Observation of stick-slip behavior with structural superlubric characteristics

Abstract

Stick-slip is typically associated with high friction and wear, whereas superlubricity is characterized by ultralow friction and negligible wear. Can these two seemingly opposite phenomena coexist? Here, we present an experimental observation of stick-slip behavior that exhibits structural superlubric characteristics, in a microscale single-crystalline Au mesa sliding against a single-crystalline graphite substrate. This behavior emerges when the applied sliding velocity falls below a critical threshold. Unlike traditional ones, this observed stick-slip phenomenon originates from the inherently superlubric Au/graphite interface and exhibits key structural superlubric features: near zero coefficient of friction and wear-free long-distance sliding. Theoretical analysis attributes this duality to the distinctive nature of Au/graphite interface: a globally atomically flat incommensurate van der Waals interface, yet locally weakly pinned by discrete point vacancy defects. Bond formation and rupture at these sites underpin the static–dynamic friction asymmetry that drives stick–slip. These findings not only deepen our understanding of stick-slip and structural superlubricity, but also open pathways for stable, long-lasting control of superlubric interfaces in micro/nanoscale actuators and sensors.

The authors report stick-slip behavior with structural superlubric characteristics at a gold/graphite contact: an interface that is globally atomically flat and incommensurate, yet locally weakly pinned by discrete point vacancy defects.

Introduction

Sliding is a fundamental and ubiquitous mode of motion that spans a wide range of disciplines, from mechanistic studies of friction dissipation (e.g., phononic¹ and electronic² mechanisms) to material design (e.g., van der Waals (vdW) flexible films³) and innovative device development⁴ (e.g., reconfigurable sliding devices⁵ and sliding ferroelectrics^6,7). Among the diverse phenomena observed at sliding interfaces, stick-slip behavior is particularly prominent, manifesting across multiple scales—from macroscopic geological processes (e.g., earthquakes⁸) and mesoscopic biological tactile perception⁹ to atomic-scale discrete stick-slip behavior¹⁰. Although the periodicity inherent in stick-slip behavior offers potential for precise control and valuable physical insights^9,11–13, its typical association with high friction and wear results in undesirable effects—such as vibrational noise¹⁴, elevated energy consumption, and surface degradation¹⁵—that severely limit its practical applications. As a result, modern interface science has increasingly focused on eliminating stick-slip to achieve low power consumption and extended operational lifetimes¹⁶, giving rise to the pursuit of superlubricity^17–22. Among this field, structural superlubricity^21,23–25 stands out, enabling specific solid contacts to achieve ultralow wear and friction between two incommensurate crystalline surfaces.

As two seemingly incompatible states, is it possible to realize stick-slip behavior possessing structural superlubric characteristics, or equivalently, to observe stable and controllable periodic stick-slip behavior at a structural superlubric interface? In principle, this might not be entirely impossible—previous works have actually provided some clues. (1) AFM-probe studies demonstrate that periodic energy corrugations on crystalline surfaces, coupled with a probe as a soft spring, can generate periodic stick-slip (Prandtl-Tomlinson (PT) model)^26–29. But the substantive role of the vanishingly small corrugations at structural superlubric incommensurate interfaces remains debated^23,30–33. (2) A distinct class of superlubric systems—metal/2D material interfaces—exhibits anomalous static friction peaks^25,34,35 that could serve as pinning sources for the stick phase³⁶. Yet, a comprehensive physical picture of these interfaces is lacking, obscured by complications like boundary lubrication layer effect³⁴, frictional ageing³⁷, chemical bonding³⁸, moiré superlattices^39,40, and edge effect⁴¹. Achieving this would not only reshape our view of sliding interfaces but also unlock stick-slip applications (with tunable dynamic-static switching) to surmount micro- and nanoscale friction/wear barriers, paving the way for practical micro- and nanodevices^11,42.

In this work, we challenge this conventional wisdom by reporting the observation of stick-slip behavior with structural superlubric characteristics (near-zero coefficient of friction (CoF) and zero wear). This state is achieved through atomically full contact sliding between a microscale single-crystalline Au mesa and a single-crystalline graphite substrate, when the dragging velocity is reduced below a critical threshold.

Results

Experimental observation

In this study, an Au/graphite contact interface was prepared in situ by thermally evaporating Au onto an epitaxial single-crystal graphite (ESCG) substrate. This setup was further integrated with photolithography techniques to create micro-scale Au mesas (3 ~ 5 μm side width, 0.2 μm thick), as shown in Fig. 1a. Details of the preparation process can be found in the Methods and Supplementary Fig. S1. Au was chosen for its chemical inertness—unlike most metals (e.g., Cu, Al, Ni), Au does not form oxide layers under ambient conditions, ensuring a true metal/graphite van der Waals interface. The ESCG surface was selected for its atomic-level flatness and almost defect-free sites⁴³, which provide the following advantages: (1) it ensures that the Au mesas deposited onto the graphite surface remain atomically smooth and single-crystalline at the interface^25,44,45; (2) it encapsulates the lower surface of the resulting Au mesas, protecting them from reconstruction^46,47 and molecular adsorption^48–50. The interfacial cleanliness of the UHV-formed Au/graphite contact is further verified by electrical transport measurements and cross-sectional STEM characterization (Supplementary Figs. S2 and S3). A detailed comparison of the surface quality between ESCG and conventional HOPG is provided in Supplementary Discussion 1 and Supplementary Fig. S4. As shown in Fig. 1b–d, we conducted AFM morphology characterization on the graphite surface exposed after the Au mesas were pushed aside, remaining atomic-level flatness (Rq ~0.1 nm, Methods). Additionally, electron backscatter diffraction (EBSD) was employed to analyze the crystallographic orientation of the samples, as shown in Fig. 1e, confirming the high single-crystal quality of both the Au and ESCG in all three directions. Further analysis reveals that the as-deposited interface adopts an R0° epitaxial orientation: $\mathrm{Au}\left(111\right)\parallel \mathrm{Graphite}\left(0001\right)$ with $\mathrm{Au}\left[1\overline{1}0\right]\parallel \mathrm{Graphite}\left[11\overline{2}0\right]$ (Supplementary Discussion 2). Finally, the friction of the Au/graphite interface was measured by AFMs (Cypher and NT-MDT successively), where an AFM probe was positioned on the Au mesa to slide against the ESCG substrate, as depicted in Fig. 1f (Methods and Supplementary Movie 1).

Fig. 1. Experimental set-up.

a SEM image of in-situ fabricated Au mesas on the epitaxial single-crystal graphite (ESCG) substrate. Scalebar 25 μm. b, c The optical images before and after pushing the Au mesa aside and exposing the graphite surface; scalebars: 3 μm. d The atomically flat morphology of the graphite surface buried under the Au mesa. Scalebar 600 nm. e Electron backscatter diffraction (EBSD) inverse pole figure maps (IPF-X, IPF-Y, and IPF-Z) of the Au mesas on the ESCG substrate; colors correspond to crystallographic orientations as indicated by the IPF color key, and the uniform color in each map confirms the single-crystalline nature. Scale bar, 5 μm. f Schematic diagram of the experimental setup for measuring the interfacial friction between an Au mesa and graphite substrate, with pure in-plane contact. Repetition numbers are provided in “Methods”.

In the Au/graphite crystalline vdW interface—traditionally regarded as a prototypical superlubric system owing to its incommensurability (sublinear friction scaling laws²⁵, superlubricity under ambient condition³⁵, ultralow electrical resistivity due to full contact⁴⁴), we observed anomalous friction behavior, particularly in the low-velocity regime.

1. Nonmonotonic velocity dependence of friction. Consistent results across three sliding distances (125, 250, and 500 nm) confirm the reliability of our findings. As shown in Fig. 2a, the driving velocity ($v_{\mathrm{s}}$) range can be divided into three distinct regimes: (a) Low-velocity regime ($v_{\mathrm{s}}$ < 300 nm/s), the friction force remains nearly constant, showing negligible velocity dependence. (b) Intermediate-velocity regime (300 nm/s < $v_{\mathrm{s}}$ < 1500 nm/s), surprisingly, friction force decreases with increasing velocity, contradicting the conventional expectation of a positive correlation⁵¹. (c) High-velocity regime ($v_{\mathrm{s}}$ > 1500 nm/s), friction force begins to exhibit sublinear positive growth, aligning with previously reported velocity dependence at superlubric interfaces^52–54.

2. Anomalous periodic stick-slip behavior and its velocity dependence. Distinct friction loop characteristics were observed for each regime (see Fig. 2b–d, with additional data available in the Supplementary Figs. S5–S7). (a) For low-velocity regime, the system displays stable periodic stick-slip behavior with a slip length of approximately 10.2 nm. (b) For intermediate-velocity regime, stick-slip behavior becomes increasingly chaotic, trending toward disorder. The slip length at stick-slip events decreases to 2.7 ~ 5.9 nm, accompanied by increased randomness. (c) For high-velocity regime, stick-slip behavior vanishes entirely, and the system transitions to steady sliding.

Fig. 2. Observation of stick-slip behavior and its velocity dependence.

All measurements were performed under a constant normal load of 17.3 μN. a Nonmonotonic variation of friction force with velocity, divided into three regimes: velocity-independent, negatively correlated, and positively correlated. The background shading indicates the three regimes, with the color gradient (pink to blue) representing the crossover between them; The two vertical dash-dotted lines at 300 nm/s and 1500 nm/s mark the regime boundaries. Three distinct sliding distances (125, 250, and 500 nm) were tested to ensure experimental reliability. b–d Friction loops corresponding to three representative velocities marked by the dashed lines in (a), illustrating stick-slip (red), chaotic (purple), and steady sliding (blue) behaviors, respectively. The upper parts present enlarged views of the 50–75 nm segments, referring to the gray box. The pair of horizontal gray dashed lines marks the nearly constant inner envelope of the friction loops. e–g Corresponding force-velocity profiles. Source data are provided as a Source Data file.

The nonmonotonic friction in Fig. 2a results from the measured friction force (“Methods”) comprising two components: the inner envelope and the stick-slip sawtooth (Supplementary Fig. S8). For velocity below 1500 nm/s, the inner envelope remains basically unchanged, while the sawtooth contribution progressively weakens with velocity. Above 1500 nm/s, only the inner envelope contributes, displaying sublinear positive growth. The velocity-driven evolution of stick-slip is further captured in the force-velocity space (as detailed in Supplementary Discussion 3): at low driving velocity, successive stick-slip cycles collapse onto a stable limit cycle (Fig. 2e); approaching the intermediate regime, the loop shape evolves from cycle to cycle, indicating the coexistence of multiple periodicity scales (Fig. 2f); at higher velocities, the force trace exhibits chaotic fluctuations, with the phase lacking periodicity (Fig. 2g).

Analysis of stick-slip transitions (Fig. 2b–d) reveals two key insights: (i) slip length is either velocity-independent (low-velocity regime) or negatively correlated (intermediate-velocity regime); (ii) slip length in the low-velocity regime (~10 nm) significantly exceeds the Au/graphite lattice constant (~0.25 nm for graphite, ~0.29 nm for Au(111)). These findings contrast with recent reports of nonmonotonic velocity-dependent atomic friction⁵⁵, where the PT model predicts a transition from single to multiple slips with increasing velocity, with slip length positively correlated to velocity and an integer multiple of the lattice constant^27,28,56. In our system, the slip length decreases with increasing velocity and far exceeds the atomic lattice spacing, suggesting a different pinning mechanism operating at the superlubric interface. Intriguingly, the observed velocity-dependent friction resembles that of oil squalane (C₃₀H₆₂) lubrication between shearing mica surfaces⁵⁷. But their mechanism, which is typically associated with molecular lubrication, should, in theory, not be expected at our intrinsic, incommensurate vdW interface. This raises two questions: Is the phenomenon we observe truly indicative of structural superlubricity? Is the phenomenon inherent to the Au/graphite interface, or influenced by external factors?

Here, we verified two characteristics of structural superlubricity—virtually null CoF and zero wear. First, as shown in Fig. 3a, near zero and even negative CoFs were measured with typical velocity from each regime selected: stick-slip regime, $-0.00029\pm 0.00003$; chaotic regime, $-0.00018\pm 0.00004$; steady sliding regime, $-0.00014\pm 0.00009$. Additionally, friction traces from each speed regime at both highest and lowest normal forces were compared, Fig. 3c, with no observable difference. The observed friction independence of normal force is very different from traditional oil-lubrication-based interfaces, revealing the structural superlubric characteristic. Second, the friction force measured over 3000 sliding cycles, as illustrated in Fig. 3b, remains stable, further supporting the robustness of this superlubric state. Lastly, we moved the Au mesa aside to expose the buried graphite surface after sliding and performed Raman spectroscopy to assess structural defects. As shown in Fig. 3d, no defect-related D peaks were detected in the Raman spectra at any of the nine selected points across the contact region (“Methods”). Further Raman mapping results of $I_{\mathrm{D}}$, as shown in Fig.3d inset, also reveal that no observable defects emerge at the graphite surface after sliding.

Fig. 3. The verification of structural superlubricity.

a Normal force dependence of friction from three regimes: stick-slip (red, 1 Hz and 0.2 μm), chaotic (purple, 4 Hz and 0.2 μm), and steady sliding (blue, 4 Hz and 0.5 μm). Solid lines are linear fits to $F_{\mathrm{f}}=\mu N+F_0$, yielding coefficients of friction (CoF) μ = −0.00029 ± 0.00003 (stick-slip), −0.00018 ± 0.00004 (chaotic), and −0.00014 ± 0.00009 (steady sliding). b The friction force recorded over 3000 cycles at three regimes, under a normal force of 113.6 μN. c Comparison of friction traces at the lowest and highest normal loads, showing no significant differences across three regimes. For (a–c), red, purple, and blue lines represent stick-slip (sliding velocity: 0.4 μm/s), chaotic (sliding velocity: 1.6 μm/s), and steady sliding (sliding velocity: 4 μm/s) regimes, respectively. d Raman spectra of the buried graphite surface after the long-cycle sliding test, acquired at nine locations across the contact region. All spectra show the characteristic G (~1580 cm⁻¹) and 2D (~2700 cm⁻¹) peaks of graphite, while no detectable defect-related D peak (~1350 cm⁻¹) is observed, indicating the absence of structural degradation. Inset: Raman mapping of the D-peak intensity ($I_{\mathrm{D}}$) over the contact region; scalebar, 3 μm. Source data are provided as a Source Data file.

To verify that the observed phenomenon arises from the intrinsic Au/graphite interface rather than edge adsorption or other extrinsic factors, we conducted a controlled experiment by actively introducing water molecules and ubiquitous organic airborne contaminants at the Au/graphite interface. The experiment was performed as follows (as detailed in Supplementary Fig. S9): (1) Based on the sample shown in Fig. 1a, we used the Au mesa array as a mask to etch the underlying graphite substrate to a depth of approximately 500 nm (Fig. 4a(i)). (2) A tungsten probe was then employed to cleave the Au mesa. Once fully detached, the Au mesa adhered to the tungsten probe due to vdW adhesion. (3) The Au mesa was subsequently transferred via this tungsten probe onto a clean graphite substrate, thereby reconstructing the Au mesa/graphite system (Fig. 4a(ii)). The primary distinction between this reassembled system (Fig. 4b(ii)) and the original (Fig. 1a) lies in the presence of water molecules and organic airborne contaminants at the Au/graphite interface, a result of air exposure of the Au underside during transfer (around 2 min)^{48,49,58–61}. Raman characterization of the detached Au mesa confirms the presence of hydrocarbon contaminants on the exposed surface (Supplementary Discussion 4 & Fig. S10). Notably, unlike the friction behavior observed in the original system (Fig. 2), this reassembled interface exhibited only a monotonic increase in friction with velocity (Fig. 4c), with no stick-slip behavior in the friction loops (Fig. 4d–f). This might be related to the flexibility of water molecular⁶² and organic airborne contaminants. All the force-velocity profiles exhibit chaotic fluctuations, as shown in Fig. 4g–i. These observations were consistent across sliding distances of 125 nm and 250 nm, underscoring the reliability of our findings. This evidence suggests that the incorporation of water molecules and organic airborne contaminants disrupts the intrinsic Au/graphite contact, thereby eliminating stick-slip behavior and modifying friction’s velocity dependence—confirming that the observed phenomenon in Fig. 2 is exclusive to the pristine interface.

Fig. 4. Experimental results under the influence of adsorption.

a Schematic illustrations of the experimental procedure. (i) The Au mesa array was used as a mask to etch the underlying graphite substrate. (ii) After cleavage and transfer using a tungsten probe, the Au mesa was reassembled onto a clean graphite substrate, with water molecules and organic airborne contaminants introduced at the Au/graphite interface. b Optical images of the sample before (i) and after (ii) the transfer. Scale bar, 2 μm. c Friction as a function of driving velocity for the reassembled system, exhibiting a monotonic increase. Two sliding distances of 125 and 250 nm were tested to confirm the experimental reliability. d–f Friction loops recorded at three typical velocities of 25, 875, and 1950 nm/s, marked by the vertical dashed lines in (c), all showing the absence of stick-slip behavior at the reassembled interface. g–i Corresponding force-velocity profiles. Repetition numbers are provided in “Methods” and source data are provided as a Source Data file.

Theoretical model

Based on the above observations, we confirm the presence of stick-slip behavior in structural superlubricity as an intrinsic phenomenon of Au/graphite interfaces. Unlike other superlubric interfaces—such as graphite/graphite⁶³, graphene/hBN, MoS₂/hBN and MoS₂/graphite⁶⁴—which exhibit negligible static friction peaks, previous studies have consistently reported that metal micro/nanoparticles (e.g., Au, Sb) deposited on 2D substrates (graphite, MoS₂, hBN) experience higher static friction than dynamic friction^{5,25,34,35,38}. However, the precise mechanisms behind this remain unclear. We note that gold surfaces have been reported to exhibit anomalous friction behavior in AFM tip-based experiments due to high atomic mobility and metallic neck formation^65–68. A detailed analysis in Supplementary Discussion 5 demonstrates that, owing to the different contact configuration and the extremely low interfacial shear stress (~10 kPa) in our system, the micrometer-scale Au mesa can be treated as effectively rigid, and the atomic mobility mechanism does not apply (Supplementary Figs. S11 and S12). Recent work by Ding et al. provides a fresh perspective: the graphite surface actually exhibits point-defect vacancy⁶⁹, which may lead to special weak bonding at the interface. To confirm the presence of these defects, we employed selective thermal oxidation (650 °C, air, 30 min) to preferentially enlarge vacancy sites to a size detectable by AFM. The resulting nanopits—with single-atomic-layer depth—provide indirect but reliable evidence that sparse point vacancies are intrinsic to the ESCG surface, with a density of ~2.8 μm⁻² on pristine graphite, increasing modestly to ~4 μm⁻² after Au deposition (Supplementary Discussion 6 and Fig. S13–S19).

According to the simulation results by Pulido et al.⁷⁰, we hypothesize that isolated Au atoms might be captured by these vacancy defects (as shown in the Fig. 5a). Combined with the recent work of Wang et al.⁷¹ on the superlubricity nature of Au twisted grain boundaries, it can be considered that the interaction between Au atoms might not be very strong. This picture is quantitatively consistent with our friction data: the measured static friction of ~0.5 μN, distributed over ~60 vacancy sites beneath a typical Au mesa (~20 μm²), yields a per-defect pinning force of ~8 nN—comparable to the rupture force of a few Au–Au bonds (~1.5 nN per bond^72,73), supporting the hypothesis that each vacancy site anchors a single Au adatom bonded to the mesa underside through multiple metallic bonds. The interaction between the isolated Au atom and the underlying Au surface, we believe, is dominated by thermally activated bond formation ($~\exp \left[-\mathrm{\Delta }{E}_{\mathrm{on}}/k_{\mathrm{B}}T\right]$) and externally forced bond-breaking ($~kv/f_{\mathrm{s}}$)⁷⁴. In the low-velocity sliding regime, where the bond formation rate exceeds the bond-breaking rate, the interface reaches a state of bond saturation (as illustrated in Fig. 5b). In contrast, at high sliding velocities, when the bond formation rate falls below the bond-breaking rate, the interface remains in a non-bonding state (Fig. 5c)⁷⁵. Molecular dynamics simulations further support this picture: an Au slab sliding on defect-free graphite exhibits ultralow friction with linear velocity dependence, whereas introducing a single point vacancy substantially increases friction in the low-velocity regime and produces a sublinear velocity dependence that progressively converges toward the pristine case at higher velocities (Supplementary Fig. S20)—qualitatively consistent with the thermally activated bonding mechanism proposed above. A semi-quantitative analysis is provided in Supplementary Discussion 7. We note that while the experimental observations presented below are fully consistent with this model and provide supporting evidence, the specific bonding and bond-breaking dynamics at the atomic scale have not been directly verified experimentally. We therefore present this interpretation as a physically motivated hypothesis that captures the key experimental trends. Alternative pinning sources—such as trace interfacial contaminants or other defect-related interactions—cannot be definitively excluded.

Fig. 5. Mechanism of this velocity-induced phase transition.

Schematics of a an isolated Au atom captured by a point vacancy defect in graphite, b, c bonding and non-bonding states at low and high velocities, respectively. d Conceptual model: (i) a rigid Au mesa is sliding against graphite substrate by an AFM probe modeled as a spring with stiffness $k_{\mathrm{s}}$ at a constant velocity $v_{\mathrm{s}}$; (ii) velocity-dependent friction illustrating the transition between static and dynamic regimes at the critical velocity $v_{\mathrm{crit}}$ (see Eq. 2); (iii) time evolution of the relative velocity $\stackrel{°}{x}$. e Numerical simulations reproducing both stick-slip and steady sliding states. f Simulated average friction as a function of $v_{\mathrm{s}}$, revealing a sharp transition near $v_{\mathrm{crit}}$, in agreement with experimental data. g Phase diagram of sliding behavior as a function of $v_{\mathrm{s}}$ and $\mathrm{\Delta }{F}_{\mathrm{r}}$, identifying stick-slip (red squares), chaotic (yellow spheres), and steady sliding (blue triangles). The critical velocity $v_{\mathrm{crit}}$ lies between the upper boundary of the stick-slip regime and the lower boundary of the chaotic regime, showing a clear linear dependence on $\mathrm{\Delta }{F}_{\mathrm{r}}$ (purple line). h Phase diagram as a function of $v_{\mathrm{s}}$ and $1/\sqrt{k_{\mathrm{s}}}$, confirms the predicted linear scaling relation. i Phase diagram as a function of $v_{\mathrm{s}}$ and temperature, consistent with a thermal activated bonding mechanism. Source data are provided as a Source Data file.

Here, we introduce a critical velocity $v_{\mathrm{crit}}$ to delineate these regimes (Fig. 5d(ii)), defined as:

$$\left\{\begin{array}{c}\hfill F_{\mathrm{f}}<F_{\mathrm{s}},\mathrm{if}\stackrel{°}{x}\le v_{\mathrm{crit}}\hfill \\ \hfill F_{\mathrm{f}}=F_{\mathrm{d}},\mathrm{if}\stackrel{°}{x}>v_{\mathrm{crit}}\hfill \end{array}\right),$$ 1

where $\stackrel{°}{x}$ is the mesa’s velocity, $F_{\mathrm{s}}$ is the maximum static friction and $F_{\mathrm{d}}$ is the dynamic friction (intercept of the linear velocity dependence, as denoted in Fig. 5d(ii)).

Based on the above assumptions and B.N. J. Persson’s work³⁶, we further developed a model system (Fig. 5d(i)) comprising a rigid Au mesa (mass $m$) on a graphite substrate, pulled by a spring (stiffness $k_{\mathrm{s}}$) at a constant driving velocity $v_{\mathrm{s}}$. The governing kinematic equation is:

$$m\ddot{x}=k_{\mathrm{s}}\left(v_{\mathrm{s}}t-x\right)-F_{\mathrm{f}}-m\gamma \stackrel{°}{x},$$ 2

where $x$ is the mesa’s position, $t$ is time, $F_{\mathrm{f}}$ is the friction force, and $\gamma$ is the interfacial damping coefficient (i.e., the slope of the linear velocity dependence of kinetic friction, Fig. 5d(ii)). Unlike a simple harmonic oscillator, this system features complex friction with transitions between static and kinetic friction regimes, as detailed in Eq. (1). See Supplementary Discussion 8 for analytical details. The mesa’s motion occurs in three phases: (1) stick phase, where the spring force is below $F_{\mathrm{s}}$ and the block remains stationary; (2) initiation phase, where friction drops abruptly from $F_{\mathrm{s}}$ to $F_{\mathrm{d}}$, causing rapid acceleration to a startup velocity $v_{\mathrm{init}}$; and (3) slip phase, where $v_{\mathrm{init}}$ > $v_{\mathrm{s}}$, the spring force diminishes, and the velocity decays exponentially, finally stabilizing at $v_{\mathrm{s}}$. The critical velocity $v_{\mathrm{crit}}$ determines the friction regime (Fig. 5d(iii)): when $v_{\mathrm{s}}$ exceeds $v_{\mathrm{crit}}$, the system stabilizes at $v_{\mathrm{s}}$, will not enter into the static friction regime; when below, the velocity decays to $v_{\mathrm{crit}}$, and motion halts. As supported in Supplementary Discussion 3, these dynamics changes manifest in the AFM probe deformation signal $F_{\mathrm{lateral}}=k_{\mathrm{s}}\left(v_{\mathrm{s}}t-x\right)$, reflecting stick-slip or steady sliding, as validated by numerical simulations (Fig. 5e). Notably, since the stick-slip periodicity is governed by $\mathrm{\Delta }x=\mathrm{\Delta }F/k_{\mathrm{eff}}$, probes with different lateral stiffnesses yield different periodicities on the same Au mesa, confirming that the periodicity reflects the spring-block mechanics rather than the interfacial defect spacing (Supplementary Fig. S21). Averaged friction forces show a sharp transition near $v_{\mathrm{crit}}$ (Fig. 5f), consistent with experimental perturbations.

Based on the model outlined above, we can make the following inferences of the critical velocity ($v_{\mathrm{crit}}$): First, it arises from the competition between thermally activated bond formation and externally forced bond breaking, thus positively correlated with temperature. Second, the measured $v_{\mathrm{crit}}$ is also influenced by external factors (e.g., environmental conditions, instrumental noise) and internal system properties (e.g., probe condition, selected Au mesa). Given the system’s simplicity, we employed dimensionless analysis to predict:

$$v_{\mathrm{crit}}\propto \frac{\mathrm{\Delta }{F}_{\mathrm{r}}}{\sqrt{m{k}_{\mathrm{s}}}},$$ 3

where $\mathrm{\Delta }{F}_{\mathrm{r}}=F_{\mathrm{s}}-F_{\mathrm{d}}$ is the difference between maximum static ($F_{\mathrm{s}}$) and dynamic friction ($F_{\mathrm{d}}$). Controlled experiments validate this prediction: (1) Using the same Au mesa and AFM probe (fixed $m$ and $k_{\mathrm{s}}$), we varied $\mathrm{\Delta }{F}_{\mathrm{r}}$ by rotating the mesa and classified friction behavior across velocities (Fig. 5g). The upper bound of stick-slip and lower bound of chaotic behavior define $v_{\mathrm{crit}}$’s range, showing a clear linear dependence on $\mathrm{\Delta }{F}_{\mathrm{r}}$. (2) With the same Au mesa and orientation (fixed $\mathrm{\Delta }{F}_{\mathrm{r}}$ and $m$), we altered $k_{\mathrm{s}}$ using different probes and observed friction behavior (Fig. 5h), revealing a linear trend with $1/\sqrt{k_{\mathrm{s}}}$. (3) Although mass ($m$) could not be systematically varied due to experimental constraints, we reason that larger $m$ increases inertia, reducing susceptibility to external perturbations and thus lowering $v_{\mathrm{crit}}$—a qualitatively consistent trend. (4) As shown in Fig. 5i, we found that critical velocity increases with temperature, which supports our hypothesis of thermally activated bond formation dominating the process at higher temperatures.

Furthermore, twist-angle-dependent friction measurements reveal that dynamic and static friction exhibit opposite dependencies on the interfacial lattice registry (Supplementary Discussion 9 and Figs. S22 and S23): dynamic friction decreases with twist angle due to reduced moiré corrugation, while static friction increases due to enhanced vacancy-bonding probability. This decoupling further confirms that the stick-slip behavior within structural superlubricity at the Au/graphite interface arises from the coupled contributions of the incommensurate van der Waals interaction and the vacancy-mediated bonding mechanism.

Discussion

This study unveils a groundbreaking duality at the Au/graphite interface, where stick-slip motion and structural superlubricity coexist below critical velocity: an intrinsic contact interface, periodic stick-slip behavior, a negligible CoF, and zero wear. Further theoretical analysis attributes this stick-slip behavior to the switch between static and dynamic friction at Au/graphite interface, with a predicted critical velocity ($v_{\mathrm{crit}}$) proportional to $\mathrm{\Delta }{F}_{\mathrm{r}}/\sqrt{m{k}_s}$ and temperature. These findings redefine our understanding of interface sliding and pave the way for innovative applications.

Yet, several unresolved questions emerge, inviting further investigation:

Critical velocity and friction regimes

To rationalize the origins of static and kinetic friction at the Au/graphite superlubric interface, we introduced a bonding-rupture model based on point vacancy defects. A critical velocity $v_{\mathrm{crit}}$ sharply delineates two regimes: below $v_{\mathrm{crit}}$, static frictional law governs, while above it, another prevails. Intriguingly, recent work by Sirorattanakul et al. has shown that, even when shear stresses remain far below the static threshold, two equal-sized polymethyl methacrylate (PMMA) plates can sustain creeping motion at vanishingly low speeds (down to ${10}^{-12}\mathrm{m}/\mathrm{s}$)⁷⁶. This raises the question of whether, within our static friction dominated regime, similarly counterintuitive shear-sliding phenomena might also arise? This may provide an additional atomic-level observation perspective for research in the field of friction.

Defect-enabled functional control

Point defects in graphite locally break lattice symmetry and introduce chemically active sites with associated electronic states⁷⁷. Metal atoms or clusters can become anchored at these sites⁷⁰, profoundly modifying the interfacial band structure⁷⁸. Functionalization of such defects—for example, by selective adsorption of specific elements—could enable tuning of electrical and magnetic properties⁷⁹ without compromising superlubricity. This strategy suggests a route toward programmable superlubric interfaces, adding an additional degree of freedom for device engineering.

Prospects for technological innovation

The interplay of stick-slip and superlubricity uncovered here holds promise for micro- and nanotechnology. The controllable periodicity of stick-slip motion could underpin step-wise micro-actuators, enabling precise positioning in devices like reconfigurable microsystems or radiofrequency switches that rely on repeated static-to-dynamic transitions.

Methods

Sample fabrication

The Au/graphite contact interface was prepared in situ using the following fabrication procedures (as illustrated in Supplementary Fig. S1): (i) Mechanically exfoliate the ESCG in a cleanroom environment to obtain a clean, atomically flat surface. (ii) Transfer the exfoliated ESCG to an ultra-high vacuum (UHV) chamber and anneal the substrate to remove any adsorbed contaminants from the graphite surface. (iii) Without breaking vacuum, thermally evaporate a 200 nm thick layer of Au onto the clean graphite substrate within the same UHV chamber—thereby forming and permanently sealing the Au/graphite interface under UHV conditions before any ambient exposure. (iv) Spin-coat AZ1500 photoresist (20 cP) onto the Au layer. (v) Pattern the photoresist to define the geometry of the Au mesas. (vi) Etch the excess Au by immersing the sample in an Au-removal solution (BC046, Beichen, China), leaving only the patterned mesas. (vii) Remove the remaining photoresist with N-Methyl-2-pyrrolidone, resulting in an array of Au mesas in direct vdW contact with the graphite substrate. We note that steps (iv)–(vii) are performed under ambient cleanroom conditions but act only on the exposed top surface and sidewalls of the Au film; the Au/graphite interface remains sealed by intimate van der Waals contact throughout these processes.

Surface characterization

(1) The morphology of the exposed graphite surface was captured in contact mode using an AFM (Cypher ES-Oxford Instruments, Asylum Research AFM software) (0.11 N/m, Au-coated tips, NT-MDT & TipsNano). (2) EBSD characterization was carried out using an Oxford NordlysMax3 instrument. EBSD data were acquired with Oxford Instruments AZtec software (version 4.0). (3) To evaluate possible damage to the graphite substrate surface, Raman spectra were collected on a LabRAM HR Evolution spectrometer using HORIBA LabSpec 6. The setup included a 532 nm laser wavelength, 1800 gr/mm grating, 0.1 cm⁻¹ spectral resolution, 4 s acquisition time, and 1 μm spot diameter.

Friction measurement

Friction experiments were conducted in an ambient atmosphere at a temperature of $25\pm 1$ °C and a relative humidity of $30\pm 4\%$. AFM probes (VIT_P/IR, TipsNano) with a force constant ranging from 25 to 95 N/m and a resonance frequency between 200 and 400 kHz were selected. (1) For the friction dependence on velocity in Figs. 2 and 4, it was measured using AFM (Cypher ES, Oxford Instruments, Asylum Research AFM software), consisting of an XYZ piezoelectric displacement platform and a high numerical aperture objective lens (×20). After setting the scanning range, the velocity dependence of friction can be obtained by further tuning the scanning frequency (from 0.1 to 200 Hz in our test). (2) For the friction dependence on normal force in Fig. 3, it was measured using a commercial NTEGRA upright AFM from NT-MDT (Nova Px 3.4.1 software). The AFM setup included a 100 µm XYZ piezoelectric displacement platform and a high numerical aperture objective lens (×50, Mitutoyo). The AFM tip’s sensitivity was calibrated in situ: normal sensitivity was determined using the Sader method^80,81, while lateral sensitivity was calibrated using a diamagnetic levitation spring system⁸² (see Supplementary Discussion 10). The friction force data in Fig. 2a are calculated from the [3/10, 7/10] part of the friction loop.

Statistics and reproducibility

No statistical method was used to predetermine sample size. The SEM image in Fig. 1a is representative of 6 different regions on the same sample, all showing similar Au mesa arrays; the in-situ fabrication yields uniform mesa arrays across the substrate, and similar arrays were observed on independently fabricated samples used in this study. The mesa displacement and exposure of the buried graphite surface shown in Fig. 1b–d were independently repeated 5 times with similar results. The EBSD maps in Fig. 1e are representative of 6 different regions examined, all confirming the single-crystalline nature of the Au mesas and graphite substrate. The reassembly and transfer experiment shown in Fig. 4b was independently repeated 5 times with similar results. Friction–velocity measurements were performed at three (Fig. 2a) and two (Fig. 4c) independent sliding distances with consistent results.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Author contributions

Q.Z., D.P., and Z.W. supervised the project. W.C., Z.W., and Q.Z. conceptualized the project. W.C., T.W., W.Z., and Y.W. conducted the experiments and the related data processing. W.C. and J.W. carried out the theoretical calculations. All authors participated in the discussion of the research.

Peer review

Peer review information

Nature Communications thanks Jose Vilhena, who co-reviewed with Oscar Gutierrez-Varela, and Nitya Nand Gosvami for their contribution to the peer review of this work. A peer review file is available.

Funding

This work was supported by National Natural Science Foundation of China (No. 12502131, No. 11921002), China Postdoctoral Science Foundation (No. BX20220181), European Research Council ULTRADISS Contract (No. 834402), Guangdong Special Support Plan Science and Technology Innovation Young Top-notch Talents (No. 2023TQ07Z553), Guangdong Basic and Applied Basic Research Foundation (No. 2022B1515120040), Shenzhen Science and Technology Program (Grant No. KQTD20240729102211015), Shenzhen Science and technology program (No. JSGG20220831095802004) and Shenzhen Key Laboratory of Superlubricity Technology (No. ZDSYS20230626091701002).

Data availability

The friction, atomic force microscopy, electron backscatter diffraction, Raman spectroscopy, and electrical transport data generated in this study have been deposited in the Zenodo database under accession code 10.5281/zenodo.21638845 (https://doi.org/10.5281/zenodo.21638845)⁸³. Source data are provided with this paper.

Code availability

The custom MATLAB code used for the numerical simulations in this study is available in the Zenodo repository at https://doi.org/10.5281/zenodo.21638845.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s41467-026-77734-3.