Anomalous Interfacial Electron-Transfer Kinetics in Twisted Trilayer Graphene Caused by Layer-Specific Localization

Interfacial electron-transfer (ET) reactions underpin the interconversion of electrical and chemical energy. It is known that the electronic state of electrodes strongly influences ET rates because of differences in the electronic density of states (DOS) across metals, semimetals, and semiconductors. Here, by controlling interlayer twists in well-defined trilayer graphene moirés, we show that ET rates are strikingly dependent on electronic localization in each atomic layer and not the overall DOS. The large degree of tunability inherent to moiré electrodes leads to local ET kinetics that range over 3 orders of magnitude across different constructions of only three atomic layers, even exceeding rates at bulk metals. Our results demonstrate that beyond the ensemble DOS, electronic localization is critical in facilitating interfacial ET, with implications for understanding the origin of high interfacial reactivity typically exhibited by defects at electrode–electrolyte interfaces.


■ INTRODUCTION
Electron-transfer (ET) reactions at electrode−electrolyte interfaces are fundamental to electrochemical energy conversion. 1−3 The collective of microscopic theories and models for interfacial ET, inclucing the Marcus−Gerischer formalism, 4−9 the so-called Marcus−Hush−Chidsey (MHC) model, 10,11 and the density of states (DOS)−incorporated MHC (MHC−DOS) model, 12 highlight the importance of the electronic structure of an electrode on heterogeneous electrochemical rates. These frameworks motivate the discovery of new approaches to manipulate the band structure of electrodes as a means of controlling the performance limits of energy conversion and storage devices. Even though the electrode DOS was originally treated as invariant with energy/overpotential and delocalized, recent work has shown that the energy-dependence of the DOS can be an important factor in electrochemical reactions. 12 Furthermore, the effect of local DOS beyond the global electrode DOS has been identified as critical in understanding interfacial ET kinetics. On semiconductor or semimetallic electrodes, local electronic structure differences have been shown to affect ET kinetics, 13 and atomic defects at electrode surfaces provide a striking, albeit challenging to control, example of the pronounced effect of local structural/electronic modifications on interfacial reactivity. Atomic vacancies, 14 kinks, and step edges 15−17 are typically associated with massively enhanced interfacial reactivity compared to atomically pristine surfaces. The effect of these defects is typically explained in the context of providing increased DOS at energies that are desirable for charge transfer or the formation of a surface-bound catalytic intermediate (such as midgap states in a semiconducting material. 14,15 ) However, the dangling bonds at such sites would invariably introduce a strong spatial localization of these large electronic DOS. For this reason, beyond the augmented DOS magnitude, we might consider that localization may play a key role in facilitating interfacial ET to the necessarily localized electronic states on the solution-phase molecule/complex/ion. However, a systematic experimental examination of the effects of electronic localization on heterogeneous interfacial charge transfer has been intractable owing to the considerable synthetic challenge of constructing pristine electrode materials that would allow a deterministic modulation of this property separate from the overall DOS.
Azimuthal misalignment of atomically thin layers produces moirésuperlattices and alters the electronic band structure, in a manner that is systematically dependent on the interlayer twist angle. 18,19 The formation of flat electronic bands, particularly at a series of "magic" moiréangles, leads to a diversity of correlated electron physics. 20−23 Notably, these flat bands imply a large DOS that is highly localized in real space. 24 Small-angle twisted bilayer graphene (TBG) exhibits recently discovered angle-dependent electrochemical behavior, 25 where outer-sphere ET kinetics can be tuned nearly 10-fold simply by varying the moirétwist angle, θ m , between 0 and 2°.
The stacking order of graphene in multilayers strongly alters the resulting electronic properties of the system. 21,26−34 As shown in SI Figure 1, whereas Bernal (ABA-stacked) trilayer graphene displays dispersive bands, rhombohedral (ABC) graphene possesses a nondispersive, or "flat", electronic band close to the Fermi level, which is responsible for the emergence of correlated electron phenomena at low temperatures. 35,36 More pronounced flat bands are produced in twisted trilayer graphene (TTG) structures. A rotationally misaligned (by a moiré"twist" angle θ m ) monolayer and a Bernal stacked bilayer form a "monolayer-twist-bilayer" (M-t-B) heterostructure ( Figure 1A). 37,38 Systematically alternating the angle between adjacent graphene layers such that the top layer is perfectly aligned with the bottom layer results in an "A-t-A" heterostructure ( Figure 1B) 21,27,34 that possesses extremely flat bands at a magic angle of around 1.5°(SI Figure 1). These flattened electronic bands, which manifest as a large DOS that is localized on AAB and AAA sites in M-t-B and A-t-A TTG, respectively ( Figure 1C,D), now introduce distinctive possibilities for systematically probing the dependence of interfacial ET on electronic structure generally and, in particular, the effects of electronic localization. For example, even within the TTG family, larger DOSs are found in A-t-A as compared to M-t-B near their respective magic angles ( Figure  1C,D), properties that naively might be expected to correlate with interfacial ET rates, based on the MHC model.

■ RESULTS AND DISCUSSION
Scanning electrochemical cell microscopy (SECCM) 17 measurements were carried out on nontwisted (ABA, ABC) and twisted trilayer graphene samples that were fabricated into devices (see Materials and Methods). 25 As shown in Figure 2A, naturally occurring ABA and ABC trilayers were mechanically exfoliated from bulk graphite and identified using optical microscopy together with confocal Raman spectroscopy (see Materials and Methods and Supporting Information). 39,40 M-t-B and A-t-A TTG samples were prepared by the "cut-andstack" approach (see Materials and Methods), resulting in samples possessing uniform θ m around the magic angles of about 1.34°for an M-t-B device and 1.53°for an A-t-A device. Piezoelectric force microscopy (PFM) and scanning tunneling microscopy (STM) were used to evaluate the twist angle distribution and uniformity across the moirésamples ( Figure  2B). 41 Using SECCM, cyclic voltammograms (CVs) were measured with 2.0 mM Ru(NH 3 ) 6 3+ −an ideal and wellestablished redox couple for interrogating outer-sphere ET kinetics 16,25 −and 0.10 M KCl as the supporting electrolyte. In Figure 2C, a representative set of CVs collected from these different trilayer samples is shown. We find that the ABA domain of the flake shown in Figure 2A exhibited the most sluggish rates of Ru(NH 3 ) 6 3+ electro-reduction, as evinced by a half-wave potential (E 1/2 ) of −0.32 V, which is cathodically shifted substantially from the equilibrium potential, E 0 , of −0.25 V for Ru(NH 3 ) 6 3+/2+ (all potentials are reported relative to the Ag/AgCl quasi-counter/reference electrode). However, the E 1/2 measured from the CV acquired in region II (ABC domain) of the same flake was −0.27 V, pointing to considerably more facile electroreduction kinetics on the rhombohedral trilayer as compared to the Bernal trilayer. For both TTG samples, reversible CVs with E 1/2 ≈ −0.25 V were obtained, indicative of highly facile electrokinetics and heterogeneous electrochemical rate constants that exceed those of both ABA and ABC graphene considerably. These observations motivated the measurement of the variation of interfacial ET rates with θ m .
To quantitatively assess differences in interfacial kinetics associated with disparate electronic structures, we compared experimental CVs to those simulated with different standard rate constants, k 0 , calculated with the Butler−Volmer model (see Materials and Methods and the Supporting Information). Here, it is critical to account for the relatively small and potential-dependent quantum capacitance, C q (see Materials and Methods and Supporting Information) 16,25 in these lowdimensional electrodes, which for a given applied potential, V app , produces a dynamic electron or hole doping of the fewlayer graphene by an energy of eV q (where e is the elementary charge and V q is the chemical potential relative to the charge neutrality potential). The remainder, V dl , persists as a drop across the electric double layer (so that V app = V q + V dl ). C q (V q ) was calculated for all trilayer systems (ABA and ABC as well as M-t-B and A-t-A at various θ m values) ( Figure 3A) using the respective computed band structures and DOS profiles (see Materials and Methods). The corresponding plots of V dl /V app as a function of V app are shown in Figure 3B. Taken together, these data reveal that flat electronic bands result in a more significant fraction of V app partitioning into V dl near the charge neutrality potential. Notably, as shown in Figure 3A, changes in θ m tune C q (V q ) and magic-angle (∼1.5°) A-t-A displays a higher C q than magic-angle (1.2−1.3°) M-t-B, consistent with its overall greater DOS ( Figure 1D).
After determining V dl in this manner, we extracted k 0 values by identifying the simulated CV that was in closest agreement with the experiment 25 (see Materials and Methods and Supporting Information). The θ m dependence of k 0 was measured by preparing M-t-B TTG devices with varying θ m between 0.08 and 8.0°(see Materials and Methods) and acquiring CVs of Ru(NH 3 ) 6 3+ electroreduction by SECCM for each sample. Figure 3C shows the strong, nonmonotonic variation in k 0 over 2 orders of magnitude from ABA and ABC graphene to θ m = 8°M-t-B. For samples with 1°≤ θ m ≤ 2°, ET appears to be reversible within our accessible scan rates, so we cannot extract any kinetic information beyond noting that within this range of θ m , k 0 ≥ 0.35 cm/s. The quenched dependence of θ m on k 0 (blue markers in Figure 3C) in analogous electrochemical measurements of the trisphenanthroline cobalt(III/II) redox couple, Co(phen) 3 3+/2+ (see  Materials and Methods and Supporting Information) provides compelling evidence that it is the moiréflat bands that drive the observed angle-dependent electrokinetic modulation in TTG, as in TBG. 25 An unexpected observation of the factors controlling interfacial ET is made by comparing the electrochemical responses of TTG polytypes. A-t-A TTG, on the basis of its massive DOS (SI Figure 1 and Figure 1D) and giant C q −which exceeds that of M-t-B ( Figure 3A)−should be expected to yield the highest ET rates. However, while an effect of θ m on k 0 is also observed in A-t-A samples (see Supporting Information  Table 1), this variant of TTG displays consistently lower k 0 than M-t-B at similar θ m values ( Figure 3C, inset). Furthermore, B-t-M heterostructures, which consist of a Bernal bilayer placed with a twist atop a monolayer (i.e., flipped versions of M-t-B), display markedly lower k 0 values than the corresponding M-t-B electrodes, notwithstanding an ostensibly identical overall electronic structure. These striking observations point clearly to effects governing the interfacial ET kinetics beyond simply the ensemble DOS.
To fully understand these θ m dependencies as well as the disparities among the interfacial electron transfer kinetics of Mt-B, B-t-M, and A-t-A, we used STM (room temperature, constant current) to evaluate the role of lattice relaxation in controlling the area fraction of stacking domains in M-t-B and A-t-A TTG. In Figure 4A, a representative STM map of smallangle (θ m = 0.14°) M-t-B shows a clear contrast among the various stacking domains. Regions with higher local DOS appear brighter than those with lower DOS since a larger tip− sample distance is required to maintain a constant current. 38 ABC domains, therefore, appear brighter than ABA domains owing to the native flat band of the ABC stacking type (SI Figure 1). These ABA and ABC domains (black and red regions, respectively) form alternating triangular patterns while the AAB region forms small circles of diameter ∼11 nm, which appear with the brightest contrast owing to the localization of the moiréflat band and associated large DOS on these AAB sites as shown in Figure 1C and SI Figure S2 (this is analogous to the localization of moiréflat bands on AA sites in TBG 24 ).
For θ m = 0.78°( Figure 4B), while the triangular ABA/ABC patterns have shrunk in size compared to those in Figure 4A, the diameters of AAB regions remained largely unchanged. For A-t-A, AAA domains are visible as bright spots ( Figure 4D,E), consistent with the localization of the large DOS on these regions ( Figure 1D and SI Figure 2), 42 with degenerate ABA and BAB regions requiring smaller tip−sample distances (dark regions) to sustain a constant STM current because of a lower local DOS.
The measured area distribution of stacking domains in TTG, therefore, differs significantly from those of rigid moireś tructures. Both structures relax as depicted schematically in Figure 4C,F minimizing (maximizing) high (low) energy domains in a manner that is conceptually analogous to that reported for TBG. 24,43,44 To support these experiments, we also performed finite element method (FEM) simulations to model relaxation in TTG (see SI Figure 3 and Supporting Information), finding results that lie in good agreement with our STM and dark-field transmission electron microscopy (SI Figure 4) data. Importantly, these structural measurements and calculations permit a quantitative determination of the area fractions in TTG after reconstruction as a function of θ m as plotted in Figure 4G (see also SI Figure 5 and Supporting Information Table 2).
These area fraction distributions after structural relaxation explain the origin of the kinetic modulation observed in Figure  3C at θ m < 2°as being driven by θ m -dependent area fractions of the "topological defect" 45,46 AAB and AAA sites. Our relaxation simulations (SI Figure 2) also show that at θ m ≤ 0.3°t he relaxation of these moirésuperlattices reestablishes nearly commensurate ABA, BAB, and/or ABC domains with local DOS that should not deviate substantially from those of freestanding ABA and ABC trilayers. This observation is in line with previous experimental 38,43,44,46 and theoretical studies 46,47 of lattice relaxation in bilayer analogues. Therefore, by considering k 0 variations at θ m < 1°in Figure 3C (which are also within the range of kinetically resolvable k 0 ), we can extract the local rate constant associated with the AAB and AAA stacking domains through eqs 1 and 2 where β i and κ i 0 As a result of the lattice relaxation effect discussed above, we can determine κ ABA and κ ABC from independent measurements of freestanding Bernal and rhombohedral trilayers ( Figures 2C  and 3C). In addition, we can assume that κ SP 0 ≈ κ ABA 0 , which is justified on the basis of the STM images and calculated local DOS (see SI Figure 2). This analysis allows us to extract standard electron-transfer rate constants for the AAB (M-t-B), ABB (B-t-M), and AAA (A-t-A) topological defects.
Combined with previous electrochemical measurements at TBG surfaces, 25 we compare the ET kinetics of Ru(NH 3 ) 6 3+/2+ among a wide array of stacking configurations from monolayer to trilayer graphene in Figure 5A. For atomic stacking orders naturally found in bulk graphite, we observed a gradual enhancement as the number of layers increases from a monolayer to a Bernal trilayer. This can be explained by a modest increase in DOS close to the Fermi level as the number of layers increases. 16 ABC graphene displays a pronounced augmentation in k 0 from that of ABA graphene due to the intrinsic flat band of the rhombohedral system (SI Figure 1). Most notably, "artificial" high-energy stacking (AA, AAA, AAB, and ABB) topological defects created by moirésuperlattices exhibit extraordinarily high k 0 values, with that of AAB exceeding 3 cm/s, which is greater than that measured on bulk platinum electrodes (0.85−1.2 cm/s), 48 notwithstanding consisting of only three atomic layers (see also Supporting Information Table 2). Figure 5A also shows the unexpected result that AAA sites display lower ET rates than AAB notwithstanding the higher DOS and C q of AAA than those of AAB (SI Figure 1 and Figure 3A). Strikingly, we also find that ABB sites yield slower ET kinetics than both AAB (despite identical overall DOS) and AA (despite higher overall DOS). Thus, while in-plane electronic localization and structural relaxation effects explain the dependence of k 0 on θ m in TTG, the relative interfacial ET rates of AAB (M-t-B), ABB (B-t-M), and AAA (A-t-A) ( Figure  3C inset and Figure 5A) appear not to correlate with DOS.
To explain these trends, Figure 5C−E shows layer-isolated local DOS(ϵ) and C q (ϵ) profiles ( Figure 5C,E) at the topological defects (AAB/ABB, AAA) along with calculated real-space DOS maps (insets in Figure 5C,E). Supporting Information Figure 6 contains layer-dependent DOS at other twist angles. These calculations show how the DOS enhancements at AAB sites are distinctly localized on the top two layers of M-t-B structures (i.e., the "AA" portions of AAB). 49 In contrast, the DOSs at AAA sites are most strongly localized on the middle layer of A-t-A. This three-dimensional electronic localization (within a thickness of only three atomic layers) arising from different symmetries of these topological defects unveils the fundamental basis for the unexpected trends in ET rate constants at AAB, ABB, and AAA ( Figures 3C and 5A): though the electrodes are only three atomic layers thick, ET rate constants are correlated only with the electronic properties precisely at the electrode−electrolyte interface. These observations strongly hint at the role of interfacial electronic coupling (between the localized states on the electrode and the electron donor/acceptor in solution), electric double-layer effects, and/or interfacial reorganization energy as even more crucial than the overall DOS alone. Indeed, theoretical calculations based on the MHC model that accounts only for the θ m -dependent DOS but with a coupling strength, ν, and reorganization energy, λ, that are invariant with θ m (see Supporting Information text and SI Figure 7) vastly underestimate the dependence of k 0 on θ m . These MHC calculations also likewise predict identical interfacial ET rates for M-t-B and B-t-M, which is clearly at odds with the experiment. Our experimental results, therefore, now motivate future theoretical work to adapt these MHC models to consider how electronic localization, which is deterministically tuned here by varying θ m or TTG structure, modifies ν 50 and/ or λ 51 to bridge the gap between theory and experiment and extend our microscopic understanding of interfacial ET.

■ CONCLUSIONS
Controlling stacking geometries and twist angles in few-layer graphene, therefore, enables the manipulation of standard ET rate constants over 3 orders of magnitude. In particular, energetically unfavorable topological defects (AAA and AAB stacking domains), which are attainable only through the construction of a moirésuperlattice, exhibit extraordinarily high standard rate constants. This electrochemical behavior arises from the moire-derived flat bands that are localized in these topological defects. In addition to the effects of in-plane structural relaxation and electronic localization, the out-ofplane localization of the electron wave function on specific layers of twisted trilayer graphene results in measurable differences in ET rates at topological defects possessing different symmetries.
These results provide a powerful demonstration of the sensitivity of interfacial ET kinetics to the three-dimensional localization of electronic states at electrochemical surfaces and raise the question of whether traditional measurements of ET rates at macroscopic electrodes might severely underestimate the true local rate constant, which may be mediated by atomic defects that strongly localize electronic DOS at these interfaces. In turn, SECCM measurements are shown to be powerful tools for probing layer-dependent electronic localization in atomic heterostructure electrodes.
Future experimental and theoretical work is needed to shed more light on the microscopic origin of these electron-transfer modulations in the context of reorganization energy, electronic coupling, and even the electric double-layer structure. This work also heralds the use of moirématerials as a versatile and systematically tunable experimental platform for theoretical adaptations of the MHC framework applied to interfaces with localized electronic states, which are representative of defective surfaces that are ubiquitous to nearly all real electrochemical systems. In an applied context, twistronics is shown to be a powerful pathway for engineering pristine 2D material surfaces to execute charge-transfer processes with facile kinetics, holding implications for electrocatalysis 52,53 and other energy conversion device schemes that could benefit from ultrathin, flexible, and/or transparent electrodes that retain high electron-transfer kinetics.
Sample Fabrication. Graphite and hexagonal boron nitride (hBN) were exfoliated from the bulk crystals with Scotch tape. Exfoliated films were surveyed with an optical microscope (Laxco LMC-5000). Monolayer, bilayer, and trilayer graphene were identified with their characteristic optical contrasts of 7, 12, and 18%, respectively, in the green channel. 54 Trilayer graphene films were further confirmed by Raman spectroscopy (HORIBA LabRAM Evo) of the 2D peak (around 2600−2700 cm −1 ). 39 The 2D peak was used to distinguish different stacking domains (ABC/ABA) as ABC trilayer graphene exhibits an enhanced shoulder at around 2640 cm −1 (see Supporting Information text). Trilayer graphene and twisted trilayer graphene samples were fabricated by the well-established "cut and stack" dry transfer method. 25 All transfers were carried out on a temperature-controlled heating stage (Instec), an optical microscope (Mitutoyo FS70), and a micromanipulator (MP-285, Sutter Instrument). For monolayer twist bilayer or bilayer twist monolayer samples, graphene flakes with both bilayer and monolayer parts were carefully selected. The monolayer section was severed from the bilayer with a scanning tunneling microscopy (STM) tip. For a-twist-a samples, a large piece of graphene (>50 μm by 20 μm) was cut evenly into three pieces. A thin piece of poly(bisphenol A carbonate) (PC) film (∼3 × 3 mm 2 ) attached to a PDMS chunk (∼7 × 7 mm 2 ) was used to pick up an hBN (∼10−20 nm) from the SiO 2 /Si substrate at 120°C. This hBN was carefully aligned with the bottom layer of the graphene stack and lowered to pick up that piece. The stage was rotated (usually to a slightly larger angle than the desired twist), and the second piece of graphene was overlapped by the already picked-up graphene and thus delaminated from the substrate. For a-twist-a samples, a third piece of graphene was picked up after the stage was rotated back to the original orientation. A piece of graphite (∼20 nm, >50 μm × 50 μm) was then picked up such that it was connected to the graphene. The PC film was carefully removed from the PDMS and placed onto a clean SiO 2 /Si. In/Sn was painted onto the graphite via microsoldering 55 to a metallic plate which is attached beneath the SiO 2 /Si.
Finite Element Simulation and Cyclic Voltammograms Fitting. All finite element simulations of electron transport were performed on a COMSOL Multiphysics v5.6 (COMSOL) to capture the effects of quantum capacitance (see Supporting Information Text). The fitting of the CVs was achieved by statistical analysis of the experimental and simulated CVs (SI Figures 8 and 9).
Raman Mapping. Confocal Raman spectra were collected by recording from 2550−2800 cm −1 with a 532 nm laser at 3.2 mW. Raman maps were generated by collecting the spectrum across the trilayer films with a step size of 2 μm. The spectrum was fitted with single Lorentzian functions. The full-width at half maxima of the fitted functions were used to differentiate ABA and ABC trilayers (see Supporting Information text).
PFM Measurements. PFMs were performed on an AIST-NT OmegaScope Reflection. Ti/Ir-coated silicon probes from the Nanosensor with a force constant of 2.8 N m −1 and a resonance frequency of 75 kHz were used. A 2 V AC bias with resonance frequencies at 820 kHz was used, and the force was set to 25 nN. STM Measurements. STM measurements were conducted using a Park NX10 STM module (Park Systems) at room temperature and atmospheric pressure. Pt−Ir tips were prepared by electrochemical etching of 0.25 mm Pt−Ir wires (Nanosurf) in 1.5 M CaCl 2 solutions. 56 The scanned images were taken with a 0.2 V tip−sample bias and a 100 pA current set point. More STM images of various samples can be found in SI Figure 10. Twist angles of various samples were determined using Delaunay triangulation on the Gaussian centers. 24,25 Electron Microscopy Measurements. The transmission electron microscopy images of the nanopipettes (SI Figure 11) were obtained with a JEOL 1200EX transmission electron microscope operated at 100 keV. The top ∼1 mm portion of the pipette was attached to the grid (PELCO Hole Grids) such that the pipette tip was positioned in the center hole, and the rest of the pipette was broken off. Selected-area electron diffraction patterns were collected on an FEI Tecnai T20 S-TWIN transmission electron microscope with a LaB 6 filament operated at 200 kV. Selected area electron diffraction was used to resolve the twist angles for samples with twist angles larger than 3°(SI Figure 12). To obtain the diffraction patterns, the fabricated TLG/hBN samples were transferred onto a holey silicon nitride membrane after electrochemical measurements. Dark-field images shown in SI Figure 4 of TLG/hBN samples were measured at the National Center for Electron Microscopy facility in the Molecular Foundry at Lawrence Berkeley National Laboratory. Low-magnification DF-TEM images were acquired using a Gatan UltraScan camera on a Thermo Fisher Scientific Titan-class microscope operated at 60 kV.
Calculation of Band Structure and DOS. The DOS for trilayer graphene structures was calculated as a function of θ m using the ab initio perturbation continuum model developed previously. 57 The low-energy electronic structure is based on a momentum expansion about the valley K point of the supercell Brillouin zone, allowing a smooth dependence of bands on the twist angle. It has been shown that the perturbation continuum model exactly reproduces the results of the more expensive ab initio tight-binding model, and both are in good agreement with full density functional theory (DFT) calculations. 57−60 The energy range of integration for the DOS was fixed at ±0.5 eV around the charge neutrality point (CNP). For evaluation of the LDOS, the normalized moirésupercell was divided into a 90 × 90 grid in real space and sampled over 36 k points in the Brillouin zone. We kept the sublattice symmetry intact and assumed no extra screening of the interlayer coupling constants.
Quantum Capacitance Calculation. Quantum capacitance (C q ) describes the variation of electrical charges with respect to the chemical potential (V q ). Theoretical C q values with respect to V q were calculated based on the following equation 61 where D(ϵ) is the density of states, which we center at the CNP, F T (ϵ) is the thermal broadening function, and k B is Boltzmann's constant. We assumed T = 300 K for our experimental conditions. The total electric double-layer capacitance is governed by the compact layer capacitance. Hence, we used a constant C dl = 10 μF cm −2 to simplify the calculation. 62 We solved the self-consistent equations relating V app , V q , V dl , C q , and C dl using Simpson integration and nonlinear least squares (6) to obtain C q vs V q and V dl /V app vs V app as shown in Figure 3.
SECCM Measurements. The SECCM nanopipettes were fabricated from single-channel quartz capillaries (inner and outer diameters of 0.7 mm and 1.0 mm from Sutter Instrument) in a laser nanopipet puller (Sutter Instrument model 2000). The program was set to heat 700, filament 4, velocity 20, delay 127, and pull 140 to generate pipettes of diameters around 200 nm, as later confirmed with bright-field TEM 25 (see SI Figure 11). The outer surfaces of the pipettes were silanized by dipping them into dichlorodimethylsilane for less than 1 s when nitrogen was flowed through the inside of the pipettes. They were then filled with either Ru(NH 3 ) 6 3+ or Co(phen) 3 3+ solutions through a microsyringe. The pipettes were gently tapped, and a gentle string of nitrogen was used to eliminate the bubbles. The pipettes were then inserted with a Ag/AgCl wire as a quasi-counter reference electrode (QCRE). The pipettes carefully approached (0.2 μm/s) the locations of interest while a −0.5 V (0.5 V for Co(phen) 3 3+ ) bias was applied. The meniscus achieved contact when a current of larger than 2 pA (or smaller than −2 pA) was observed. The pipette was allowed to stabilize for 30 s. Cyclic voltammograms (CVs) were then conducted by sweeping the potential at 100 mV s −1 between −0.6 and 0 V (0 to 0.8 V for Co(phen) 3

3+/2+
) for five cycles. Multiple CVs were collected for each sample, and for small twist samples (θ ≤ 0.15°) with moireẃ avelengths of more than 80 nm, only CVs recorded with nanopipettes of more than 200 nm in diameter were included to ensure that they surveyed multiple stacking domains. To survey electrochemical activities across a large sample, the pipette was retracted by 1 μm after CVs were measured and horizontally moved to a new location for a new approach. ■ ASSOCIATED CONTENT
Raman maps of ABA and ABC graphene, calculations of the areal fraction from STM and dark-field images, finite element simulation of cyclic voltammagrams, Marcus− Hush−Chidsey calculations, area fraction determinations based on rigid and relaxed moire, calculations of relaxation and the local twist angle of TTL, Supplementary Figures 1−19, and Supplementary Tables 1−3  (PDF)