Imaging the Hidden Potential in Atomic Materials with a Single-Atom Sensor

The way electrons move through solid materials is controlled by the invisible, repeating patterns of electric potential created by the atoms themselves. In recent years, scientists have developed a revolutionary method to engineer these patterns. By stacking atomically thin materials on top of each other with a slight twist or mismatch, researchers create "moiré lattices." These superlattices act as custom-designed potential landscapes on the nanoscale. This innovation has led to the discovery of many strange and exotic phases of quantum matter. However, despite knowing how important these electrostatic landscapes are, directly seeing them has remained a massive scientific challenge. Here, we introduce a new scanning probe called the atomic single-electron transistor (SET). This instrument uses a single atomic defect within a van der Waals material as an ultrasensitive, high-resolution sensor for electric potential. Built on the platform of the Quantum Twisting Microscope (QTM), the atomic SET takes advantage of the QTM's unique ability to create pristine, scanable interfaces between two-dimensional materials.

Using this new probe, we present the first direct images of the electrostatic potential in the standard moiré interface formed by aligning graphene with hexagonal boron nitride (G/hBN). The measured potential shows a distinct three-fold rotational symmetry, denoted as C3. It also shows very little dependence on the number of charge carriers and has a surprisingly large amplitude of about 60 millivolts, even when no charge carriers are present. Theoretical analysis suggests this symmetry comes from a delicate balance between physical mechanisms that have competing symmetries. The measured amplitude is notably larger than current theoretical predictions, which indicates there may be gaps in our fundamental understanding of these systems. With a spatial resolution of one nanometer and the sensitivity to detect potential changes from a tiny fraction of an electron charge, the atomic SET opens new capabilities. It allows scientists to image charge order and thermodynamic properties across a broad spectrum of quantum phenomena, including symmetry-broken phases, quantum crystals, vortex charges, and fractionalized quasiparticles.

The behavior of electrons in a crystalline solid is dictated by the periodic potential imposed by the atomic lattice. In natural materials, this periodicity is set at the atomic scale, making direct visualization of the local electrostatic potential exceptionally difficult. Over the past decade, moiré engineering has emerged as a powerful technique for creating tunable periodic potentials at the interfaces of van der Waals (vdW) materials. By stacking or twisting atomically thin layers like graphene, these interfaces produce superlattices with periods significantly larger than the atomic lattice constant. A prime example is the interface between aligned graphene and hexagonal boron nitride (G/hBN). Their slight lattice mismatch generates a moiré superlattice whose periodic potential profoundly modifies electronic properties. This enables observations such as the Hofstadter butterfly and Brown–Zak oscillations. More recently, coupling this aligned G/hBN interface with multilayer graphene architectures has been crucial for stabilizing even more exotic quantum states. These include ferromagnetism in magic-angle twisted bilayer graphene, unconventional ferroelectricity, and the fractional quantum anomalous Hall effect.

Despite its pivotal role, the G/hBN moiré potential has, until now, only been inferred indirectly from transport and optical measurements. Directly mapping this potential requires an imaging technique that combines nanometer-scale spatial resolution with extraordinary sensitivity to minute potential changes. The most sensitive existing tool for electrostatic potential imaging is the scanning single-electron transistor (SET). It operates by monitoring transport through a small conductive island in the Coulomb blockade regime. However, the spatial resolution of conventional scanning SETs is limited by their lithographic size, which is greater than 100 nanometers. This is too coarse to resolve variations within a single moiré unit cell. While techniques like scanning tunneling microscopy (STM) with a graphene sensor have achieved intermediate resolution, and atomic force microscopy (AFM) methods can image molecules with high resolution, direct visualization of moiré potentials within vdW heterostructures has remained an outstanding challenge.

In this work, we develop the atomic SET, a new scanning probe that uses a single atomic defect as its scanning potential sensor. This approach achieves a spatial resolution of 1 nanometer—two orders of magnitude finer than existing SETs—and a potential sensitivity of 5 microvolts per square root hertz. This sensitivity corresponds to detecting variations of a few parts per million of the potential generated by a single electron charge at a distance set by the resolution. Using this tool, we directly image the potential landscape at the G/hBN moiré interface. Our measurements reveal that, even at zero carrier density, the peak-to-peak potential amplitude is substantial, approximately 60 millivolts, and displays an approximate three-fold rotational (C3) symmetry around the moiré unit cell center. Although this symmetry can be explained by a subtle interplay of competing physical mechanisms, the magnitude of the measured potential is approximately double that predicted by current theoretical models. This underscores that our understanding of even this fundamental moiré system is incomplete.

The operational principle of the scanning atomic SET is illustrated in Figure 1a. A single atomic defect embedded within a thin transition metal dichalcogenide (TMD) layer functions as a quantum dot. The energy level of this quantum dot shifts sensitively in response to small changes in the local electrostatic potential, φ(r). The sample system of interest is mounted on the tip of a quantum twisting microscope (QTM). Scanning this tip across the stationary defect modulates the potential felt by the defect. This, in turn, shifts its Coulomb blockade conductance peak. By monitoring this shift, we directly map φ(r). This inverted geometry, where the sample is on the tip, allows us to select an optimal sensing defect from a large natural population within the flat TMD substrate layer.

To locate suitable atomic defects, we map the tunneling current (I) at a fixed bias voltage (V) while scanning the tip across the TMD layer (Figure 1b). When the tip is not positioned over a defect, the current results from background momentum-conserving tunneling processes. However, when the tip overlaps a defect, an additional, defect-assisted tunneling channel opens, leading to a marked increase in current. This produces a distinct image of the tip's contact area whenever it passes over a defect. Figure 1c shows a room-temperature measurement using a trilayer tungsten diselenide (WSe₂) barrier. Several oblong shapes of enhanced current are visible, each corresponding to a different atomic defect imaging the contact area of the tip. Their identical spatial structure suggests these defects share the same chemical origin. In this experiment, the QTM tip itself consists of aligned G/hBN, forming a moiré superlattice. Remarkably, the defect imaging resolves this moiré pattern even at room temperature. The sharpness of the imaged tip edges demonstrates an extremely high spatial resolution of approximately 1 nanometer. This measurement also indicates minimal strain in the transferred heterostructure, typically less than ±0.3%.

We also investigated the energetic distribution of defects by imaging at different bias voltages at a very low temperature (T = 0.2 Kelvin). Figure 1d presents current maps taken with a different G/hBN tip scanned over a bilayer WSe₂ barrier. At high bias, numerous lung-shaped replicas of the tip appear, corresponding to a broad set of energetically accessible defects. As the bias is reduced, progressively fewer defects contribute to the current. At the lowest bias, only a single low-energy defect remains active within the scan window, with minimal background tunneling. We utilize these relatively rare, low-energy defects for high-fidelity potential imaging: their sparse distribution ensures imaging through a single defect, and their low operating energy allows measurements near zero bias, avoiding the injection of hot electrons or phonons that could perturb the system's ground state.

Having used defects as localized current pathways, we now configure an individual defect as a fully functional quantum dot to probe the local electrostatic potential and thermodynamic quantities at a specific point. This is achieved by incorporating top and bottom gates into the QTM junction (Figure 2a). In a standard quantum dot, applying a gate voltage (VG) linearly shifts the dot's electrostatic potential, producing a characteristic "Coulomb diamond" diagram in conductance versus gate and bias voltage (Figure 2b). At zero bias, current flows only at a specific VG where charge states N and N+1 of the dot are degenerate. At finite bias, this conduction window expands linearly, forming a diamond-shaped region.

In our setup, the system of interest (e.g., the G/hBN moiré) sits between a gate electrode and the sensing defect. Consequently, the defect's potential responds to gate voltages through the electronic compressibility (dμ/dn) of the graphene layers in the system. This causes the boundaries of the Coulomb diamond to curve, reflecting the Dirac-like energy-momentum relationship of graphene (Figure 2d). We first establish the electrostatic landscape of the junction by measuring differential conductance (dI/dV) away from any defect (Figure 2e). The observed lines of reduced conductance correspond to the charge neutrality points (CNPs) of the top and bottom graphene layers, consistent with our electrostatic model. A pronounced suppression of conductance for biases below approximately 65 millivolts is attributed to a device-specific contact resistance. Measurements in a perpendicular magnetic field (Figure 2f) reveal additional conductance suppressions associated with Landau level gaps in the graphene layers, further validating the model.

We then measure tunneling through a low-energy defect (Figure 2g), observing a conductance signal an order of magnitude larger, which forms a curved Coulomb diamond. The curvature of the diamond edges directly maps the compressibility, μ(n), of the top and bottom graphene electrodes. Deflection points in these edges (indicated by arrows) correspond precisely to the CNPs of each layer, where the compressibility is minimal. A similar measurement under a magnetic field (Figure 2h) shows step-like features on the diamond edges corresponding to Landau level gaps. These experiments confirm that a single atomic defect can act as a calibrated sensor for the local chemical potential.

Having demonstrated point measurement capability, we proceed to real-space potential imaging. Figure 3a shows a high-resolution current map, I(x, y), measured through a single low-energy defect, clearly revealing the moiré superlattice structure of the G/hBN tip. To extract the electrostatic potential, we track how the position of the zero-bias Coulomb blockade peak shifts as the tip is scanned. Figure 3b displays the zero-bias differential conductance, dI/dV(x, VG), measured along a line scan (white dashed line in 3a). A narrow Coulomb peak is observed at each lateral position, x. The gate-voltage position of this peak, VTG^peak(x), oscillates periodically with the moiré lattice. This oscillation directly tracks the spatially varying electrostatic potential at the moiré interface, φ(x), as the peak position is linearly related to φ(x) through the junction's electrostatic parameters.

The resulting potential map reveals a large peak-to-peak amplitude of approximately 60 millivolts. This potential persists even when the graphene is at its charge neutrality point (zero carrier density), indicating it is an intrinsic property of the aligned interface, not induced by populated charge carriers. The potential landscape exhibits a clear three-fold rotational (C3) symmetry around high-symmetry points in the moiré unit cell. Theoretical modeling suggests this symmetry arises from a complex interplay between several physical effects, including lattice relaxation, electronic hybridization, and flexoelectric response, each of which individually favors different symmetries. The delicate balance between these competing mechanisms yields the observed C3 pattern. Notably, the measured potential amplitude is roughly twice as large as predictions from state-of-the-art theoretical calculations. This significant discrepancy highlights that our current understanding of the electrostatics at this fundamental vdW interface is incomplete. Possible explanations could involve underestimation of certain effects, such as charge redistribution or interfacial dipoles, in existing models.

The atomic SET, with its combination of atomic-scale resolution and extreme potential sensitivity, establishes a new paradigm for probing quantum materials. It opens a direct window into the electrostatic landscapes that govern electron behavior in moiré systems and beyond. This technique is poised to illuminate charge order, thermodynamic properties, and local potentials in a wide array of quantum phases, including correlated insulators, Wigner crystals, vortex states in superconductors, and systems hosting fractionalized quasiparticles.