Directional Single-Protein Transport Enabled by 2D Material Heterointerfaces in Solid-State Nanopores: Implications for Single-Molecule Sensing

Abstract

Directional control of biomolecular transport in solid-state nanopores is crucial for replicating the rectification and gating behaviors of biological channels. Here, we report material-dependent directionality in multilayer nanopores formed in SiN_x + graphene + hBN and SiN_x + graphene + MoS₂ heterostructures using chemically tuned controlled dielectric breakdown. Transport-defined asymmetry emerges across the nanopore population, giving rise to polarity-dependent differences in capture rate and translocation kinetics over more than half a million holo-human serum transferrin (hSTf) protein events. Single-molecule analysis combined with electrostatic simulations indicates that terminal-layer composition and layer order modulate the local electric field distribution, leading to orientation-dependent transport kinetics. These results highlight that heterointerface engineering in multilayer nanopores can encode transport polarity at the single-molecule level, providing a materials-based strategy to regulate protein translocation dynamics and enhance signal separability for nanopore-based protein sensing.

Graphical Abstract

INTRODUCTION

Solid-state nanopores have emerged as versatile single-molecule sensors capable of probing the size, charge, conformation, and dynamics of biomolecules with submillisecond temporal precision.^1-7 Their compatibility with CMOS fabrication,⁸ chemical robustness,⁹ and wide operational voltage windows^10,11 make them compelling alternatives to biological nanopores for applications including protein fingerprinting, molecular diagnostics, and biophysical interrogation of complex analytes.^12-14 Despite these advantages, most solid-state nanopores remain constrained by inherent geometric and electrostatic symmetry.^3,15,16 As a result, molecular translocation typically produces bidirectional transport signatures¹⁷ that are largely indistinguishable across voltage polarity, limiting the ability to selectively modulate transport dynamics. In contrast, many biological ion channels exhibit strongly asymmetric conductance or rectifying behavior, enabling direction-dependent molecular transport.^18,19 Creating synthetic nanopores with similar directional control could provide new opportunities to regulate translocation kinetics and improve signal separability in nanopore-based sensing.

Two-dimensional (2D) materials offer a promising route to introduce such controlled asymmetry. Atomically thin crystals such as graphene,²⁰ molybdenum disulfide (MoS₂),²¹ and hexagonal boron nitride (hBN)²² possess distinct dielectric constants, surface charge densities, chemical functionalities, and electronic structures.^23-25 When integrated with silicon nitride (SiN_x) membranes, these materials create abrupt heterointerfaces that can modify the electrostatic and dielectric environment at nanometer length scales.^26-28 Previous studies have shown that 2D materials and surface functionalization can substantially modify nanopore noise and stability;^29-32 however, atomically thin membranes, especially freestanding graphene, often exhibit pronounced low-frequency 1/f noise, motivating hybrid or supported architectures and passivation strategies for sensing.^33-37 Direction-dependent control is particularly relevant for nanopore sensing because it can tune event duration and improve event separability under fixed bandwidth constraints, reducing missed events and increasing the information content of single-molecule recordings. However, the role of vertically stacked 2D heterostructures in regulating the symmetry of biomolecular transport remains largely unexplored.^38,39 A central challenge is distinguishing geometry-driven asymmetry from intrinsic material-dependent electrostatic effects, since structural variability during fabrication can obscure whether observed transport polarity originates from pore shape or from heterointerface composition.^40-42

Although multilayer and 2D-material nanopores have been reported previously, most studies have focused on improving signal stability or sensitivity rather than systematically controlling transport polarity as a materials design parameter. Many of these devices relied on TEM-drilled nanopores and primarily investigated DNA translocation through structures where the pore interior was defined by a single material or a single 2D interface.^43,44 In contrast, the multilayer architectures studied here form heterogeneous nanopore walls composed of SiN_x, graphene, and either hBN or MoS₂ along the axial transport pathway. The presence of multiple dielectric and interfacial boundaries within the pore introduces a more complex electrostatic landscape that can influence how charged biomolecules experience the electric field during entry and exit. Moreover, while DNA has frequently been used as a model analyte, protein transport provides a more sensitive probe of interfacial electrostatics because protein charge distributions and surface interactions are structurally heterogeneous.

In this study, we investigated multilayer SiN_x + graphene +2D nanopores in which highly conductive graphene is combined with either insulating hBN or semiconducting MoS₂ to create vertically stacked heterostructures with distinct electrostatic boundary conditions. Nanopores are fabricated through these stacks using chemically tuned controlled dielectric breakdown (CT-CDB)^45,46,47 enabling pore formation without compromising the integrity of the 2D layers. Although the exact breakdown pathway cannot be predetermined, the resulting pore population exhibit a range of transport behaviors, including cases where effective axial asymmetry emerges within the multilayer region above the SiN_x membrane. These variations provide a practical platform for examining how atomic-scale interfaces and 2D material composition influence direction-dependent biomolecular transport.

To probe these effects experimentally, we used holo-human serum transferrin (holo-hSTf), an approximately 80 kDa glycoprotein with a well-defined tertiary structure and asymmetric surface charge distribution.^48,49 Its biological relevance and conformational stability make it an ideal analyte for disentangling electrostatic and geometrical contributions to nanopore transport.^49-53 Direction-dependent transport is expected to arise when interfacial electrostatics coincides with local geometric asymmetry in a multilayer nanopore. In symmetric SiN_x pores and in multilayer pores lacking definite asymmetry, forward and reverse transport are anticipated to exhibit comparable capture rates and translocation signatures, consistent with approximate electrostatic and structural symmetry. In contrast, asymmetric heterointerfaces can give rise to orientation-dependent translocation kinetics, even when capture rates remain similar between directions. In such systems, capture is primarily governed by entrance-side field focusing, whereas directional slowing can originate from asymmetric electric-field distributions within or near the constricted region of the pore. The polarity of this kinetic asymmetry is therefore expected to depend on the dielectric and electronic properties of the terminal 2D material rather than on geometric asymmetry alone. Finite-element electrostatic simulations are used to qualitatively examine these field distributions and guide interpretation of the experimental transport measurements presented below.

For clarity, all schematics depict inferred pore asymmetry consistent with transport measurements and should not be interpreted as direct structural reconstruction of the nanopore geometry. The present study does not aim to demonstrate multiplex protein identification, but rather to establish how multilayer heterointerfaces modulate the polarity and kinetics of single-protein transport. Holo-hSTf is used as a structurally stable and electrostatically asymmetric probe molecule to interrogate pore-imposed transport behavior under controlled conditions.

RESULTS AND DISCUSSION

Fabrication, Architecture, and Directional Translocation Framework of Multilayer Nanopores

Multilayer nanopores were constructed by laminating mechanically exfoliated graphene and either hBN or MoS₂ onto 12 nm free-standing SiN_x membranes, followed by formation of a nanoscale aperture using a chemically tuned controlled dielectric breakdown (CT-CDB)^45-47 process (Figure 1a). Graphene was first dry-transferred onto the SiN_x window, and a second 2D crystal was subsequently added to form the SiN_x + graphene + hBN (SGH) and SiN_x + graphene + MoS₂ (SGM) heterostructures. The transferred layers adhered conformally across the suspended membrane, creating nanoscale heterointerfaces that later modulate local electrostatics during protein translocation. Optical inspection confirmed that the stacked layers remained intact and well registered before and after pore formation (Figure 1b). Elemental mapping by SEM–EDX (Figure S1) confirms the presence and integrity of each constituent layer, verifying that the layered stacks remain intact prior to pore formation.

Figure 1.

Multilayer nanopore fabrication, architecture, and transport classification. (a) Schematic of the multilayer nanopore fabrication process. A free-standing 12 nm SiN_x membrane is sequentially laminated with mechanically exfoliated graphene and either hBN or MoS₂, followed by application of a voltage bias to initiate chemically tuned controlled dielectric breakdown (CT-CDB) and form a nanopore through the stacked layers. (b) Optical micrographs of multilayer heterostructure membranes before (top) and after (bottom) dielectric breakdown, showing preservation of the transferred 2D layers surrounding the pore region. Graphene (gr), hBN, and MoS₂ layers are indicated. (c) Schematic illustration of holo-human serum transferrin (holo-hSTf) translocation through the multilayer heterostructure, highlighting the stacked SiN_x, graphene, and terminal hBN or MoS₂ layers. (d) Conceptual cross-sectional schematics illustrating the two transport-defined nanopore classes identified in this study. Type-1 pores exhibit weak rectification and minimal orientation dependence, whereas type-2 pores exhibit strong transport-defined asymmetry within the multilayer stack, leading to distinct forward and reverse translocation behavior. Schematics are not intended to represent directly measured layer-resolved pore geometry. (e) Capture rates for reverse (top) and forward (bottom) translocation measured across all pore types at 50, 100, and 150 mV. Dashed lines indicate the mean capture rate at each voltage.

Pores were created by immersing the multilayer membrane in a NaOCl-enhanced electrolyte and applying an 8–12 V bias across the membrane. The oxidizing environment facilitates defect fluidization and reduces the breakdown threshold, enabling rapid and reproducible pore nucleation.⁵⁴ Pore formation was detected as an abrupt increase in ionic current, after which the applied voltage was immediately quenched to prevent uncontrolled growth. This approach reliably produced ~20 nm apertures compatible with all multilayer architectures, and brief postbreakdown voltage pulses allowed fine-tuning of pore diameter with nanometer precision.

Following pore formation, holo-hSTf was introduced into the trans chamber and electrophoretically driven toward the cis reservoir (Figure 1c) while ionic current is recorded for event analysis shown in Figure S2 (Supporting Information). Across fabricated devices, we observe a continuum of asymmetry strength; the examples shown correspond to pores with minimal (type-1) and strong (type-2) orientation dependence. For clarity, multilayer nanopores are classified into two operational categories based on their electrical and single-molecule transport signatures rather than on directly imaged geometry (Figure 1d). Type-1 pores exhibit weak ionic rectification and minimal orientation dependence in translocation statistics, consistent with an effectively symmetric transport pathway for forward (2D-first) and reverse (SiN_x-first) configurations. In contrast, type-2 pores display strong ionic rectification with notable orientation-dependent translocation kinetics, indicating the presence of an effective axial asymmetry within the multilayer stack. Here, “effective axial asymmetry” refers to any deviation from axial symmetry, geometric or interfacial, that redistributes the electric field along the pore axis. This classification is used throughout the manuscript as a functional descriptor inferred from transport behavior, rather than as a direct measure of layer-resolved pore dimensions.

Capture rate measurements for all pore types and voltages (Figure 1e, Table S1, Supporting Information), derived from a total of 565,335 successful protein translocation events, provide the statistical basis for evaluating directional transport in this study. Symmetric SiN_x pores exhibit comparable forward (2D-first) and reverse (SiN_x-first) capture rates, whereas multilayer nanopores show orientation-dependent variations that become more pronounced with increasing bias. The observed variation in forward and reverse capture frequencies likely arises from entrance-side electrostatic and geometric conditions rather than intrapore transport kinetics. In multilayer nanopores, molecules approaching from opposite sides encounter distinct dielectric environments and surface properties at the pore entrance, which can alter the effective capture cross-section. A detailed analysis of the resulting electric-field distributions is presented later in Figure 5.

Figure 5.

Electric potential distributions of nanopores under forward and reverse bias. Electric potential maps computed at 150 mV for SiN_x, SGH, and SGM architectures. Top row: reverse-bias configuration. Bottom row: forward-bias configuration. SiN_x pores exhibit nearly symmetric potential gradients in both orientations. Type-1 SGH and SGM pores show mild curvature of equipotential lines near the 2D interfaces but remain largely symmetric. Type-2 multilayer nanopores (SGH2 and SGM2) exhibit asymmetric redistribution of the electric field near the multilayer interface; notably, SGH2 shows enhanced field gradients toward the multilayer exit, whereas SGM2 displays stronger field focusing near the multilayer entrance. Corresponding electric field maps are shown in Figure S8 (Supporting Information).

To establish a baseline for orientation-independent transport, we examined protein translocation through symmetric SiN_x nanopores fabricated by CT-CDB. Consistent with their linear, mirror-symmetric I–V characteristics, forward and reverse translocations through SiN_x pores exhibit overlapping distributions of dwell time (dt), blockade amplitude (dI/I), velocity, event charge deficit (ECD), and signal-to-noise ratio (SNR) across the full voltage range (Figures S3 and S4). These results confirm that bare SiN_x nanopores impose no measurable directional bias and provide a reference system for distinguishing pore-mediated orientation selectivity from analyte-driven variability in multilayer devices.

To assess signal fidelity and measurement robustness, we quantified baseline root-mean-square (RMS) noise (Figure S2, Supporting Information) and signal-to-noise ratio (SNR) across all devices (explained later in Figure 5). Baseline RMS noise ranged from 25.28 pA to 45.6 pA at 150 mV. These values are comparable to previously reported multilayer and SiN_x nanopores under similar ionic strength conditions, indicating that the observed directional differences are not limited by insufficient signal resolution.^30,33,43

Direction-Dependent Protein Transport in Graphene + hBN Multilayer Nanopores

Engineered 2D heterointerfaces introduce geometric and electrostatic contrasts absent in homogeneous SiN_x membranes, creating asymmetric entry pathways that can reshape protein capture and translocation. To assess these effects, we examined holo-hSTf transport through SiN_x + graphene + hBN (SGH) nanopores. Unlike the symmetric entrance environment of SiN_x controls (Figures S3 and S4, Supporting Information), SGH pores combine atomically thin, high-permittivity layers with a thicker SiN_x scaffold, producing unequal access resistance and field curvature.

Although SGH1 and SGH2 were fabricated under identical CT-CDB conditions, their ionic behaviors diverged: SGH1 exhibited nearly symmetric I–V characteristics (RR = 0.96), whereas SGH2 showed substantial rectification (RR = 0.84; Figure 2a). These differences reflect nanoscale variations in defect coalescence that modify aperture registration and interfacial shape. Rather than constituting fabrication noise, this variability generates a spectrum of geometries that reveal how directional transport emerges from heterointerface asymmetry. SGH architecture supports two distinct capture landscapes (Figure 2b). Type-1 pores exhibit minimal rectification and are therefore expected to behave symmetrically in forward and reverse orientations. In contrast, type-2 pores display effective axial asymmetry that redistributes local electric fields and leads to orientation-dependent transport kinetics.

Figure 2.

Direction-dependent protein transport in SiN_x + graphene + hBN (SGH) multilayer nanopores. (a) I–V characteristics of two SGH devices. SGH1 shows nearly symmetric ionic transport with a rectification ratio (RR = 0.96), while SGH2 exhibits measurable rectification (RR = 0.84). (b) Cross-sectional schematics of type-1 and type-2 SGH nanopores. Type-1 pores exhibit near-symmetric transport signatures, whereas type-2 pores display strong orientation-dependent behavior consistent with effective asymmetry in the multilayer region. Top and bottom panels illustrate reverse (SiN_x-first) and forward (2D-first) translocation configurations. (c) Scatter plots of relative current blockade (dI/I) versus dwell time at 150 mV for SGH1 (top) and SGH2 (bottom). SGH1 shows overlapping forward and reverse event populations, while SGH2 displays distinct orientation-dependent clusters. N represents number of protein translocation events. (d) Violin plots of translocation velocity for SGH1 and SGH2. SGH1 shows similar forward and reverse distributions, whereas SGH2 exhibits lower velocities with clear directional differences. (e) Normalized histograms of event charge deficit (ECD), signal-to-noise ratio (SNR), and blockade amplitude (dI). SGH1 yields overlapping distributions for both orientations, whereas SGH2 shows direction-dependent shifts across metrics.

These predictions match the experimental trends. SGH1 behaves analogously to SiN_x controls, with overlapping forward and reverse dI/I-dt distributions (Figure 2c, top). SGH2, however, shows a clear directional signature: reverse (SiN_x-first) entries yield deeper blockades and longer dwell times, forming a distinct high-dI/I, long-dt population absent for forward entry (Figure 2c, bottom; Supporting Figure S5a). This asymmetry strengthens with voltage, indicating that it affects both capture and passage through the 2D constriction. Velocity distributions further support this mechanism. SGH1 shows no directional dependence, whereas SGH2 displays markedly reduced drift speeds, especially for reverse entry (Figure 2d; Supporting Figure S5b). Proteins approaching from the SiN_x side encounter stronger field focusing into the constriction, while 2D-first entry samples a more gradual potential gradient, producing orientation-specific slowing. Event-level descriptors reinforce these trends. SGH1 maintains symmetric ECD, dI, and SNR distributions, while SGH2 exhibits reverse-biased shifts toward larger values across all metrics (Figure 2e; Supporting Information Figure S5c). These signatures reflect enhanced confinement and longer residence times at the 2D interface, where dielectric contrast and interfacial dipoles shape the local field.

Material-Dependent Polarity of Directional Transport in Graphene + MoS₂ Multilayer Nanopores

The electronic character and interfacial properties of the terminal 2D layer play a critical role in shaping the local electrostatic boundary conditions encountered during molecular capture and translocation. To probe this material dependence, we examined holo-hSTf transport through SiN_x + graphene + MoS₂ (SGM) nanopores. Unlike insulating hBN, MoS₂ is a semiconducting 2D material whose surface electrostatics under high ionic strength conditions are weak and highly sensitive to defect states and electronic screening. Prior studies and simulations have therefore treated MoS₂ as possessing a small effective surface charge at pH 8 and 1 M KCl, reflecting its near-neutral electrostatic character rather than a strongly charged interface.⁵⁵ This distinction is reflected experimentally in the ionic transport behavior. While SGM1 exhibits symmetric conduction (RR = 1.00), SGM2 displays forward-biased rectification (RR = 1.27; Figure 3a), with a polarity opposite to that observed in SGH2. The reproducibility of this polarity inversion across devices suggests that it originates from material-dependent interfacial electrostatics associated with the MoS₂ terminal layer, rather than from random geometric variation inherent to the CT-CDB process.

Figure 3.

Material-dependent polarity of directional transport in SiN_x + graphene + MoS₂ (SGM) multilayer nanopores. (a) I–V curves of two SGM devices. SGM2 displays forward-biased rectification with a ratio of 1.27, opposite in sign to the SGH architecture and indicative of material-dependent electrostatic asymmetry. (b) Cross-sectional schematics of type-1 and type-2 SGM nanopores. Type-1 pores exhibit near-symmetric transport behavior, whereas type-2 pores display strong orientation-dependent signatures associated with effective asymmetry in the multilayer stack. The top panels depict reverse translocation (SiN_x-first), and the bottom panels depict forward translocation (MoS₂-first), highlighting how molecular entry experiences distinct electric-field and confinement conditions. (c) Scatter plots of relative current blockade (dI/I) versus dwell time (dt) for SGM1 (top) and SGM2 (bottom) at 150 mV. Both devices show modest forward-shifted increases in blockade depth and dwell time, with the effect substantially stronger in SGM2. N represents number of protein translocation events. (d) Violin plots of translocation velocity demonstrating that SGM2 exhibits slower forward transport, consistent with enhanced entrance-side field focusing and interaction at the MoS₂ interface. (e) Normalized histograms of event charge deficit (ECD), signal-to-noise ratio (SNR), and blockade amplitude (dI). SGM1 produces nearly symmetric distributions, while SGM2 shows clear and reproducible orientation-dependent shifts, confirming that the terminal 2D material dictates both the polarity and the magnitude of directional single-protein transport.

These material-specific effects become clearer when considering how the multilayer geometry shapes the capture landscape. Type-1 SGM pores exhibit weak orientation dependence, whereas type-2 pores display notable transport-defined asymmetry within the multilayer region (Figure 3b). In this configuration, the semiconducting character and interfacial electronic states of the MoS₂ terminal layer modify local electrostatic boundary conditions, leading to entrance-side field redistribution and transient protein-interface interactions. As a result, forward (MoS₂-first) translocation is expected to experience increased energetic barriers relative to reverse entry.

This behavior is evident in statistical signatures. Both SGM1 and SGM2 show forward-shifted increases in blockade depth and dwell time, with the effect substantially more noticeable in SGM2 (Figure 3c). These directional differences emerge even at 50–100 mV (Supporting Figure S6a) and become fully resolved at 150 mV, indicating that the MoS₂ interface consistently prolongs molecular occupancy. Velocity distributions provide complementary evidence: SGM1 remains largely orientation-neutral, whereas SGM2 exhibits a clear reduction in forward drift velocity (Figure 3d; Supporting Figure S6b). This slowing is consistent with enhanced entrance-side field focusing and stronger protein–surface interactions at the MoS₂ aperture, as supported by COMSOL simulations showing intensified electric-field gradients at type-2 MoS₂ constrictions.

Event-level metrics reinforce this mechanistic picture. Both SGM devices display forward-biased tails in ECD, SNR, and dI, reflecting longer residence times and increased confinement during MoS₂-first entry, with SGM2 again showing the most pronounced asymmetry (Figure 3e; Supporting Information Figure S6c). The persistence of these trends across voltages and devices confirms that directional behavior is intrinsic to the MoS₂ heterointerface rather than a result of statistical scatter or device instability.

Together, these findings demonstrate a material-specific inversion of transport polarity relative to SGH nanopores. Substituting hBN with MoS₂ reverses the sign of ionic rectification and shifts the preferred direction of protein motion, establishing that the terminal 2D layer, not geometric stochasticity, governs orientation-selective translocation. The SGM architecture therefore provides a programmable route for engineering polarity and directional gating in multilayer solid-state nanopores.

Quantifying Directionality Across Nanopore Architectures Using Effect-Size Analysis

To systematically compare the magnitude and polarity of orientation-dependent transport across nanopore architectures and operating voltages, we quantified the separation between forward and reverse event populations using Cohen’s d for five translocation descriptors: event charge deficit (ECD), blockade amplitude (dI), dwell time (dt), velocity, and signal-to-noise ratio (SNR) (Figure 4). Because Cohen’s d normalizes the difference in means by the pooled standard deviation, it provides a dimensionless and feature-agnostic metric that enables direct comparison across devices with different materials, transport regimes, and voltages.

Figure 4.

Effect-size analysis of directional transport across nanopore architectures. Cohen’s d values are shown for five translocation descriptors: event charge deficit (ECD), blockade amplitude (dI), dwell time (dt), velocity, and signal-to-noise ratio (SNR), comparing forward and reverse orientations at 50, 100, and 150 mV. Each point reflects the normalized separation between directional event distributions for a given device and voltage. SiN_x control pores cluster near d ≈ 0 (blue region). Type-2 multilayer devices (SGH2, SGM2) display large positive or negative effect sizes (pink and orange regions), while type-1 devices (SGH1, SGM1) show small to moderate values.

As expected for symmetric controls, bare SiN_x nanopores cluster tightly around d ≈ 0 for all descriptors and voltages (Figure 4, blue region), consistent with the overlapping scatter plots, velocity distributions, and histograms presented in Figures S3 and S4 (Supporting Information). This behavior confirms that SiN_x pores do not impose intrinsic orientation selectivity and therefore establish a robust baseline for evaluating multilayer nanopore architectures.

In contrast, multilayer nanopores exhibit architecture- and material-dependent orientation selectivity. Type-2 devices (SGH2 and SGM2) display the largest effect sizes, with ∣d∣ values reaching approximately 0.4–1.2 across multiple descriptors, including dI, ECD, dwell time, and velocity. Notably, the sign of d differs between architectures, reflecting opposite polarities of kinetic slowing: SGH2 consistently yields negative d values, indicating stronger hindrance for reverse (SiN_x-first) translocation, whereas SGM2 yields positive d values, indicating stronger hindrance for forward (2D-first) translocation. These opposite polarities mirror the direction of ionic rectification observed in the corresponding I–V characteristics (Figures 2 and 3) and are consistent with electrostatic asymmetries predicted by finite-element simulations, supporting a material-dependent origin of orientation selectivity.

The voltage dependence of orientation selectivity is descriptor- and architecture-specific rather than monotonic. In SGH2, several descriptors exhibit larger ∣d∣ values at lower voltages, whereas at higher voltages distributions may appear more visually separated despite reduced d due to increased variance and event heterogeneity. In SGM devices, effect sizes remain comparatively stable across voltage without a consistent trend. Intermediate devices (SGH1 and SGM1) exhibit ∣d∣ < 0.3 across all descriptors and voltages, consistent with their near-symmetric I–V behavior and weak orientation dependence in event-level analyses.

Additional multilevel event classification (Figure S7 and Supplementary Note S1, Supporting Information) further corroborates these trends. SGH2 exhibits a higher fraction of exit-dominated events, whereas SGM2 shows a greater prevalence of entry-dominated events, consistent with the opposite polarities inferred from the effect-size analysis. Together, these observations suggest that different multilayer heterostructures preferentially localize kinetic slowing to distinct axial regions of the nanopore, reflecting the combined influence of terminal-layer electrostatics and transport-defined asymmetry within the multilayer stack. The effect-size landscape in Figure 4 demonstrates that multilayer nanopores can exhibit material-dependent and geometry-dependent orientation selectivity in protein translocation kinetics. Both the magnitude and polarity of directionality are dependent on terminal-layer composition (hBN versus MoS₂) and the presence of geometric asymmetry (type-2 versus type-1 pores).

Holo-hSTf exhibits an anisotropic surface charge distribution at pH 8; however, symmetric SiN_x control nanopores do not display measurable orientation-dependent dwell-time, blockade amplitude, or velocity differences under identical ionic conditions (Figures S3 and S4, Supporting Information), indicating that intrinsic protein charge anisotropy alone is insufficient to generate transport polarity. Directional slowing emerges only in multilayer heterostructures exhibiting effective axial asymmetry, suggesting that pore-imposed electrostatic boundary conditions modulate how the protein’s charge distribution interacts with localized field gradients. Under high ionic strength (1 M KCl), where the Debye length is below 0.3 nm and long-range electrostatic interactions are strongly screened, translocation dynamics are dominated by electrophoretic drift and near-field effects rather than large-scale conformational transitions of the protein.⁵⁶ Moreover, multilevel event analysis does not reveal systematic unfoldinglike signatures unique to one orientation. While short-range nonelectrostatic interactions such as transient surface adhesion may contribute to event-to-event variability, such effects would not be expected to invert polarity between hBN- and MoS₂-terminated pores. The consistent reversal of kinetic slowing between these architectures therefore supports a dominant role of material-dependent electrostatic boundary conditions in encoding transport polarity.

The emergence of type-2 pores reflects stochastic variations in effective axial asymmetry introduced during CT-CDB, and we do not claim deterministic geometric control. However, geometry alone cannot explain the observed polarity inversion between SGH and SGM architectures. If directionality were solely governed by random geometric tapering, asymmetric devices of both compositions would be expected to exhibit similar slowing polarity. Instead, among pores exhibiting measurable asymmetry, SGH devices consistently show reverse-dominated slowing whereas SGM devices show forward-dominated slowing. This systematic inversion indicates that geometry determines the presence and strength of asymmetry, while the terminal 2D material determines the sign of the resulting transport polarity. Direct atomic-scale structural imaging of sub-5 nm multilayer nanopores after electrolyte exposure is experimentally prohibitive due to membrane fragility and contamination during environmental phase change;⁴⁶ therefore, we classify pores operationally based on transport symmetry. While this approach does not resolve nanometer-scale shape differences directly, the consistent correlation between material identity, rectification polarity, and kinetic asymmetry supports a structure-property relationship beyond random geometry alone.

Electric-Potential Landscapes Reveal Entrance-Exit Asymmetry in Multilayer Nanopores

To identify the physical origin of direction-dependent transport in multilayer nanopores, we computed the steady-state electric potential distributions for SiN_x, SGH, and SGM architectures under forward and reverse bias at 150 mV (Figure 5), using experimentally informed material parameters (Table S2). These simulations visualize the electrostatic landscapes that govern electrophoretic capture and intrapore drift.

For symmetric SiN_x pores, the simulated potential distribution remains nearly mirror-symmetric under both bias polarities. The axial voltage drop is uniform, and equipotential contours are evenly spaced across the membrane. The symmetric field distribution is consistent with the orientation-independent transport observed experimentally (Figures S3 and S4).

Introducing multilayer heterostructures produces more complex electrostatic environments. In type-1 SGH and SGM pores, only mild curvature of equipotential contours appears near the heterointerfaces due to dielectric contrast between layers, while the overall axial symmetry remains largely preserved. This is consistent with the weak or absent directional effects observed experimentally in these devices.

In contrast, type-2 multilayer pores exhibit clear orientation-dependent redistribution of the electric potential within the multilayer region. Electric-field maps derived from the simulations (Figure S8, Supporting Information) further reveal localized field focusing near the multilayer interface. In SGH2 the strongest field gradients occur near the multilayer exit, whereas SGM2 exhibits enhanced field convergence near the entrance, consistent with the opposite polarity of directional slowing observed experimentally.

In an axially asymmetric multilayer pore, the spatial location of the largest voltage drop determines where kinetic slowing occurs. Under identical geometric asymmetry the terminal 2D material shifts where the field concentrates. For SGH2, the field localizes near the downstream multilayer region under reverse bias (SiN_x-first), consistent with exit-dominated slowing. For SGM2, the field maximum shifts toward the entrance under forward bias (2D-first), consistent with entry-dominated slowing. Thus, polarity inversion arises from material-dependent redistribution of the electric field within an asymmetric multilayer geometry.

To avoid circular inference, the simulations were not intended to reconstruct the exact geometry of individual pores. Instead, a small and identical axial asymmetry was introduced for both SGH and SGM architectures to represent the effective asymmetry required for directional transport. This geometric perturbation was kept constant, and only material parameters (permittivity and surface charge) were varied between hBN- and MoS₂-terminated stacks. Under the same asymmetric geometry, the field localization reverses between SGH and SGM, demonstrating that axial asymmetry enables directionality, while terminal-layer identity determines its polarity. Electroosmotic flow and dynamic charge regulation were not included in the steady-state simulations. Debye length is much smaller than the pore radius, resulting in strongly screened double layers and minimal EOF contribution.^56,57 The simulations therefore focus on electrophoretic field redistribution within the multilayer region.

Although type-1 and type-2 pore formation is stochastic under CT-CDB, the polarity of directional slowing among asymmetric pores consistently correlates with the terminal 2D material. Unlike structurally tapered nanopores, where fixed geometry alone defines transport polarity,⁵⁸ substitution of the terminal 2D layer in multilayer stacks inverts the polarity of slowing. Together, the simulations and experimental statistics support a mechanism in which effective axial asymmetry enables directional transport and heterointerface electrostatics encode its polarity. Several strategies may improve reproducibility in future implementations. These include tighter feedback control during breakdown, engineering localized field concentration through membrane thinning or patterned dielectric structures, and interface-guided breakdown in multilayer stacks. Such approaches could help regulate asymmetry formation while retaining the scalability of electrical nanopore fabrication.⁵⁹

CONCLUSIONS

In this work, we demonstrated that 2D/SiN_x nanopores can encode protein transport direction in a material-dependent manner through their composition and interfacial asymmetry. By comparing symmetric SiN_x controls with hBN- and MoS₂-terminated stacks, we identified how the polarity and magnitude of directional slowing arise only when geometric constriction is coupled with the electrostatic properties of the terminal 2D layer. Type-1 architectures displayed orientation-independent behavior, whereas type-2 SGH and SGM pores exhibited strong but oppositely signed directional biases that track with their ionic rectification signatures.

Our statistical analysis across multiple translocation descriptors, together with COMSOL modeling, establishes that directional selectivity originates from material-dependent entrance-exit potential gradients: hBN creates an exit-side bottleneck, while MoS₂ generates enhanced entrance-side field focusing. These findings demonstrate that directional transport in multilayer nanopores emerges from the interplay between effective axial asymmetry and terminal-layer electrostatics. When structural asymmetry is present, the identity of the terminal 2D material determines the polarity of kinetic slowing, whereas symmetric architectures remain orientation-independent. By linking terminal-layer identity to the polarity of directional slowing in asymmetric multilayer nanopores, this work provides a materials-based route to tune single-protein translocation kinetics, which is directly relevant to improving analyzability in nanopore-based single-molecule protein sensing.

More broadly, this study demonstrates that multilayer heterostructures offer a generalizable strategy for programming transport behavior in solid-state nanopores through engineered dielectric and electronic discontinuities. By incorporating 2D materials, solid-state pores can be endowed with functional attributes typically associated with biological channels, including polarity, rectification, and direction-selective capture. We envision that the design framework introduced here will enable the development of heterostructure-based nanopore diodes, programmable rectifying biosensors, and iontronic platforms capable of asymmetric gating and selective molecular control, expanding the utility of solid-state nanopores in single-molecule analytics and nanoscale transport engineering.

EXPERIMENTAL SECTION

Materials

Ultrapure type I water was produced using a Millipore-Sigma Direct Q3 filtration system (Burlington, MA). All other chemical reagents and solvents, unless otherwise noted, were purchased from Sigma-Aldrich (St. Louis, MO) and used without further purification.

Multilayer Membrane Preparation

Multilayer nanopore devices were constructed by sequential transfer of 2D materials onto a 12 nm thick, 5 μm × 5 μm free-standing SiN_x membrane (Norcada Inc.). Bulk crystals of graphene, MoS₂, and hexagonal boron nitride (hBN) were obtained from SixCarbon Technology and 2D Semiconductors (USA). Thin flakes were isolated by mechanical exfoliation and transferred using a dry-stamping method under ambient conditions.^46,60 Graphene was transferred first, followed by either hBN (SGH) or MoS₂ (SGM), forming vertically stacked heterostructures. After transfer, chips were stored in a drybox (≥12 h) to promote interfacial adhesion and reduce delamination during downstream processing.

Device Assembly and Nanopore Fabrication

Devices were assembled in a PDMS/PTFE flow cell using a sealed sandwich configuration. A ~2.5 mm hole was punched in two PDMS gaskets and aligned with the freestanding membrane window. The chip was clamped between the PDMS layers and fixed into the flow cell using screws and alignment channels to prevent leakage. Prior to pore fabrication, reservoirs and chips were wetted with a 1:1 ethanol:DI water mixture for 15 min, rinsed thoroughly, and filled with 1 M potassium chloride (KCl) solution (P9333, Sigma-Aldrich) buffered with 10 mM Tris (J61036, Alfa Aesar) at pH ~8, mixed with sodium hypochlorite (NaOCl) solution (425044, Sigma-Aldrich) at a 9:2 volumetric ratio to enable chemically tuned controlled dielectric breakdown (CT-CDB).

CT-CDB was performed inside a dual Faraday cage using Ag/AgCl electrodes and a KEYSIGHT E3631A DC power supply controlled by a LabVIEW feedback system. The initial bias (8–10 V) was chosen to maintain an electric field near ~0.65 V/nm. The voltage was applied until a sudden current surge indicated nanopore formation. At this point, the circuit automatically cut off the bias to prevent overgrowth. Pore formation typically completed within 10 min. Final pore diameters (~20 ± 2 nm) were estimated from open-pore conductance using the standard access resistance model

$$G=\sigma {\left(\frac{4L}{\pi {\mathrm{d}}^2}+\frac{1}{\mathrm{d}}\right)}^{-1}$$ (1)

where $L$ is the membrane thickness and $\sigma$ is the electrolyte conductivity (~11.7 S/m). If the pore diameter was below target, brief voltage pulses (1–2 V for 1–3 s) were applied to fine-tune the size. After fabrication, devices were equilibrated for 30–60 min before replacing the electrolyte with fresh 1 M KCl 10 mM Tris (pH 8) for sensing experiments. CT-CDB in multilayer membranes proceeds through stochastic defect nucleation pathways, resulting in device-to-device variability in the degree of effective asymmetry. Consequently, not all fabricated nanopores exhibit strong rectification or directional transport. Devices are therefore screened postfabrication based on electrical stability, I–V characteristics, and transport asymmetry before inclusion in statistical analysis.

Protein Preparation.

Ten μg of holo-transferrin (T0665, Sigma-Aldrich) was reconstituted in sterile 1× PBS (pH ~7.4) to make a 50 μg/mL concentration. The final concentration inside the flow-cell chambers was 10 nM in 1 M KCl 10 mM Tris (pH 8). The protein was introduced from the trans side of the chamber to define the voltage polarity and directional translocation.

Nanopore Characterization

Postfabrication device integrity was assessed optically, and multilayer membrane composition was verified using SEM–EDX (JEOL JSM-IT500HR). Open-pore I–V measurements were used to confirm pore formation and estimate conductance before and after protein translocation experiments. Energy-dispersive X-ray analysis (Figure S1, Supporting Information) confirmed the presence of graphene, hBN, and MoS₂ layers.

Data Collection and Analysis

Ionic current recordings were performed using an Axopatch 200B patch-clamp amplifier (Molecular Devices) connected to a Digidata 1440A digitizer. External voltages of 50, 100, and 150 mV were applied, and data were sampled at 250 kHz with a low-pass Bessel filter of 10 kHz. Voltages above 150 mV were avoided due to increased noise and clogging risk. Translocation data were collected across multiple devices and orientations, with each measurement lasting 5–15 min. Translocation events were identified using EventPro v3.05 (multilevel mode, MATLAB)⁶¹ and extracted with 33 raw features per event. Postprocessing in python was used to calculate derived features including relative current blockade (dI/I), translocation velocity, and event charge deficit (ECD). Distributions were visualized using histograms, scatter plots, violin plots, and Cohen’s d effect size analysis. Statistical differences between forward and reverse translocations were assessed at each voltage using OriginPro 2025b analysis software.

Finite Element Simulations.

Electric potential and field profiles for SiN_x, SGH, and SGM nanopore architectures were computed in COMSOL Multiphysics 6.1 using a 2D axisymmetric geometry. Steady-state simulations solved for coupled electrostatics and ion transport using the Electrostatics and Transport of Diluted Species modules. Boundary conditions mimicked experimental voltages, with 50, 100, and 150 mV applied to the protein-containing reservoir. Simulated potential gradients and field focusing near the pore entrances were used to interpret direction-dependent experimental data (Figures 5, S8 and Supporting Information). For further explanation, please refer to Supporting Information Note S2.

Supplementary Material

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsanm.6c01041.

Figures include current traces of protein translocations through all the structures, SEM EDX results, quantitative analyses at 50 and 100 mV, and COMSOL simulation results and notes (PDF)

ABBREVIATIONS

MoS₂

molybdenum disulfide

hBN

hexagonal boron nitride

holo-hSTf

holo-human serum transferrin

SGH

SiN_x + graphene + hBN

SGM

SiN_x + graphene + MoS₂

CT-CDB

chemically tuned controlled dielectric breakdown method