene into a bandgap, therebyforming a narrow QPC constriction between two conductingregions. Although graphene lacks an intrinsic bandgap, one formsin a perpendicular magnetic field at zero density due to exchangeinteractions (20). Therefore, in the quantum hall regime, we canstudy the edge mode transmission through the constriction at dif-ferent Landau level filling factors and QPC separations by holdingthe dual-gated region at the charge neutrality point while sweepingthe back-gate voltage (21, 22).To adjust the QPC separation, the top gates are physically movedwith an AFM tip at ambient conditions, modifying the QPC con-finement mechanically (Fig. 2A). We then cool the sample to 1.5 K,apply a 9-T out-of-plane magnetic field, and measure the resistanceversus top-gate and back-gate voltages. From these measurements,we determine the QPC conductance, referred to as GQPC, by takingthe inverse of the measured resistance after subtracting a contactFig. 1. AFM friction measurements for gold squares sliding on hBN. Scale bars, 3 μm. (A and B) Optical images of ~170-nm-tall gold squares on hBN before and aftermanipulation with an AFM tip. (C) AFM height image of a 3-μm-wide gold square on atomically flat hBN surface with contaminants swept aside by sliding. The root meansquare roughness of the swept hBN is 1 Å, and the height of the surface contaminants is roughly 8 nm. A nonlinear color scale is used to highlight features across a widerange of heights. (D) Schematic illustrating AFM lateral friction measurement: before contact (left), during static friction (middle), and during kinetic friction (right). (E)AFM friction linetrace for a 3-μm-wide square with the tip moving at 1 nm/s. The peak voltage corresponds to the Au-hBN static friction, and the subsequent constantvoltage corresponds to the kinetic friction. (F) Lateral deflection voltage versus interface area between gold and hBN for 0.5-, 0.75-, 1-, 2-, and 3-μm-wide squares beforeand after annealing at 350°C for 30min. Each data point is the average of multiple measurements for each size. Error bars show SD. Lines are linear fits through zero, fittingonly the 4 and 9 μm2 data points; this excludes smaller deflection data points that have variable AFM sensitivity (see the “Friction measurements” section in Materials andMethods for more details).Barabas et al., Sci. Adv. 9, eadf9558 (2023) 7 April 2023 2 of 8SC I ENCE ADVANCES | R E S EARCH ART I C L EDownloaded from https://www.science.org at National Institute for Materials Science on April 14, 2023resistance (see the “QPC device” section in Materials and Methodsand the Supplementary Materials for more details).Adjusting the QPC separation modulates the tunneling couplingbetween counterpropagating edge modes, thereby tuning theirtransmission through the QPC constriction. This is illustrated inFig. 2 (B and C), which shows different gate separations of theQPC but at identical gate voltage conditions. The Landau levelfilling factors shown are νbg = −2 for the back gate and νd = 0 forthe dual-gated regions. When the QPC separation is large, edgemodes transmit across the device unimpeded, resulting in a GQPCof 2 e2/h (Fig. 2B). In contrast, at the same filling factors, asmaller QPC separation causes the counter-propagating edgemodes to tunnel couple and backscatter, decreasing GQPC ≤ 2 e2/h (Fig. 2C).We measure the QPC conductance with νd = 0 for four separa-tions: 1110, 170, 80, and 10 nm (Fig. 2D). It is apparent that phys-ically narrowing the QPC generally decreases GQPC at a given back-gate voltage. At filling factor νbg = −2 (vertical dashed line atVbg = −1.65 V), a 2 e2/h plateau is observed for the 1110-nm sepa-ration, corresponding to the edge modes in the back-gated regiontransmitting across the device unimpeded, equivalent to Fig. 2B.At the same filling factor, narrowing the QPC separation to 170nm decreases GQPC to between 1 and 2 e2/h, indicating partial re-flection of one edge mode. Further narrowing to 80 nm results in a 1e2/h plateau. This surviving quantized plateau is explained by thespatial separation of the edge modes. The innermostcounterpropagating modes are close enough to completely back-scatter via tunneling, while the outer modes are still too far apartto couple and instead transmit through the QPC fully. Narrowingthe QPC separation further to 10 nm results in partial reflection ofthe remaining edge mode such that GQPC < 1 e2/h (as illustrated inFig. 2C). Similarly, for νbg = −1 (Vbg = −0.65 V), a 1 e2/h plateau isobserved in the 1110-nm separation, which we reduce to 0.14 e2/hby narrowing the QPC separation, demonstrating our ability to me-chanically pinch-off the conductance. In the full device conduc-tance map (Fig. 2, E to H), the gate voltage region where pinchoff is attained (right of diagonal line) grows in size as the gate sep-aration is reduced.The mechanical gate tuning we demonstrate offers an unprece-dented level of control, as confinement geometry and physical po-sition of the QPC can be modified independent of gate voltages.Such an approach will be highly useful for tuning the propertiesof gate-defined quantum dots and QPCs in vdW heterostructures.In situ heterostructure and cryogenic manipulationAn exciting aspect of the low friction between gold and hBN is thepotential for true in situ manipulation of a device’s atomic structure.Here, in situ means simultaneous manipulation and measurementunder the extreme conditions often required for quantum experi-ments, such as cryogenic temperatures, high magnetic fields, andhigh vacuum. Of these conditions, cryogenic manipulation presentsthe biggest challenge because friction typically increasesFig. 2. Measurement of a mechanically reconfigurable QPC device. (A) Schematic of an hBN-encapsulated graphene device with a local graphite back gate andflexible serpentine leads connected to the movable QPC top gates (metal contacts to the graphene and graphite not shown). (B and C) QPC edge mode schematicfor νd = 0 and νbg = −2. (B) For a large QPC separation, all edge modes are completely transmitted, as in the 1110-nm separation. (C) Reduced QPC separation suchthat the innermost edge mode is completely backscattered, while the outer edge mode is partially backscattered (indicated by the dotted lines), as in the 10-nm sep-aration. (D) Linecuts of full 2D conductance color plots taken at 9 T and 1.5 K along νd = 0 for each of the four separations. The vertical dashed line at Vbg = −1.65 Vindicates the νbg = −2 filling. (E to H) Conductance color plots versus graphite back-gate and QPC top-gate voltages at separations of 1110, 170, 80, and 10 nm, respec-tively. Dashed lines correspond to νd = 0 linecuts presented in (D). Insets are false color AFM amplitude images of QPC gates. Scale bar in (E) is 500 nm and applies to allAFM images.Barabas et al., Sci. Adv. 9, eadf9558 (2023) 7 April 2023 3 of 8SC I ENCE ADVANCES | R E S EARCH ART I C L EDownloaded from https://www.science.org at National Institute for Materials Science on April 14, 2023significantly at low temperatures due to reduced thermal vibrationsand the freezing of gas within the cryogenic vacuum space (23).To advance vdW manipulation beyond pushing individual flakesat ambient conditions, we aim to achieve deterministic lateralmotion of flakes and even whole heterostructures by creating arigid mechanical connection to them. The conventional methodfor vdW flake manipulation, as demonstrated in Figs. 1 and 2 andprior works (9–12), uses a sharp AFM tip to push a flake from theside and then reimages the flake position using the same tip. This,however, does not result in deterministic, one-to-one motion of theflake and makes certain manipulation applications, such as scan-ning, infeasible. Likewise, this manipulation technique is not wellsuited to overcome the high friction forces at cryogenic tempera-tures and for large interface areas due to the small contact areabetween the sharp tip and the flake. We encounter the limits ofthis style of motion with very large gold contacts in our QPCdevices (area > 35 μm2), which are cut by the AFM tip as itpushes laterally. To address these issues, we have created metalhandles that interface the AFM tip to a vdW heterostructure.The handle grips the vdW flakes/heterostructures by overlappingthe flake edges so that it conforms to the flake and distributes forcealong the flake’s edges. We press-fit a flattened AFM tip into adonut-shaped hole in the handle, which deforms the metal tomatch the tip shape and provides increased grip. This strong con-nection enables deterministic sliding of gold on hBN at cryogenictemperatures (T = 7.6 K; see Fig. 3A and movie S1).Despite the increased friction at cryogenic temperatures, as evi-denced by visible tip flex in movie S1, we observe that the hBNsurface is left pristine and undamaged after more than 100motions at a speed of 30 μm/s (Fig. 3B). See the “In situ sliding”section in Materials and Methods for details about the manipulationtechnique and setup. Cold sliding can enable a variety of experi-ments including reconfigurable vdW heterostructures at cryogenictemperatures, which would allow for rapid, continuous measure-ments with respect to physically reconfigurable parameters.While mechanical linkage and motion is useful in its own right,electrical contact to moveable structures is also critical to performmany experiments. To this end, we fabricate flexible serpentine-shaped electrodes connected to our donut handles, which are an-chored at one end of the hBN flake on SiO2, shown in Fig. 3C.We are able to oscillate these electrodes at 10 Hz with an amplitudeof 2 μm by actuating with an AFM tip and the same donut interfacedescribed above (video available online). We find that these accor-dion geometries with a wire cross section of 1 μm thick and 1 μmwide are able to stretch over 10 μm before breaking. Note that,except for extreme displacements, the friction force is highenough to prevent the electrodes from springing back when theAFM tip is disengaged.By combining mechanical motion and flexible electrodes, wecreate a sliding scanning top gate, shown in Fig. 3 (D to F). Atroom temperature, we raster a gold top gate by sliding it over an en-capsulated graphene-hBN device, modulating the device resistanceFig. 3. In situ mechanically reconfigurable devices. (A) Optical images showing gold sliding on hBN (pink) at 7.6 K, actuated by an AFM tip (gray). Arrows denote therange and direction of motions. Dark purple on the left is the SiO2 substrate. See movie S1 for a video recording of the motions. (B) AFM image of hBN surface aftercryogenic scanning motions from (A) showing that the hBN surface is left undamaged with only swept-up surface contaminants. AFM area is the solid red boxed area in(A). (C) Optical images of gold serpentine electrodes on hBN (pale yellow/green) showing ~2-μm longitudinal and transverse motions. Red dotted lines outline the initialposition. Video recordings of oscillating motion shown in movies S2 and S3. (D) Side profile schematic of a sliding top-gate hBN-encapsulated graphene device, actuatedwith an AFM tip. Top-gate slides over stationary graphene to change local gating and device resistance. (E) Top-down optical image of the same device. The graphene isoutlined with a dotted white line, and the light purple background is hBN. Red rectangle is 2.4 × 9.5 μm. (F) Graphene resistance versus top-gate position. Scanning rangeshown as the red rectangle in the optical image. Dashed lines indicate graphene edges. (G) Side profile schematic of a slidable graphene-hBN device on a stationary hBNsubstrate, actuated with an AFM tip. The slidable features in the schematic are outlined in black. (H) Top-down optical image of the same device. The pale green back-ground is hBN. (I) Two-probe resistance of the slidable graphene device versus sliding position (see movie S4 for the video recording). 0 μm corresponds to the initial,transferred position. The increase in resistance over subsequent motions is likely due to photodoping from the light source used for imaging.Barabas et al., Sci. Adv. 9, eadf9558 (2023) 7 April 2023 4 of 8SC I ENCE ADVANCES | R E S EARCH ART I C L EDownloaded from https://www.science.org at National Institute for Materials Science on April 14, 2023by changing the overlap between the graphene and top gate. Theresistance versus gate position is plotted in Fig. 3F, which can beinterpreted as a coarse image of our graphene device convolvedwith the geometry of the sliding gate. This constitutes a new mech-anism for scanning probe microscopy (24), where a scanned gate isin direct atomic contact with the sample, obviating the need for thefeedback control of the probe-sample distance that is typical withscanning probes.Taking advantage of the low friction of both graphene-hBN andAu-hBN interfaces, we apply our technique to make a slidable, con-tacted vdW heterostructure, shown optically and schematically inFig. 3 (G and H). Here, an entire graphene device is translatedover an hBN substrate, actuated via a metal handle. The graphene,edge-contact electrodes, and top hBN all slide as a single unit andallow for continuous measurement of the graphene as it is moved.Figure 3I shows the change in graphene resistance as it is translatedback and forth. As the graphene slides 1.2 μm, we observe a repro-ducible modulation of the device resistance corresponding to amaximum change of 10 to 15 ohms. Naively, one would notexpect any change in the graphene resistance due to translatingthe device. One explanation for this effect is that the graphene isgated by charge inhomogeneity in the hBN (25), modulating its re-sistance and causing it to act as a local charge sensor. Another effectthat can arise in this device geometry is strain in the graphene or atthe graphene-gold interface that develops in response to frictionforces during the motion. These effects will be isolated and exploredin future studies.DISCUSSIONThe ability to move both metal and vdW layers within a deviceoffers an unprecedented level of control and flexibility in bothdevice function and experiment design. The mechanically reconfig-urable devices we demonstrate enable experimental studies wherestructure and geometry are continuously tunable parameters. Thisallows for dense sampling of the device and heterostructure param-eter space while keeping local disorder constant, something that isimpossible to achieve with the conventional approach of fabricatingmultiple devices. Reconfiguration by sliding makes possible themodification of quantum confinement via moveable gate elec-trodes, as well as the continuous tuning of lattice interfaces invdW moire heterostructures. Our demonstration of deterministicin situ sliding also introduces the possibility of dynamic structuralstudies, where time-varying modulations of the device geometry,strain, and interfacial moires induce electronic effects such as topo-logical charge pumping (26–28). Last, the proof-of-principle slidingscanning probe experiments show a new approach to spatialmapping of local material properties at the extreme limit of proxim-ity, i.e., direct atomic contact, as well as with the full flexibility ofplanar nanofabrication.MATERIALS AND METHODSGeneral fabrication techniquesThe following techniques are universal to our device fabricationexcept when specified otherwise.LithographyAll lithography performed is EBL using a poly(methyl methacry-late) (PMMA) resist. We use PMMA 950 A5 spun at 2000 rpmfor 2 min, resulting in a ~500-nm-thick layer for depositions lessthan 300 nm in thickness and for etch masks. EBL patterns arewritten at 1.6 or 3.2 nAwith 30-kV excitation. The PMMA is devel-oped for 3 min in a cold mixture of 3:1 isopropyl alcohol(IPA)/water.One-dimensional edge contactsOne-dimensional (1D) edge contacts for our graphene encapsulatedin hBN devices are written with EBL and developed before reactiveion etching with 10 standard cubic centimeters per minute (SCCM)of SF6, 2 SCCM of O2, 30 W of radio frequency power, at 100 mtorrfor 30 s (29). Then, 3 nm of Cr and ~100 nm of Au are deposited at 1Å/s in an electron beam metal vapor deposition system. Liftoff isperformed by soaking the sample in acetone for 1 to 2 hours andagitating with a pipette.Exfoliation and dry transfersWe exfoliate hBN and graphene from bulk crystals. Stacks are as-sembled using stamps consisting of polycarbonate (PC) film on apolydimethylsiloxane (PDMS) square on a glass slide (30). Wehave used hBN ranging from ~15 to ~230 nm thick as a substratefor sliding gold structures.Friction measurementsFabrication for gold-hBN friction measurementsGold-only squares for friction measurements are fabricated by spin-ning PMMA on a silicon chip of exfoliated hBN, writing squaresusing EBL, depositing 170 nm of gold, and lifting off in acetone.AFM lateral friction measurementsTo measure lateral friction, we use the lithography mode of a ParkSystems NX10 AFM and a Budget Sensors Tap300Al-G tip to ma-nipulate gold on hBN in ambient conditions. First, the top surfaceof the gold squares is measured using lithography set point modewith 100 nN of downward force and a dwell time of 8 s. The tipis then moved next to the gold square, lowered 100 nm below thetop surface of the gold, and moved laterally, transverse to theAFM cantilever, and into the gold square at 10 nm/s. The lateraldeflection voltage is recorded throughout the motion. Measure-ments were also made at 1 and 100 nm/s, and no dependence onspeed was observed in this range. Care is taken for the motion tobe through the center of mass of the gold to avoid rotation, andmotions with rotation are excluded from our analysis. Thesquares are also oriented, so their edge is perpendicular to the di-rection of motion. Note that no permanent deformation of the goldis observed in AFM images taken after manipulations.The regions before contact, during static friction, and duringkinetic friction are identified to extract the average baselinevoltage, average kinetic friction, and the peak static friction value,respectively. We include some example linetraces to demonstratethe scales and overall appearance of typical linetraces (fig. S1). Al-though some traces do not exhibit the ideal lineshape, their kineticand static friction values do not deviate from other traces. The exactmechanisms that cause nonidealities are not clear. To measure forceusing the AFM, we assume a linear model where deflection voltageis related to the force on the cantilever as Ftip = Vtip k/S, whereVtip isthe lateral deflection voltage of the AFM tip, k is the tip spring cons-tant, and S is the AFM sensitivity.The cantilever is simulated in COMSOL Multiphysics to deter-mine its spring constant, referencing optical and scanning electronmicroscopy images for its dimensions (6). To simulate the springconstant, a lateral force is applied 100 nm above the apex of theBarabas et al., Sci. Adv. 9, eadf9558 (2023) 7 April 2023 5 of 8SC I ENCE ADVANCES | R E S EARCH ART I C L EDownloaded from https://www.science.org at National Institute for Materials Science on April 14, 2023tip and the displacement at this position is determined, resulting ina force per distance displaced of k = 250 ± 10 N/m for our tip. Thesimulations are parameterized with respect to the cantilever dimen-sions to estimate an uncertainty for the lateral spring constant. Thematerial used is single-crystal anisotropic silicon with the top of thecantilever as the <100> plane and the cantilever pointing in the<110> direction.To determine the sensitivity, S, which is the ratio of the lateralvoltage deflection to tip displacement, we take the slope of thestatic region of the deflection linetrace when the tip deflectsbefore the gold starts moving. This assumes that the lateral displace-ment of the AFM piezo stage is equal to the tip deflection during thestatic portion of the pushing. However, we expect the tip deflectionto be less than the stage displacement due to other effects, such asthe elastic deformation of the gold, or due to the tip slipping as itcomes into contact with the gold edge. These effects are evidencedby nonlinearity in the slope of the static region and by the variablesensitivities we observe for smaller squares. The net effect is that ourapproach will overestimate the displacement of the cantilever,which would result in our extracted forces providing an upperbound on the friction force. Because of the variable sensitivity weobserve for smaller squares (1 μm2 and smaller), we only use the4- and 9-μm2 linetraces to calculate an average lateral sensitivityof S = 27 ± 8 mV/nm.Annealing gold on hBNTo test the effect of heat annealing, the gold squares on hBN arevacuum-annealed for 30 min at 350°C in a tube furnace. Measuringtheir friction again, we see that the tip deflections decreased by~50%. AFM imaging shows that the grain sizes increased from~20 to 80 nm in diameter. This qualitative behavior is expectedfor polycrystalline materials, but it may also be the result oftrapped contaminants escaping from the gold-hBN interface.QPC deviceQPC device fabricationOur reconfigurable QPC device consists of a graphene strip encap-sulated in hBN, with a local graphite back gate on a Si/SiO2 sub-strate. 1D edge contacts are added to the graphene and graphiteback gate. The moveable top gates are 170-nm-thick gold-only de-posited with long, flexible electrodes to allow the gates to be movedwhile maintaining electrical contact. The Au-hBN interface frictionis relatively large for the top gates and flexible electrodes due to theirlarge surface area. To avoid cutting the gates while attemptingmotions, we cross-link 500-nm-tall PMMA rectangles onto thegates (fig. S4A). These tall features provide more surface area forthe AFM tip to push into to move the top gates. Although theystill deform from manipulations, they serve as a sacrificial handle.We dose the PMMA with 15,000 μC/μm2 at 30 kV and 3.2 nA tocross-link it. A small, isolated square of gold is also depositedonto the hBN (at the same time as the gold-only top gates) tosweep contaminants from the hBN surface, seen in fig. S4B.To determine the QPC constriction width, we measure the top-gate separation using AFM. Because of the height of the top gates,the separation at the base of the gate differs from what is observedusing a standard AFM tip. To account for this, we measure the side-wall profile using a Nanosensors ATEC-NC cantilever and subtractthat from what is measured with our standard tips, referencing fea-tures on the top surface of the gate.The graphite back gate for our device is smaller than the gra-phene. This is so that the 1D edge contacts to the graphene donot short to the back gate. We refer to regions of the graphenethat are not gated by the graphite as the graphene contacts, andthey are doped to a higher carrier density by the silicon back gate.QPC measurement detailsThe resistance data were taken in a four-probe configuration bymeasuring the current at the drain electrode via a Femto currentpreamplifier (1E6 V/A gain) and the longitudinal voltage dropwith an SR830 lock-in amplifier using low-frequency lock-in tech-niques. Before performing the 2D gate sweeps, we hole-dope thegraphene contacts by biasing the silicon back gate with −45 V cor-responding to a filling factor of ~7 at 9 T (nominal 285 nm SiO2thickness). For this reason, when both the dual-gated and back-gated regions are electron doped, the device is unable to effectivelytransmit quantum hall edge modes across the resulting pn junction,and it appears insulating as evident in the upper right corner of eachconductance color plot in Fig. 2 (E to H).In situ slidingMetal handle and flexible serpentine electrode fabricationTo fabricate the “thick” metal handles and flexible serpentine elec-trodes for in situ sliding, much thicker PMMA than normal is used:950 A11 spun at 4000 rpm for 5 s and then 2750 rpm for 2 min. Thisproduces a film of PMMA that is ~2.25 μm thick. EBL is performedusing our standard parameters described in the “General fabricationtechniques” section. The metal deposition consists of 80 nm Au, 10nm Cr, 1 μm Cu, 10 nm Cr, and 50 nm Au, all at 1 Å/s, except for thecopper, which is deposited at 3 Å/s. The bottom layer of gold is forlow friction with the hBN substrate, the top gold protects againstoxidation, and the chromium acts as a sticking layer between thegold and copper.Flexible serpentine electrode widths (1 μm and 500 nm) weretested, and we find that 500-nm-wide electrodes are more flexiblebut also more fragile. Both work well for manipulation, but weprefer the 500 nm because of the decreased interface area and,hence, reduced friction. We have also fabricated 1-μm and 500-nm-wide “thin” serpentine electrodes, which are 150-nm-tallgold-only instead of the thick multilayer metal combination, andfind that the 500-nm-wide electrodes are quite fragile in this caseand can break more easily.Typical metal handle donut dimensions we use have a nominalinner diameter of 3 μm and an outer diameter of 9 μm. The C shapeis to help with liftoff as well as to add compliance in being stretchedopen upon press-fitting with the AFM tip.In situ manipulation techniqueBefore performing in situ manipulations using our metal handles,we first flatten a 100 N/m, 1200 MHz MicroMasch 4XC AFM tip toincrease the tip-handle contact area. This is carried out by oscillat-ing the tip back and forth and side to side while in contact with SiO2of our sample until it is >3 μm wide, slightly larger than the innerdiameter of the donut. We choose this tip for its high force constantand the protruding “tip view” style, which makes it easier to alignwith the donuts.In general, our technique for performing in situ manipulationsinvolves the sample with a metal handle donut mounted on an XYZpiezo scanner that engages into a stationary flattened AFM tip. Thisprocess is carried out by first aligning the donut with the tip andraising the piezo stage. The stage is raised until the donut contactsBarabas et al., Sci. Adv. 9, eadf9558 (2023) 7 April 2023 6 of 8SC I ENCE ADVANCES | R E S EARCH ART I C L EDownloaded from https://www.science.org at National Institute for Materials Science on April 14, 2023the tip, as determined by optically observing a change in the lightreflected off the cantilever (seen through a 20× objective). After theinitial contact, we press-fit the tip into the donut by raising the stagefurther. At room temperature, we engage the donut into the tip by~1.5 to 2.5 μm to achieve a rigid connection with the structuresshown in Fig. 3C. In higher-friction situations, such as for largerobjects or at cryogenic temperatures, engaging more than ~2.5μm, corresponding to a larger downward force of the tip on thedonut, is necessary to reduce the slippage between the tip anddonut and to achieve deterministic, one-to-one sliding motions.For the sliding done at 7.6 K, we engaged ~5 μm as opposed to~2.5 μm at room temperature to get a similar one-to-one determin-istic motion. When finished, the tip can be removed by lifting itfrom the donut, which results in a slight lateral motion.Room temperature manipulation setupRoom temperature in situ sliding experiments, including the scan-ning top gate and the sliding graphene “hockey puck” heterostruc-ture, were performed at ambient conditions. The setup consists ofan AFM tip glued to a glass slide, mounted on a coarse manual XYZstage, and the sample/chip carrier mounted on a Thorlabs 3-axisNanoMax open loop piezo stage. A Mitutoyo VMU microscopewith 20× and 2× objectives is used for optical imaging. In boththe room temperature and cryogenic manipulation setups, nanoma-nipulation is performed using the piezo positioners, which arebrought into range by coarse screw-based positioners.Cryogenic manipulation setupCryogenic manipulations are performed in a continuous flow JanisST-500 optical cryostat using the same microscope as for the roomtemperature manipulation setup. ST-500 is cooled using a Janishelium recirculation setup and achieves a sample temperature of7.6 K. The sample is mounted on an Attocube ANSxyz100std/LTpiezo scanner (with 55 μm of XY range and 25 μm of Z range at~4 K), and the AFM tip is mounted to a custom flexural positionerfor coarse positioning at room temperature (fig. S6). Accounting forthermal contraction, the tip is coarsely positioned at room temper-ature so that it will be within the piezo scanner range of the sampleonce at base temperature.Sliding hockey puck heterostructureWe fabricate our encapsulated slidable graphene hockey puckdevice by transferring ~200-nm-thick top hBN onto monolayer gra-phene, writing rectangular PMMA etch masks, and etching withSF6 and O2 (same recipe as 1D edge contacts) to leave behind rect-angles of hBN on graphene. We then write and deposit 150-nmgold-only “wrap-around contacts,” which provide edge contacts tothe graphene. The thick top hBN and wrap-around contacts addmechanical support to prevent buckling and provide a rigid gripto hold the hockey puck heterostructures together while it is trans-lated. The hockey pucks are picked up using a PC/PDMS stamp andtransferred onto a large bottom hBN substrate before writing anddepositing thick flexible electrodes and donuts to electricallycontact and manipulate them in situ. Of the five hockey puckdevices we attempted to transfer and electrically contact, all butone were successfully contacted (fig. S7F).Two-probe resistance measurements were performed by currentbiasing and measuring the voltage drop across the device to deter-mine the resistance. The resistance versus displacement trace wasmeasured by displacing in 10-nm steps and then recording theresistance after a short pause. Here, we refer to the full forwardand backward measurement sequence as a single “motion.” Eachmotion takes about 30 s. A video of the motions was recorded,and a light source illuminated the sample during all of the measure-ments. In addition, all measurements were performed with thesilicon back gate grounded.In Fig. 3D, the zero position corresponds to the initial trans-ferred position of the hockey puck before any motion. After beingtransferred and contacted, the device was slid to the leftmost posi-tion, at about −275 nm, before the subsequent 1.2-μm back-and-forth motions.Scanning top-gate deviceThe scanning top-gate device was fabricated by encapsulating gra-phene in hBN and 1D edge-contacting it. For this device, the thickmetal top-gate serpentine electrode structure was initially writtenand deposited on a separate SiO2 chip and then picked up and trans-ferred onto the completed graphene device using a PC/PDMSstamp. This electrode was transferred to a position so that oneend overlapped with a previously written Cr/Au contact, which pro-vided the electrical connection to the top gate as well as a high fric-tion anchor point (fig. S8).Two-probe resistance measurements were performed in an iden-tical manner to the sliding hockey puck device described earlierwith the addition of two dimensions of motion. The fast scan direc-tion was perpendicular to the graphene channel. The top-gatevoltage was held at 0 V for the data presented here.Supplementary MaterialsThis PDF file includes:Supplementary TextFigs. S1 to S8Legends for movies S1 to S4Other Supplementary Material for thismanuscript includes the following:Movies S1 to S4REFERENCES AND NOTES1. S. D. Senturia, Microsystem Design (Kluwer Academic Publishers, 2002).2. M. Dienwiebel, G. S. Verhoeven, N. Pradeep, J. W. M. Frenken, J. A. Heimberg,H. W. Zandbergen, Superlubricity of graphite. Phys. Rev. Lett. 92, 126101 (2004).3. O. Hod, E. Meyer, Q. 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We also acknowledge the use of the UCI Laser Spectroscopy Laboratory. We thankL. Jauregui and M. Yankowitz for productive discussions, as well as the technical assistance ofQ. Lin, R. Chang, M. Kebali, J. Hes, and D. Fishman. Funding: This work was supported byNational Science Foundation Career Award DMR-2046849. I.S. acknowledges fellowshipsupport from the UCI Eddleman Quantum Institute. Author contributions: Investigation:A.Z.B., I.S., Y.Y., A.H.B.-A., and J.D.S.-Y. Sample preparation: A.Z.B., I.S., and A.H.B.-A. Supervision:J.D.S.-Y. Writing and review: A.Z.B., I.S., J.D.S.-Y., and A.H.B.-A. hBN crystal growth: T.T. and K.W.Competing interests: The authors declare that they have no competing interests. Data andmaterials availability: All data needed to evaluate the conclusions in the paper are present inthe paper and/or the Supplementary Materials.Submitted 29 November 2022Accepted 7 March 2023Published 7 April 202310.1126/sciadv.adf9558Barabas et al., Sci. Adv. 9, eadf9558 (2023) 7 April 2023 8 of 8SC I ENCE ADVANCES | R E S EARCH ART I C L EDownloaded from https://www.science.org at National Institute for Materials Science on April 14, 2023https://arxiv.org/abs/2204.10296Use of this article is subject to the Terms of serviceScience Advances (ISSN ) is published by the American Association for the Advancement of Science. 1200 New York Avenue NW,Washington, DC 20005. The title Science Advances is a registered trademark of AAAS.Copyright © 2023 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claimto original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).Mechanically reconfigurable van der Waals devices via low-friction gold slidingAndrew Z. Barabas, Ian Sequeira, Yuhui Yang, Aaron H. Barajas-Aguilar, Takashi Taniguchi, Kenji Watanabe, and JavierD. Sanchez-YamagishiSci. Adv., 9 (14), eadf9558. DOI: 10.1126/sciadv.adf9558View the article onlinehttps://www.science.org/doi/10.1126/sciadv.adf9558Permissionshttps://www.science.org/help/reprints-and-permissionsDownloaded from https://www.science.org at National Institute for Materials Science on April 14, 2023https://www.science.org/content/page/terms-service INTRODUCTION RESULTS Low-friction gold on hBN Mechanically tunable QPC In situ heterostructure and cryogenic manipulation DISCUSSION MATERIALS AND METHODS General fabrication techniques Lithography One-dimensional edge contacts Exfoliation and dry transfers Friction measurements Fabrication for gold-hBN friction measurements AFM lateral friction measurements Annealing gold on hBN QPC device QPC device fabrication QPC measurement details In situ sliding Metal handle and flexible serpentine electrode fabrication In situ manipulation technique Room temperature manipulation setup Cryogenic manipulation setup Sliding hockey puck heterostructure Scanning top-gate device Supplementary Materials This PDF file includes: Other Supplementary Material for this manuscript includes the following: REFERENCES AND NOTES Acknowledgments