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Device fabrication

Micrometre-sized apertures were etched into silicon-nitride-coated silicon substrates (500 nm SiNx) using photolithography, wet etching and reactive ion etching, following the protocol previously reported8. Our devices had several apertures next to each other and were 2 μm in diameter each (Extended Data Fig. 1). Monolayers of graphene and hBN were obtained by micromechanical cleavage31 and identified using a combination of optical microscopy, AFM and Raman spectroscopy, as previously reported8,32,33. The monolayers were suspended over the apertures in the SiNx substrate. The resulting free-standing membranes were coated on one side by drop-casting the Nafion polymer (5%, 1,100 equivalent weight) to obtain ≈10-μm-thick films. The devices were annealed in a water-saturated environment at 130 °C to crosslink the polymer. The collector electrode was prepared by laminating a Pt foil (10 × 10 mm, 99.95% purity, Goodfellow) onto a cylindrical carbon block with a hot compression mounting machine (SimpliMet). The exposed Pt surface was then subjected to mechanical and electrochemical polishing. Gaskets were used to cover the carbon block and expose only the Pt surface for contact with Nafion–2D crystal devices34. For measurements, the Nafion film was hydrated with deionized water and allowed to equilibrate before placing it in contact with the Pt collector.

SECCM probes

Nanopipettes for SECCM were fabricated from quartz theta capillaries with filaments (WAR-QTF120-90-100, Friedrich & Dimmock). The capillary (outer diameter, 1.2 mm; inner diameter, 0.90 mm; length, 100 mm) was pulled to form a fine sharp point with a tip opening diameter of about 200 nm, using a CO2-laser puller (Sutter Instruments P-2000). The nanopipette was then filled with 100 mM HCl electrolyte, and a silicone oil layer was added on top of the electrolyte solution in the tip to minimize evaporation during prolonged scanning procedures35. Two AgCl-coated Ag wires, fabricated by electrochemically oxidizing Ag wires (0.125 mm in diameter) in saturated KCl solution36, were used as quasi-reference counter electrodes (QRCEs). Each of the nanopipette channels was fitted with a QRCE positioned about 3–4 cm away from the tip end36.

SECCM instrumentation

SECCM was carried out using a home-built workstation37. The SECCM probe was mounted on a z piezoelectric positioner (P-753.1CD LISA, Physik Instrumente) whereas the studied graphene or hBN device was mounted on an xy piezoelectric positioner (P-622.2CD PIHera, Physik Instrumente). The SECCM probe was moved to the initial scan position using an XY-micropositioner (M-461- XYZ-M, Newport) controlled with Picomotor Actuators (8303, Newport). An optical camera provided a visual guide for the probe positioning. The microscopy stage and all positioners were enclosed in a Faraday cage with heat sinks and vacuum panels to minimize noise and thermal drift. The Faraday cage was placed on an optical tabletop with tuned damping (RS 2000, Newport) balanced on a high-performance laminar flow isolator (S-2000 Series, Newport).

Data acquisition and instrumental control were carried out using an FPGA card (PCIe-7852R) running the Warwick Electrochemical Scanning Probe Microscopy software ( Two home-built electrometers were used for current measurements, together with home-built eighth-order brick-wall filters with the time constant of the current amplifier set to 10 ms. Influence of acquisition parameters on the noise level is detailed elsewhere38. The current data were acquired every 4 μs, and 256 samples were averaged to give a data acquisition rate of about 1 ms.

Scanning protocol

SECCM was deployed in the hopping mode34,39,40 by recording spatially resolved current versus time (It) traces of the reduction of protons at the bottom Pt collector electrode (Extended Data Fig. 2). The hopping mode protocol involved the approach of the probe to the 2D crystal surface until the electrolyte meniscus at the end of the tip (not the nanopipette itself) made contact (as detailed below). After a measurement on one site was completed, the probe was retracted and moved to the next site to generate a map of It traces over the entire device surface.

Two voltage controls are important in this protocol. The first is the potential difference, Ebias, between the QRCEs in each of the two channels of the nanopipette (Extended Data Fig. 2a). This gives rise to an ion current between the two channels in the nanopipette, Idc, which is used as a feedback signal to detect whether the meniscus is in contact with the surface. When the droplet meniscus touched the device surface, a spike in Idc 100 pA signified ‘jump-to-contact’41 (detected with a feedback threshold of 45 pA; Extended Data Fig. 2b,c). When this threshold was reached, the probe motion was stopped. Note that this signal provided a means of landing the meniscus on the 2D crystal surface, irrespective of its local proton permeability. Further details of the Idc transients are provided in the section entitled Consistency of meniscus-surface wetting.

The second voltage, Eapp, between the nanopipette probe and the proton-collecting working electrode sets the potential of the Pt collector electrode with respect to the QRCEs as Ecollector = −(Eapp + Ebias/2) (ref. 42). This potential is chosen as Ecollector = −0.5 V versus Ag/AgCl QRCE (equivalent to an overpotential of about 0.2 V versus the standard potential for the hydrogen evolution reaction). This was the maximum voltage used in ref. 8 in which the linear-response proton transport was studied in similar devices. Ecollector drives the electrochemical proton reduction at the Pt electrode, which results in current Icollector (inset of Extended Data Fig. 2). Icollectort measurements were made for 500 ms and involved the area defined by the meniscus between the SECCM nanopipette and the substrate. After each measurement within this temporary and spatially localized droplet cell, the probe was retracted at a speed of 4 µm s−1 (Extended Data Fig. 2b) and moved to the next location where the above procedure was repeated. This allowed us to obtain a spatial- and time-resolved dataset for Icollector. Proton-current maps in our figures are presented as an average of the last 100 ms of the Icollectort transients.

The z-position of the probe was recorded synchronously throughout the whole measurement procedure, with the value at the end of each nanopipette approach yielding a topographical map of the studied 2D-crystal device. Nonlinear sample-tilt and piezo-drift effects in such topographical maps were corrected using the scanning probe image processing software package (v6.0.14, Image Metrology). SECCM topographical maps of mechanically exfoliated graphene devices (not shown) were similar to those subsequently obtained by AFM, as expected. Such maps, recorded synchronously with proton transport activity, were especially valuable as they revealed morphology around proton-conducting sites in CVD graphene (Extended Data Fig. 5).

Consistency of meniscus-surface wetting

The SECCM maps of proton transport through graphene and hBN monolayers exhibit a marked spatial inhomogeneity. To establish that this is an intrinsic property of the 2D crystals and not a result of variations in surface–probe contact, we investigated the consistency of meniscus-surface wetting by analysing the current Idc flowing between the two channels in the nanopipette. Below we explain how Idc is used as a feedback signal that unequivocally detects meniscus-surface wetting, regardless of proton transport through a 2D crystal.

Extended Data Fig. 3 illustrates the steps that take place during the SECCM scan and how Idc changes during each step. Initially, the probe is not in contact with the sample (step i (approach)) and \({I}_{{\rm{dc}}}^{{\rm{i}}}\) is constant as a function of time (about 400 pA in this case). As the probe gets closer, the meniscus encounters the sample (step ii, (meniscus touch)). In this step, \({I}_{{\rm{dc}}}^{{\rm{ii}}}\) sometimes decreased very slightly with respect to \({I}_{{\rm{dc}}}^{{\rm{i}}}\)Idc = \({I}_{{\rm{dc}}}^{{\rm{ii}}}\)\({I}_{{\rm{dc}}}^{{\rm{i}}}\) < 0), attributed to slight squeezing of the meniscus. However, this depended on a specific 2D material measured. For graphene samples, we typically see a decrease of about 1% or 5 pA (Extended Data Fig. 3b,c), whereas for hBN we do not see such a drop (Extended Data Fig. 3e,f). We attribute this difference in behaviour to a stronger attraction of the electrolyte in the probe to hBN than graphene. The next step is meniscus wetting (step iii (meniscus wets)). This step is characterized by a sharp increase in current, ΔIdc = \({I}_{{\rm{dc}}}^{{\rm{iii}}}\)\({I}_{{\rm{dc}}}^{{\rm{i}}}\) > 200 pA, which is an unmistakable indicator that the meniscus has fully wetted the sample (Extended Data Fig. 3b,d and Extended Data Fig. 3e,g for graphene and hBN, respectively). The d.c. current then drops to a steady state (step iv) during which the meniscus stabilizes. After the pre-programmed measurement period (500 ms of meniscus contact), the tip is retracted (step v (meniscus stretch) and step vi (meniscus detached)), with Idc first sharply increasing and then returning to the initial value. These steps were clearly visible throughout scanning of entire samples.

The described behaviour was observed independently of Icollector (that is, whether the proton current is being pumped or not through the device into the proton collector). Extended Data Fig. 3b,c also show that Idc exhibits the same features both in areas of high proton conductivity (blue curve) and in areas where no proton transport takes place (red). This shows that meniscus wetting of the sample is independent of proton transport through 2D crystals. Note, however, that the magnitude of Idc does change for active and inactive areas because the Ag/AgCl electrodes are also the counter electrodes for proton conductivity measurements42. This change served as independent confirmation of those sites where there was notable proton permeation through 2D crystals.

Note that the above also rules out changes in the droplet cell size as the source of the observed spatial inhomogeneity of the proton currents. The consistency of the SECCM cell size across the surface is also in accord with the following considerations. First, wrinkles protrude at most a few nanometres from flat areas of graphene, which leads to only small variations in the involved surface area as compared to the area probed in each pixel (about 200 nm in diameter). Therefore, this cannot explain the orders of magnitude difference in the observed SECCM activity. Second, the roughness associated with the wrinkles is much less than a typical surface roughness of a wide range of samples previously studied by SECCM for which consistent meniscus cell size was observed or deduced34,35,37,40,42,43,44.

AFM and scanning electron microscopy characterization

High-resolution topography and adhesion AFM imaging was carried out under ambient conditions with a Bruker Dimension Icon AFM using the PeakForce mode. The instrument was equipped with SCANASYST-AIR silicon tips (Bruker). The tips had a nominal spring constant, k = 0.4 N m−1, resonant frequency of 70 kHz and a tip radius of 2 nm. The resulting AFM maps were used to estimate strain across different areas of the 2D membranes. From AFM traces through the membrane centre, we estimate that the membranes were globally strained by typically 0.5%. However, the strain ε was distributed not uniformly but accumulated around the aperture rim23, leading to ε several times higher than away from it23. This yields ε of a few percent around the rim. Such strain is also expected to accumulate around wrinkles in the 2D membranes, whose complex morphology cannot be attained using strain-free (bending alone) deformations24,26. From the height (h) and base (L) of the wrinkles measured in AFM, we also estimate strain of a few percent, consistent with the above expectations.

For scanning electron microscopy (SEM) characterization, we used a Zeiss Gemini500 scanning electron microscope, using an In-lens secondary electron detector, accelerating voltages of 0.5–2 keV and a working distance of about 2 mm.

Additional examples of devices studied by SECCM

Extended Data Fig. 4 (graphene) and 6 (hBN) show further examples of SECCM and AFM maps. In all of the measured devices (more than twenty 2D membranes), we observed a clear correlation between high-activity areas in the SECCM maps and morphology of 2D membranes. In particular, Extended Data Fig. 6 provides an example in which proton conductivity becomes sharply suppressed crossing the boundary from monolayer hBN to a 4-layer region. Previously, it was shown that hBN monolayers were highly proton permeable, whereas hBN crystals of four or more layers in thickness exhibited indiscernible proton conductance8. The images of Extended Data Fig. 6 illustrate this property with nanoscale resolution across individual membranes in the same experiment. An additional notable feature seen in the AFM maps is two wrinkles that extend along the SiNx substrate beyond individual apertures. These wrinkles exhibit notable proton-conducting activity in the SECCM maps that occurs not only above the Nafion region but extends onto the SiNx substrate. We attribute this observation to water that fills the space between the substrate and wrinkles and thus provides a proton-conducting medium inside the wrinkles.

Absence of defects in mechanically exfoliated 2D membranes

Suspended membranes made from exfoliated 2D crystals have previously been characterized extensively using AFM, SEM, Raman spectroscopy, transmission electron microscopy and scanning tunnelling microscopy2,5,6,8,9,25,45,46 as well as gas permeation measurements1,2,4,5. None of those studies could detect any structural defects in the membranes. Nevertheless, it was important to ensure that the fabrication procedures used in the present report did not lead to accidental tears, cracks or pinholes that would break the continuity of the graphene lattice and leak protons through.

The formation of wrinkles in supported thin sheets is a universal phenomenon that arises from non-uniform adhesion between the sheet and the substrate. For example, this phenomenon has been extensively studied for 2D polymers47, and graphene is no exception. To understand the formation of wrinkles in our devices we note that graphene sheets are initially suspended over holes, rather than supported. The membranes are therefore stretched laterally because of adhesion to the holes’ sidewalls and free to relax in the out-of-plane direction. In most cases, this results in wrinkle-free membranes2. The situation changes after depositing Nafion. Adhesion to sidewalls disappears in the presence of water (as observed in ref. 48) so that graphene is no longer stretched over the holes. The membrane therefore becomes looser, which unavoidably results in the formation of wrinkles. In addition, the now loose graphene sheets conform to the porous Nafion polymer surface, which further contributes to the wrinkling and rippling. Importantly, the wrinkles and roughness do not lead to cracks, tears or pinholes that would allow unimpeded proton permeation through them. This conclusion is supported by many experimental observations. For the sake of brevity, we describe below only three of them.

First is the Raman spectra observed for the wrinkled membranes on Nafion. Any defects in graphene leading to breakdown of its continuous crystal lattice (cracks, tears, holes or even individual vacancies) activate the so-called D peak in its Raman spectrum. The intensity of this peak increases with defect density (for example, refs. 33,49). Our graphene monocrystals do not exhibit any discernible D peak, which allows us to put an upper bound on the atomic-scale defect density of about 109 cm−2. This translates into no more than 10 single-atom vacancies for our entire membranes of 2 μm in diameter (for example, refs. 8,9,45). By contrast, the reported wrinkles are hundreds of nanometres long, and if there were any breakdown of crystallinity along them, an intense D peak would also be apparent. Occasionally, we found devices with accidental cracks formed during fabrication, and those exhibited a strong D peak. They were discarded. All of the devices reported in the manuscript had no discernible D peak (Extended Data Fig. 1c). Also note that the found upper bound of about 10 atomic-scale defects in our devices cannot possibly explain the observed proton conductance. Indeed, our SECCM maps typically reveal about 100 active pixels and, to provide their proton conductance, not individual vacancies but large multi-atom pinholes would be required. This would lead to a very intense D peak, easily observable experimentally.

The second piece of evidence that rules out lattice defects in our membranes comes from measurements using liquid electrolytes (refs. 6,8). These experiments have found similar proton conductivity as in devices measured using Nafion. Unfortunately, we cannot remove Nafion after measurements, but we could remove electrolytes. In the latter case, the membranes did not show any D peak or any damage under AFM or SEM, which demonstrates that the membranes were not damaged during proton conductivity measurements. As the conductivity using electrolytes is the same as in the case of Nafion, we can safely conclude that Nafion does not damage graphene membranes either.

Finally, gas impermeability of our graphene–Nafion devices also proves the absence of defects induced by deposition of Nafion. Unlike graphene, which is completely impermeable to helium, thin Nafion films (after graphene was removed) exhibited notable helium leakage. This was measured using a He-leak detector that allowed us to resolve flows as low as 108 atoms s−1. Nafion-coated graphene devices with an accidental crack exhibit notable helium permeability, whereas undamaged devices remain leak free, despite the presence of wrinkles.

SECCM of CVD graphene

For these measurements, centimetre-scale pieces of CVD graphene (grown on Cu) were transferred onto a Nafion N212 film as reported previously50. To this end, the Cu foil that was covered on both sides with graphene was first exposed from one side to oxygen plasma, which removed graphene from that side. The CVD graphene remaining on the other side was then hot-pressed against the Nafion film, and the Cu foil was etched away in an ammonium persulfate solution. The resulting graphene-on-Nafion stack was left in deionized water for days to remove etchant residues. For SECCM measurements, centimetre-sized graphene-on-Nafion samples were fixed17 to the Pt electrode (as described above) and characterized using the same procedures as for micrometre-sized 2D crystals.

Extended Data Fig. 5 shows that proton currents detected by SECCM for our CVD graphene were below 100 pA. There were no spots with very high currents similar to those observed for lower-quality CVD graphene devices15,17. Statistics of the currents collected over large areas (Extended Data Fig. 5c) can be separated into two groups. The first group of pixels exhibits currents of 0.1–10 pA; this is similar to those found in mechanically exfoliated graphene reported in the main text. The second group of pixels exhibits a normal distribution with the mode at about 20 pA, which is about 10 times higher than currents in the first group. AFM and SEM images revealed that the higher-activity areas resulting in the second group came mostly from grain boundaries (Extended Data Fig. 5b–e). The higher permeability for these pixels can be attributed to multiple crystal-lattice defects present in grain boundaries (for example, 8-atom rings that are highly proton conductive7,20 or even bigger defects). We have also found that grain boundaries in CVD graphene were often accompanied by local corrugations (Extended Data Fig. 5d,e) with h ≈ 60 nm and L ≈ 500 nm, which may also have contributed to their proton permeability (h/L ≈ 0.1).

The experiments described in this section provide important insights into the large variability in proton permeability reported in the literature for CVD graphene films51. Even in the absence of gross defects (for example, cracks and tears), which sometimes are prevalent in CVD graphene films17, nanoscale pinholes can result in isolated hotspots with proton currents17 up to 1 nA. For higher-quality CVD graphene without such defects, proton conductivity is likely to be dominated by grain boundaries. Even in the last case, considerable variability in proton permeability is expected because of different grain sizes, depending on growth conditions, so that graphene films with smaller grains and thus higher density of grain boundaries would exhibit higher proton conductivity, in agreement with the previous report7.

Density functional theory calculations

We used the projector augmented-wave method52 implemented in the Vienna ab-initio Simulation Package53 to model pseudopotentials of protons, and C and H atoms. The exchange-correlation potential was taken into account by considering the generalized gradient approximation within the Perdew–Burke–Ernzerhof form54. The weak van der Waals forces between graphene and proton were also included by using the DFT-D2 method of ref. 55. For geometry optimizations, a kinetic energy cutoff of 500 eV was used for the plane-wave basis. The convergence criterion of the total force on each atom was reduced to 10−5 eV Å−1 and the convergence criterion for the energy was set at 10−6 eV. For calculating the proton barrier, we used the proton pseudopotential from the hydrogen atom and then removed an electron from the whole system.

The flat and rippled graphene were simulated as a relatively large circular-shaped crystal consisting of 150 carbon atoms (about 22 Å in size), which was sufficient to prevent proton–proton interactions between neighbouring supercells. The carbon cells were isolated with a vacuum gap larger than 10 Å, which ensured the absence of edge-to-edge interactions. The ripples were modelled by fixing the out-of-plane positions of carbon atoms so that the crystal forms a Gaussian profile of height h (Extended Data Fig. 7). The atoms were allowed to relax in-plane. Interatomic distances for atoms near the ripple top (\({d}_{cc}^{{\rm{s}}{\rm{t}}{\rm{r}}{\rm{a}}{\rm{i}}{\rm{n}}{\rm{e}}{\rm{d}}}\)) were compared with that of the flat strain-free structure (\({d}_{cc}^{0}\)) and the amount of biaxial strain was calculated as ε = (\({I}_{cc}^{{\rm{s}}{\rm{t}}{\rm{r}}{\rm{a}}{\rm{i}}{\rm{n}}{\rm{e}}{\rm{d}}}\) − \({d}_{cc}^{0}\))/\({d}_{cc}^{0}\). To calculate barriers for strained flat graphene (without ripples), the in-plane positions of carbon atoms were obtained by applying biaxial strain. Extended Data Fig. 7b shows the energy barriers E found for the three cases.

We calculated the total energy of the proton–graphene system as a function of the position of the proton in the direction perpendicular to the centre of the hexagonal ring in the graphene crystal lattice (Extended Data Fig. 7). Our calculations showed that the proton became physisorbed at about 1 Å away from the graphene lattice, which corresponded to the minimum energy of the system. The maximum was reached when the proton was in the middle of the hexagonal ring. The barrier E for proton permeation is calculated by subtracting the minimum energy from the maximum one. For the case of flat unstrained graphene, the energy barrier found using these approximations is about 1.37 eV, in good agreement with the earlier theory14. As various approaches used to calculate E yield a rather large spread in the predicted values10,11,13,14,18 and the exact value of the energy barrier for flat monolayer graphene remains debatable14, here we avoid this uncertainty by focusing on relative changes in E that are arising from strain and curvature. Finally, note that E is expected to vary across membranes becoming lower around wrinkles and ripples and higher in flatter and unstrained areas. As this strain is mostly random, it is reasonable to expect that in the first approximation the distribution of E is normal (that is, Gaussian). As proton currents depend exponentially on E, their distribution should then be log-normal, which is consistent with our SECCM observations.

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