Introduction

The failure and degradation induced by friction is a critical challenge in modern mechanical, electronic and biological systems, causing considerable global energy consumption (~23%)1. Understanding and manipulating frictional dissipation at the nanoscale interfaces is of great significance for achieving superlubricity2,3,4,5,6,7,8,9 and further designing tunable friction regimes10,11. However, numerous nanoscale frictional behaviors have been observed to deviate from the classical Amontons’ law12, i.e. linear friction-loading relationship. These include the negative coefficient of friction13, the moiré-tile manipulation-induced friction switch10,11,14 and the diameter-dependent flow slippage15,16. Notably, these anomalous frictional phenomena appear to be attributed to the curved geometries: bubbled graphene, wavy moiré superlattices and carbon nanotubes (CNTs). In general, low-dimensional materials with nanoscale curved geometries consistently exhibit diverse electronic and magnetic properties, such as strain-induced pseudomagnetic fields17,18,19, nonlinear Hall effects20,21 and direction-dependent magnetotransport22,23. Therefore, curved geometries with these unique quantum states are suggested to establish the bridge towards the novel frictional behaviors at the nanoscale.

Folded graphene, a combination of curved graphene and flat step edges24, has emerged as a promising candidate for exploring curvature-driven effects. It is well-established that step edges exert a more pronounced influence on friction compared to interior atoms, even in a superlubric state4,25. This is attributed to the higher potential barrier26,27 and enhanced chemical reactivity28,29 at atomic step edges. Conversely, the curved edge of graphene introduces an additional parameter: curvature, which can be precisely tuned by the number of folded layers. This folding technique not only significantly reinforces the mechanical properties of graphene nanocomposites30,31,32,33, but also provides a platform for realizing tunable electronic structures and quantum states. For instance, the abnormal frictional behaviors of water inside sub-10 nm CNTs16 originate from the quantum effects of plasmon-hydron resonance34. The folded tubular edge, with its unique chirality and varying widths, generates one-dimensional (1D) electronic states and facilitates tunable flat bands24. However, ambiguities persist regarding energy dissipation associated with edge nano-curvature, and the ability to regulate friction through modulation of edge quantum states remains limited.

In this study, we report a quantum friction phenomenon at folded graphene edges, characterized by a nonlinear increase in friction. This violates the linear law between friction and layer numbers at exposed graphene edges. The nonlinear friction is primarily attributed to the splitting of strain-induced pseudo-Landau levels (PLLs) and the corresponding pseudomagnetic field (PMF) at folded edges. This electronic reconstruction gives rise to a non-uniform energy gap structures that provide a viable pathway for quantum friction dissipation. The electronic energy dissipation is significantly suppressed by the PLLs, whereas the energy dissipation mediated by phonon emission remains unaffected, as supported by ultrafast spectroscopy and the elimination of alternative classical mechanisms. The curved topology-induced quantum states allow for precisely manipulating friction energy dissipation modes.

Results and discussion

Construction of folded graphene

To achieve graphene folding, monolayer and multilayer graphene flakes were mechanically exfoliated onto a Si/SiO2 substrate. By lateral scanning with an applied normal load at the atomic force microscope (AFM) tip, graphene was folded as illustrated in Fig. 1a with the topography measured by AFM shown in Fig. 1b (further details on tearing and folding are shown in Supplementary Figs. 1–4). The lattice spacing of the pristine graphene (Fig. 1d), as indicated by the height profile, was measured to be 0.25 nm (Supplementary Fig. 2f). This spacing is slightly enlarged in the folded graphene in Fig. 1c.

Fig. 1: Nano AFM-tip driven graphene tearing and folding at step edges.
figure 1

a Schematic illustration of the mechanical exfoliation process and the tip-induced tearing and folding of graphene at a step edge. b Atomic force microscope (AFM) images of 2 L + 2 L folded graphene. Inset: height profile along the white dashed line and the thickness of the fold. Scanning tunneling microscope (STM) images of folded (c) and exposed region (d), with inset 1 × 1 nm2 atomic-resolution images in the upper right corner. The graphene hexagonal lattice (white lattice model) superimposed on the inset shows the folded edge lattice stretched. e The Raman signatures in the G peak region of folded and unfolded single-layer graphene. Electron energy loss spectroscopy (EELS) spectra of C K-edge of the folded (f) and exposed (g) graphene edges obtained from the annular dark-field scanning transmission electron microscopy (ADF-STEM) images on the right side of (f) and (g). Scale bars: 400 nm (b), 1 nm (c, d).

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In addition to the topography and lattice constant, the Raman spectra and electron energy loss spectroscopy (EELS) spectra further elucidate the distinctions between pristine and folded graphene. The G peak of 1 L + 1 L folded graphene is split into two peaks, as shown in Fig. 1e, due to the folding strain-induced broken rotational symmetry35. Additionally, the 2D peak of 1 L + 1 L folded graphene is blue-shifted by ~10 cm-1 (Supplementary Fig. 5), indicating that the twist angles between folded graphene layers induce a reduction of Fermi velocity36. As shown in the EELS spectra in Fig. 1f, g, the two characteristic peaks in EELS spectra are the π* transition at ~286 eV and the σ* transition at ~292 eV, which are typical of bulk carbon atoms in graphene. However, the intensity ratio of π*/σ* in the folded graphene edge decreases from 1.0 at the edge to 0.6 towards the terrace, corresponding to a continuous variation in the orientation of the electron beam relative to the graphene layers from parallel to perpendicular37 (Supplementary Fig. 6).

Friction force measurements

To investigate the effect of folding curvature on graphene friction, we conducted nanofriction experiments on folded graphene edges with varying layer numbers using the lateral force mode of AFM under an argon atmosphere, comparing them to exposed edges at the same heights. Here, ΔFL denotes the increase in lateral force (FL) for the AFM tip climbing the graphene edges (Fig. 2a). For fewer graphene layers shown in Fig. 2a, the ΔFL at the 2 L + 2 L folded edge (1.67 nN) is less than that at the 4 L exposed edge (5.94 nN) with a normal load (FN) of 4.2 nN and scanning rate of 2.44 Hz. However, as the number of graphene layers increases, the ΔFL at the 7 L + 7 L folded edge (14.89 nN) becomes comparable to that at the 14 L exposed edge (14.80 nN) (Fig. 2b). To further elaborate on friction regulation through folding curvature, we investigated the detailed variation of ΔFL with FN for exposed and folded graphene edges in layers 2-18. Analogous to the classical coefficient of friction μ = Ff/FN, we defined the coefficient of the ΔFL at the edges as μL = ΔFL/FN. The μL is obtained by fitting the mean ΔFL measured at five locations along the edge as a function of FN, ensuring consideration of spatial distribution and avoiding the issue of loading-independent generalizability26,38. As shown in Fig. 2c, μL of the exposed edges exhibits a strong linear dependence on the increasing number of graphene layers, explicable by the Prandtl-Tomlinson (PT) model introducing the tip-sample interaction at the edge26. In contrast, as the number of folded layers increases, a two-stage variation of μL becomes discernible: (i) below 14 L, μL exhibits an exponential growth tendency and consistently remains lower than that of the exposed edges; (ii) after reaching 14 L, μL transitions to a linear relationship. (detailed experimental and simulated friction results are shown in Supplementary Figs. 8–15 and Supplementary Data 1).

Fig. 2: Nano friction experiments under lateral force mode of atomic force microscopy (AFM).
figure 2

Topographical images and lateral force signals of folded and exposed graphene edges with 4 layers (a) and 14 (b) layers. Inset: height profile along the white dashed line and the thickness of the fold. The ΔFL denotes the increase in lateral force (FL) for the AFM tip climbing the graphene edges. c Curves of the μL versus layer number for folded and exposed edges. Error bars represent the standard deviation obtained by measuring the μL of three different graphene flakes at the same layer number. d Adhesion Fad at folded edges and exposed edges with increasing graphene layers, respectively. Error bars represent the standard deviations obtained by measuring three different locations at the same layer number Scale bars for (a) and (b): 100 nm. e Raman G peaks of exposed and folded graphene edges with the number of layers from 2−18. f G peak frequencies as a function of layer number at the folded and exposed graphene edges. Error bars represent the standard deviations obtained by measuring three different locations at the same layer number. The black dashed lines in (c−f) are the fittings of corresponding data points, and the functional forms and fittings are shown in Supplementary Note 14.

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Since the nanofriction of two-dimensional materials depends on both the sample and the tip39,40, we verified the anomalous friction behavior of folded graphene edges under multiple testing conditions (tip category: DLC1, DLC2 and Al-G; scanning velocities: 12.2 and 24.4 μm/s) (Supplementary Fig. 13). This strongly suggests that the origin of frictional singularity stems from the folding topologies rather than the testing conditions. In addition, nanofriction is known to be influenced by the interfacial adhesion force Fad41, which can be derived from the force spectroscopy (Supplementary Fig. 16). Both Fad of the folded and the exposed graphene edges linearly decrease with increasing layers, as shown in Fig. 2d, due to the reduced contact between the tip and surface as the edge height rises. Given that the curved surface of the folded edge increases the contact area (Supplementary Fig. 16), folded edges exhibit relatively high adhesion forces compared to exposed edges. Furthermore, the heights of multilayer folded edges (>12 L) align with those of exposed edges due to reduced curvature (Supplementary Fig. 13d), leading to convergent adhesion. However, the measured adhesion force does not correlate with the observed friction changes at the folded graphene edges.

Notably, strain is prevalent in graphene nanostructures42,43,44 and affects friction2,45. Atomic-scale STM images clearly show that the graphene lattice is stretched at the folded edge (Fig. 1c, d), and we therefore characterized the fold-induced strain via Raman spectroscopy. As shown in Fig. 2e and f, taking the exposed edge as the reference state with its G peak frequency near 1586 cm-1, the G peak of folded edge undergoes a redshift, the largest of which is at the 1 L + 1 L folded edge (~4.2 cm-1). Figure 2f shows the fitted frequencies of G peaks at the folded and exposed edges as a function of the number of layers. This strain law, which varies continuously with the number of layers and the strain is still present at the 9 L + 9 L folded edge, is not in agreement with our experimentally observed friction law. In light of the above discussion, to reveal the intrinsic mechanism of nonlinear friction law at folded graphene edges, it is necessary to delve into the electronic structure associated with the folding strain.

Formation of PMF in folded graphene edges

It has been shown that local strain fields in graphene with curvature geometries (nanobubbles17, buckled supperlattices18, corrugations46) can generate strong PMFs, forcing electrons to move circularly as if subjected to an external magnetic field19. Such cyclotron motion of charge carriers corresponds to the emergence of PLLs, significantly modifying the material properties. Therefore, the local electronic structure of the folded and exposed graphene edges was characterized using spatially resolved scanning tunneling spectroscopy (STS), as shown in Fig. 3. The dI/dV spectra measured below and above the exposed graphene edge exhibit a smooth V-shaped structure (Fig. 3a), which is inherent to the local density of states of graphene. In contrast, the spectrum at the folded edge reveals a succession of peaks with different energy intervals (Fig. 3b), which can be attributed to separated electron Landau levels (LLs) arising from a fold-induced PMF47. Other possible origins, which we have ruled out as unlikely, include 1D electron confinement and defect induction (Supplementary Note. 8).

Fig. 3: Electronic structures of folded and exposed graphene.
figure 3

a, b Scanning tunneling microscope (STM) topographic images of the 2 L exposed edge and 1 L + 1 L fold and the corresponding spatial resolved dI/dV spectra obtained at the marked positions, respectively. c Linear pseudo-Landau level (PLL) energies versus \({{\mathrm{sgn}}}\left(n\right)\sqrt{\left|n\right|(\left|n\right|+1)}\) extracted from (b). The black dashed line is linear fit against the experimental data. d Experimental topographic line scan and experimental calculated Bs profile along the direction perpendicular to the 1 L + 1 L folded edge. Inset: radius of the curvature at different positions. Error bars represent the standard deviations obtained by measuring four different locations along the axial direction of the folded edge. e Extracted Bs at different positions along the folded edge axis for 1 L + 1 L, 3 L + 3 L and 5 L + 5 L. Inset: topographic images where the black arrows represent the measured positions of the corresponding STS spectra. f, g Representative dI/dV spectra and corresponding Bs values of 1 L + 1 L, 3 L + 3 L, 5 L + 5 L, 7 L + 7 L folded graphene edges and bulk graphite, respectively. Error bars represent the standard deviations obtained by measuring ten different locations along the axial direction of the folded edges at the same layer number. h A schematic illustration of energy band structures in differ-layer-fold graphene. Folded graphene edges exhibit discrete pseudo-Landau levels below 14 layers and demonstrate a continuous energy band structure beyond 14 layers.

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In the case of monolayer17, bilayer47,48 and trilayer graphene49,50, the energies of the LLs are linearly related to \(\sqrt{{|n|}}\), \(\sqrt{{|n|}(\left|n\right|+1)}\) and \(\sqrt{{|n|}(\left|n\right|+1)(\left|n\right|+2)}\), respectively, where n is the PLLs index. Since the folded edge is formed in monolayer graphene, the possibility of massless Dirac fermions was first considered, whereas the linearity of the PLLs energies with respect to \({{\mathrm{sgn}}}(n)\sqrt{{|n|}}\) is not obvious (Pearson’s r is 0.98844) (Supplementary Fig. 18). In contrast, the linear relationship between PLLs energies and \({{\mathrm{sgn}}}(n)\sqrt{{|n|}(\left|n\right|+1)}\) exhibited the best fitting (Pearson’s r is 0.99977), which is used to describe the massive Dirac fermions in bilayer graphene48:

$${E}_{n}-{E}_{D}={{\mathrm{sgn}}}\left(n\right){{\hslash }}{\omega }_{c}\sqrt{\left|n\right|\left(\left|n\right|+1\right)}$$
(1)

where \({{E}}_{n}\) and \({E}_{D}\) are the energy of the nth LL and the Dirac point with respect to the Fermi level, \(\hslash\) is the reduced Planck constant, \({\omega }_{c}=e{B}_{s}/{m}^{*}\) is the cyclotron frequency, \({m}^{*}\) ~0.028\({m}_{e}\) is the effective mass of the electrons and holes47, \({m}_{e}\) is the free-electron mass, \(e\) is the electron charge and \({B}_{s}\) is the strength of the PMF. A plot of energy \(({E}_{n}-{E}_{D})\) versus \({{\mathrm{sgn}}}(n)\sqrt{{|n|}(\left|n\right|+1)}\), shown in Fig. 3c, complied from dI/dV spectra of five positions at 1 L + 1 L folded edge (Fig. 3b), follows the expected scaling behavior for LLs in bilayer graphene.

The spacing of the peaks changes over different positions along the direction perpendicular to the folded graphene edge (Supplementary Fig. 19), indicating a spatial evolution of Bs. The spatial Bs profile was extracted from the spectra measured along different lines perpendicular to the 1 L + 1 L folded edge (Supplementary Fig. 19). As shown in Fig. 3d, the Bs reaches the maximum at the highest position of the folded edge (~30.86 ± 1.58 T), corresponding to the smallest radius of curvature (R2 ~ 3.45 nm), compared to the position before the highest position (R1 ~ 6.85 nm). The spatial distribution of the PMF, induced by folded curvature-dependent strain field, aligns with the observed reduction in friction at folded edge. Moreover, considering the absence of defects at the folded edges, the discrete PLLs of the folded edges can alter the electron distribution, leading to the reduced intrinsic resistance linked to the electron-phonon interaction51(Supplementary Fig. 22).

Since the PMF induces Landau level quantization without an external magnetic field, the Bs is in turn related to the inherent strain in the folded edges, the PLLs demonstrates a pronounced layer dependence. For folded edges with more than two layers, the PLLs energies meet the linear relationship with \({{\mathrm{sgn}}}(n)\sqrt{{|n|}(\left|n\right|+1)(\left|n\right|+2)}\) (Supplementary Fig. 18), which is used to describe the massive Dirac fermions in trilayer graphene49:

$${E}_{n}-{E}_{D}=sgn\, (n)\left[{\left(2{{e}}{{\hslash }}{\nu }_{F}^{2}\right)}^{3/2}/{\gamma }_{1}^{2}\right]{B}^{3/2}\sqrt{|{n}|({|n|}+1)({|n|}+2)}$$
(2)

where \({\gamma }_{1}\) is the interlayer hopping energy in trilayer graphene and \({v}_{F}\) is the Fermi velocity. Due to the uniform curvature along the axial direction of the folded edges, the spatial distribution of Bs at the 1 L + 1 L, 3 L + 3 L and 5 L + 5 L folded edges is relative stable and tends to decrease significantly (Fig. 3e and Supplementary Fig. 20). Figure 3f shows five representative dI/dV spectra obtained on each folded graphene edges. By combing the slopes of the linear fits for each dataset with Eqs. (1) and (2), the Bs are estimated to be 31.56 ± 0.97 T, 27.61 ± 0.86 T and 20.76 ± 1.18 T for 1 L + 1 L, 3 L + 3 L and 5 L + 5 L folded edges (Fig. 3g), respectively. Notably, the 7 L + 7 L folded graphene edge does not exhibit PLLs peaks and instead approaches the electronic structure of bulk-phase graphite (Fig. 3f). The trend of Bs at folded edges aligns with the fact that strain decreases with the number of folded layers (Fig. 2f). As the curvature of the folded edges decreases with layer numbers, leading to insufficient strain to induce the PMF at the 7 L + 7 L folded edge.

This segmented evolution of PMF strength with layer number correlates precisely with the anomalous friction behavior at folded graphene edges. Based on the foregoing analysis, it can be concluded that splitting of PLLs induced by PMF plays a crucial role in modulating frictional dissipation at folded graphene edges. As opposite to the step barrier-dominated friction of exposed graphene edges, the frictional dissipation with the increasing folded layers is the consequence of the competitive mechanism between conventional step barrier and quantized LLs. Notably, LLs have been reported to affect the energy dissipation of optically pumped hot electrons and enable the switching of multiple energy dissipation modes in graphene52, although direct experimental evidence is still lacking.

Analysis of excited hot carrier dynamics

Slower hot carrier cooling was observed at folded graphene edges compared to exposed edges, as revealed by femtosecond (fs) pump-probe spectroscopy53,54. As shown in Fig. 4a, the 1 L + 1 L folded edge and 2 L exposed edge were pumped at 3.54 eV, respectively, with transient absorption (TA) spectrum obtained through the time-delayed probe laser (Fig. 4b and c). The ΔA of folded graphene edges, as shown in Fig. 4d, decayed over a longer timescale (1.44 ps) compared to exposed edges (0.99 ps), indicating a deteriorating effect of PLLs during the carrier relaxation processes. Moreover, carrier temperature (Tc) is extracted by fitting the high-tails of the TA spectrum using the Maxwell-Boltzmann function55 (Fig. 4b, c and Supplementary Fig. 23). The cooling time of hot carriers for folded edges (0.49 ps) and exposed edges (0.32 ps) (Fig. 4e) further indicates a slower energy dissipation process at folded graphene edges.

Fig. 4: Analysis of excited hot carrier dynamics.
figure 4

a, Schematic diagram of the transient absorption (TA) measurement, with a pump and a probe pulse directed onto a graphene sample with a variable delay. Transient absorption (TA) mapping and the corresponding normalized TA spectra (0.6-10 ps) of folded (b) and exposed (c) graphene edges pumped at 350 nm. d, e The normalized decay dynamic and carrier cooling curves for the folded and exposed graphene edges, respectively. f Energy loss rate of hot carriers plotted as a function of carrier temperature (Tc), extracted from the cooling curve in (e). The solid lines are fitted using a longitudinal optical (LO)-phonon emission model. g Schematic illustration of the relation of friction excited carriers in pristine graphene with massless Dirac cones (left) and folded graphene attaining PLLs (right). The three axes represent the electron cooling time, LO phonon emission lifetime (τLO) and acoustic phonon temperature (Ta), respectively. The black lines in (d−f) represent the fitting results of corresponding data, and the functional forms and fitting parameters are shown in Supplementary Note 11 and 14.

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Furthermore, a longitudinal optical (LO)-phonon emission model was used to obtain the energy loss rate of per carrier (Jr) during the carrier cooling process as follows56,57:

$${J}_{r}=\frac{3}{2}\frac{\hslash {\omega }_{0}}{{\tau }_{{LO}}}\left({{{{\rm{e}}}}}^{\frac{\hslash {\omega }_{0}}{k{T}_{a}}}-{{{{\rm{e}}}}}^{\frac{\hslash {\omega }_{0}}{k{T}_{c}}}\right)\frac{{N}_{{LO}}\left({T}_{a}\right)}{{N}_{{LO}}\left({T}_{c}\right)}{\left(\frac{k{T}_{c}}{\hslash {\omega }_{0}}\right)}^{2}{{{e}}}^{\frac{-\hslash {\omega }_{0}}{k{T}_{c}}}$$
(3)

where \({\tau }_{{LO}}\) is the LO phonon emission lifetime, Ta is the acoustic phonon temperature, NLO(T) is the LO-phonon occupation number at temperature T, and \(\hslash {\omega }_{0}\) is the characteristic LO-phonon energy. As illustrated in Fig. 4f, the initial energy loss rate (from 0.22 to 0.076 eVps-1) of exposed edge is over 1.7 times higher compared to folded edge with high Tc (500-900 K). This difference is attributed to electron-phonon interaction, during which hot carriers dissipate extra energy primarily through the dominant Fröhlich interaction via LO phonon emission58. Subsequently, Jr decreases rapidly as the Tc approaches the lattice temperature, driven by the interaction between LO and acoustic phonons. The fitted characteristic LO-phonon lifetime τLO (Fig. 4f) in folded edges is 0.48 ps as compared to 0.35 ps for exposed edges. It is suggested that the reduced frictional dissipation at folded graphene edges mainly originates from the suppression of electron-phonon coupling strength by the folding-induced quantum states, and is independent of the acoustic phonon emission, and phonon-phonon interaction.

The strength of the electron-phonon coupling crucially depends on the energy difference between electronic transition and phonon energy, which is significantly suppressed due to the mismatch of optical phonon energy and inter-Landau level spacing59 (Supplementary Fig. 24). Meanwhile, the non-equidistant of PLLs in folded graphene, without enabling energy conservation, retrains Auger heating effects60 (Supplementary Fig. 25). Therefore, the emergence of PLLs in folded graphene edges enables the quantum state contribution to compete with that of the potential barrier in classical PT model26, achieving the manipulation and switching of multiple-particle-induced energy dissipation modes.

In summary, we engineered folded graphene with varying layer numbers via nano-AFM tip manipulation, thereby achieving continuous curvature modulation. Experimental findings reveal an anomalous quantum friction behavior, as the friction at the folded graphene edge exhibits an exponential relationship up to 14 layers, transitioning to a linear relationship beyond this threshold. This nonlinear friction behavior is predominantly governed by the folding-induced quantum states of PLLs, rather than by the edge potential barriers that scale linearly with step height as described by the classical PT model. We elucidated the precise modulation mechanism of the folding topologies on multiple energy dissipation modes during graphene edge friction using ultrafast spectroscopy. Friction electronic dissipation, including electron-phonon coupling is significantly suppressed as evidenced by the increase electron cooling time from 0.32 ps to 0.49 ps, due to the mismatch of phonon energies with discrete spacing of PLLs. Conversely, friction phononic dissipation arising from acoustic phonon emission is not influenced due to its proximity to the graphene lattice temperature (~303 K). This topology-induced quantum state enables the regulation of a single channel in the frictional dissipation process, and even the switching between dissipation channels, which is crucial for understanding and controlling friction of low-dimensional materials. Controlling dissipation based on edge topology opens new avenues for investigating local dissipation mechanisms in electrical transport and exploring the development of dissipation-free, nonlinear quantum devices61,62,63.

Methods

Sample preparation

Single-layer, bi-layer, tri-layer, and multi-layer graphene flakes ranging from 20 to 30 µm in length were prepared through the mechanical exfoliation of highly oriented pyrolytic graphite (HOPG, HQ graphene). These graphene layers were then transferred onto a Si/SiO2 substrate, and their topography and thickness were characterized using AFM in tapping mode. Folded graphene samples were fabricated by AFM (Cypher ES, Asylum Research Inc) tip with a spring constant ~28 N/m. A normal load (~µN) was applied to the AFM tip to sweep the edge along the upward direction, and the folded graphene was formed by repetitive lateral-mode tracing and retracing (details in Supplementary Fig.1).

Structural and chemical characterization

The detailed bond structure was characterized by micro-Raman spectrometer (Horiba JobinYvon HR800, France) with an excitation wavelength of 532 nm. The power density on the sample was carefully controlled at 0.5 mWm-2 to avoid sample damage. High-resolution transmission electron microscopy (HRTEM) images and EELS spectra were obtained on a Cs CETCOR Image Corrector TEM/STEM (Spectra 300, ThermoFisher Scientific) operated at 300 kV and equipped with a monochromator, Gantan image filter (GIF Quantum ER/965, Gatan, USA).

Atomic force microscopy

The frictional properties of exposed and folded graphene edges across different layers were thoroughly investigated using a friction force microscope (FFM) (Cypher ES, Asylum Research Inc). During the experiment, under the argon atmosphere, the inside temperature of the Cypher cabinet was 30 ± 1 °C, and the humidity was 5%-7%. Two types of tips were used for friction measurements, ContDLC (Budgetsensors, tip radius ~15 nm) and ContAl-G (Budgetsensors, tip radius ~8 nm). The cantilever in the vertical and lateral direction were calibrated by the standard Sader’s method64 and a non-contact method65. For detailed calibration parameters, see Supplementary Table 1. The currents at graphene edges were measured by conductive atomic force microscopy (CAFM) with a Cr-Au coated Si tip (HQ: CSC38/Cr-Au, Mikromasch). The adhesive force was obtained by measuring the pull-off forces as the DLC tip (ContDLC Budgetsensors) detached from the graphene substrate with AFM and the adhesive force mapping was obtained by measuring the pull-forces at 576 sites.

STM and STS measurements

The STM system utilized was an ultrahigh vacuum single-probe scanning probe microscope LT SPM XP from Omicron. All STM and scanning tunneling spectroscopy (STS) measurements were performed at liquid-nitrogen temperature (77.5 K), and the images were taken in a constant-current scanning mode. Lateral dimensions observed in the STM images were calibrated using a standard graphene lattice as well as a Si(111)-(7 × 7) lattice, and the STS spectra were calibrated using an Au (111) surface. The STS (dI/dV-V) measurements were conducted using a standard lock-in technique with an a.c. bias modulation of 20 mV and 919 Hz. All the STS measurements were not recorded unless the typical standard spectrum of graphite was obtained.

Femtosecond TA measurements

The femtosecond transient absorption setup is based on a regenerative amplified Ti:sapphire laser system from Coherent (800 nm, 35 fs, 6 mJ/pulse, and 1 kHz repetition rate), nonlinear frequency mixing techniques and the Helios spectrometer (Ultrafast Systems LLC). Briefly, the 800 nm output pulse from the regenerative amplifier was split in two parts with a 50% beam splitter. The transmitted part was used to pump a TOPAS Optical Parametric Amplifier (OPA) which generates a wavelength-tunable laser pulse from 250 nm to 2.5 μm as pump beam. The reflected 800 nm beam was split again into two parts. One part with <10% was attenuated with a neutral density filter and focused into a 2 mm thick sapphire window to generate a white light continuum (WLC) from 420 nm to 800 nm used for probe beam. The probe beam was focused with an Al parabolic reflector onto the sample. After the sample, the probe beam was collimated and then focused into a fiber-coupled spectrometer with CMOS sensors and detected at a frequency of 1 kHz. The intensity of the pump pulse used in the experiment was controlled by a variable neutral-density filter wheel. The delay between the pump and probe pulses was controlled by a motorized delay stage. The pump pulses were chopped by a synchronized chopper at 500 Hz and the absorbance change was calculated with two adjacent probe pulses (pump-blocked and pump-unblocked). All experiments were performed at room temperature.