Researchers have instantly imaged the electrostatic panorama inside a single moiré unit cell for the primary time, utilizing a brand new atomic-scale sensor constructed from a single defect in a two-dimensional materials.
Examine: Imaging the sub-moiré potential utilizing an atomic single electron transistor. Picture Credit score: MZinchenko/Shutterstock.com
Printed in Nature, the examine introduces an atomic single electron transistor (SET) that achieves ~1 nm spatial decision and a possible sensitivity of 5 μV Hz-1/2.
Constructed on the quantum twisting microscope (QTM) platform, which permits the formation of pristine, scannable interfaces between van der Waals (vdW) supplies, the probe can resolve the sub-moiré potential panorama in graphene aligned to hexagonal boron nitride (G/hBN).
This canonical moiré system’s electrostatic construction has beforehand solely been inferred not directly.
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Electrons in solids transfer by periodic potential landscapes set by atomic construction. In standard supplies, these potentials fluctuate on atomic size scales, making them practically not possible to picture instantly.
Moiré engineering adjustments that. When two barely mismatched lattices are stacked collectively, like graphene and hexagonal boron nitride, they type a larger-scale periodic sample.
In aligned G/hBN, this produces a moiré superlattice with a wavelength of roughly 14 nm, dramatically bigger than atomic spacing and key to many sudden quantum phenomena.
Regardless of its significance – together with roles in Hofstadter physics, correlated states, and fractional quantum anomalous Corridor phases – the G/hBN moiré potential itself had by no means been instantly mapped.
Scanning single-electron transistors are among the many most delicate instruments out there for measuring electrostatic potentials, however their lithographic dimensions (>100 nm) restrict their spatial decision, stopping them from resolving construction inside a moiré unit cell.
Different scanning probes have achieved excessive decision in molecular programs, however not in buried vdW heterostructures.
Utilizing an Atomic Defect as a Quantum Sensor
The brand new strategy replaces a lithographically outlined island with a single atomic defect embedded in a skinny transition steel dichalcogenide (TMD) layer. That defect is basically a quantum dot.
Within the experiment’s inverted geometry, the system of curiosity, aligned G/hBN, is mounted on the QTM tip and scanned over the stationary defect.
Because the spatially various electrostatic potential (r) passes over the defect, it shifts the defect’s Coulomb blockade peak. Monitoring that shift instantly maps the native potential.
The gadget achieves roughly 1 nm spatial decision, which makes it two orders of magnitude finer than standard scanning SETs, with a possible sensitivity of 5 μV Hz-1/2.
This sensitivity and determination correspond to detecting variations of just some components per million of the potential generated by a single electron cost at that distance.
By including high and backside gates, the researchers use the defect as a spectroscopic probe.
The curvature of the ensuing Coulomb diamonds displays the digital compressibility of the graphene layers, permitting native thermodynamic properties to be measured alongside the electrostatic potential.
A Robust and Symmetric Potential
The ensuing maps reveal a transparent triangular moiré lattice with a wavelength of ~14 nm.
Extra strikingly, the electrostatic potential inside every unit cell exhibits an approximate C6 symmetry – practically sixfold rotational symmetry – quite than the C3 symmetry usually anticipated for unrelaxed G/hBN constructions.
The potential amplitude is substantial: roughly 60 mV peak-to-peak, starting from 52 to 62 mV relying on filling. Even at zero service density (ν ≈ 0), the amplitude stays giant.
Throughout fillings the place ν = 1 corresponds to 1 electron per moiré unit cell, the amplitude adjustments by solely about 10 %, indicating that the moiré potential is essentially set by intrinsic interface properties, quite than service screening.
Principle Matches Symmetry, Not Magnitude
To interpret the measurements, the researchers mannequin three contributions to the moiré Hamiltonian: a stacking pseudopotential, a deformation pseudopotential arising from lattice rest, and a pseudomagnetic area time period.
Individually, the main stacking and deformation phrases every exhibit sturdy C3 symmetry. Nevertheless, their contributions partially cancel, producing a mixed potential with near-C6 symmetry – in keeping with experiments.
Self-consistent Hartree calculations present that digital screening reduces the magnitude of the pseudoelectric potentials by roughly an element of two whereas preserving their spatial construction.
The pseudomagnetic and mass-term contributions are small, scale linearly with filling, and vanish at ν = 0, in keeping with the weak carrier-density dependence noticed experimentally.
But the theoretical whole potential is barely about half as giant because the measured ~60 mV.
The authors take into account whether or not underestimated pressure may clarify the discrepancy, however rising pressure alone would improve C3 symmetry quite than produce the near-C6 symmetry noticed.
This hole between idea and experiment factors to an incomplete understanding of this extensively studied interface.
Why is Atomic-Scale Proximity Vital?
The workforce additionally measured how the potential decays with distance from the interface.
Two defects situated roughly 0.8 nm and 1.5 nm from the G/hBN interface confirmed a couple of 60 % discount in amplitude between these heights.
The decay is steep. Extrapolation means that at distances akin to the moiré wavelength, the detectable sign would drop to a negligible fraction of its interface worth.
The end result highlights the significance of atomic-scale proximity and why earlier probes positioned farther away couldn’t seize the complete potential panorama.
A Way forward for Atomic-Scale Decision?
The atomic SET combines nanometre-scale spatial decision with distinctive potential sensitivity inside pristine vdW interfaces.
Past G/hBN, the approach forges a path to imaging cost order and thermodynamic construction in an enormous vary of quantum programs, together with Wigner crystals, topological edge states, vortex fees, symmetry-broken phases, and fractionally charged quasiparticles.
As moiré supplies proceed to function platforms for correlated and topological states, direct potential imaging may develop into a key device for testing idea and guiding gadget design in next-gen 2D heterostructures.
Journal Reference
Klein D.R. et al. (2026). Imaging the sub-moiré potential utilizing an atomic single electron transistor. Nature. DOI: 10.1038/s41586-025-10085
