Imaging the Sub-Moiré Potential Landscape using an Atomic Single Electron Transistor

Technical Summary: Imaging the Sub-Moiré Potential Landscape using an Atomic Single Electron Transistor

Problem Statement
The electronic properties of solids are fundamentally governed by the periodic potential landscapes they experience. While the advent of moiré engineering—creating tunable periodic potentials at the interface of van der Waals (vdW) materials like graphene and hexagonal boron nitride (G/hBN)—has revolutionized the field, leading to discoveries such as the Hofstadter butterfly and fractional quantum anomalous Hall effects, a critical gap remains: the direct imaging of these electrostatic potential landscapes. Existing techniques, such as transport and optical measurements, only infer these potentials indirectly. Furthermore, while scanning single-electron transistors (SETs) offer high sensitivity, their spatial resolution is typically limited by lithographic constraints to >100 nm, which is insufficient to resolve features within a moiré unit cell (typically ~10–14 nm). Similarly, while scanning tunneling microscopy (STM) offers atomic resolution, it lacks the direct electrostatic sensitivity required to map the potential variations in vdW heterostructures without the complications of band-edge markers found in transition metal dichalcogenides.

Methodology: The Atomic Single Electron Transistor (SET)
To address these limitations, the authors introduce the "Atomic SET," a novel scanning probe integrated into a Quantum Twisting Microscope (QTM) platform. The core innovation is the use of a single, naturally occurring atomic defect within a few-layer-thick transition metal dichalcogenide (TMD) barrier (specifically WSe₂) as the sensing element.

• Device Architecture: The setup involves a QTM tip, which carries the system of interest (an aligned G/hBN moiré interface), scanning over a fixed sensor device. The sensor consists of a graphene source electrode, a bilayer WSe₂ barrier containing a single atomic defect, and a graphene drain electrode (the QTM tip).
• Operation Principle: At cryogenic temperatures (~0.2 K), the atomic defect functions as a quantum dot (QD) exhibiting single-electron tunneling. The tunneling current is extremely sensitive to the local electrostatic potential gating the defect. As the QTM tip (carrying the G/hBN interface) scans across the stationary defect, the spatially varying electrostatic potential of the moiré interface gates the defect, modulating the tunneling current.
• Imaging Strategy: By monitoring the zero-bias Coulomb blockade resonance condition (the gate voltage required to align the defect's energy level with the electrodes) as a function of position, the authors directly map the local electrostatic potential. The inverted geometry (scanning the sample over a fixed sensor) allows for the selection of optimal, low-energy defects from a large pool, ensuring single-defect operation.
• Characterization: The authors characterize the defects by mapping current variations to identify the tip contact area and by analyzing Coulomb diamond diagrams to extract local electronic compressibility and confirm the defect's role as a local detector of chemical potential.

Key Contributions and Results
Using the Atomic SET, the authors present the first direct, high-resolution images of the electrostatic potential landscape in a G/hBN moiré interface.

1. Spatial Resolution and Sensitivity: The technique achieves a spatial resolution of approximately 1 nm, two orders of magnitude better than conventional scanning SETs. The potential sensitivity is measured at ~6 µV/√Hz, corresponding to the detection of potential variations from a few millionths of an electron charge at the resolution distance.
2. Moiré Potential Magnitude and Symmetry: The direct imaging reveals that the electrostatic potential in the G/hBN interface exhibits an approximate $C_{6v}$ symmetry (six-fold) around the moiré center, despite the underlying lattice having $C_3$ symmetry. The potential magnitude is substantial, with a peak-to-peak amplitude of approximately 60–63 mV, even at zero carrier density.
3. Carrier Density Dependence: The measurements show that the magnitude of the potential varies minimally (~10%) with changes in the moiré filling factor (carrier density), indicating that the potential is largely intrinsic to the interface structure rather than being dominated by carrier redistribution.
4. Theoretical Discrepancy: The authors compare their experimental results with self-consistent Hartree calculations that account for stacking potentials, lattice relaxation (deformation potentials), and pseudomagnetic fields. While the theoretical model successfully predicts the approximate $C_{6v}$ symmetry through the cancellation of competing $C_3$-symmetric terms, it significantly underestimates the magnitude of the potential. The experimental potential is roughly twice as large as the theoretical prediction. The authors note that increasing strain in the model would enhance the magnitude but would restore $C_3$ symmetry, contradicting the experimental $C_{6v}$ observation. This suggests that current theoretical understanding of even this canonical moiré interface is incomplete.
5. Distance Dependence: Measurements using defects at different heights (0.8 nm and 1.5 nm) from the interface demonstrate a rapid decay of the potential amplitude, underscoring the necessity of the Atomic SET's extremely close standoff distance for detecting these sub-moiré features.

Significance and Claims
The paper claims that the Atomic SET opens a new avenue for the ultrasensitive imaging of charge order and thermodynamic properties in quantum materials. By combining the pristine interface capabilities of the QTM with the atomic-scale resolution of a single-defect sensor, this technique extends the reach of electrostatic imaging to phenomena occurring on scales below the Fermi wavelength and magnetic length. The authors posit that this method is applicable to a broad range of quantum phenomena, including symmetry-broken phases, quantum crystals, vortex charges, and fractionalized quasiparticles.

Crucially, the work highlights a fundamental gap in the theoretical description of G/hBN interfaces. The large discrepancy between the measured potential magnitude and theoretical predictions implies that existing models may be missing key physical mechanisms, which has direct consequences for the design and interpretation of experiments involving moiré-engineered states of matter, such as the fractional quantum anomalous Hall effect in pentalayer graphene. The paper concludes that despite G/hBN being one of the most extensively studied moiré systems, its electrostatic landscape remains partially misunderstood.