In 1801, British physicist Thomas Young passed light through two slits spaced about 1 mm apart and showed that bright and dark fringes appeared beyond them—decisive proof that light behaves as a wave. This "double-slit experiment" has since been extended to electrons, neutrons, atoms, and even huge molecules like fullerenes, remaining a textbook staple that confirms the wave nature central to quantum mechanics. In 1989, Dr. Akira Tonomura of Hitachi and colleagues filmed interference fringes gradually emerging as electrons were fired one at a time, offering a striking visual demonstration of quantum weirdness.
But these experiments share a common premise: the slits are artificial structures, with spacings ranging from nanometers to micrometers. Interferometry—the technique of precisely reading physical quantities from changes in interference fringes—has already been applied in gravitational-wave detectors like LIGO and in atomic clocks. So what would happen if the slits themselves were replaced by atoms inside a material? Could the arrangement and motion of atoms be probed directly, down to the level of a single atomic bond? The idea had been around for some time, but no one had realized it.
Turning a Crystal into a "Natural Double Slit"
The challenge was fundamental. Because atoms in a crystal are arranged with strict regularity, atoms fixed at lattice points should, in principle, function as a "double slit" with a well-defined spacing. But extracting local information requires confining the interaction to an atomic-scale region. In conventional electron diffraction, the electron beam strikes many atomic columns simultaneously, making it impossible to isolate the interference from a single pair of atoms.
What broke through this barrier were recent advances in scanning transmission electron microscopy (STEM). Aberration correction technology has made it possible to focus the electron probe down to a full width at half maximum (FWHM) of 1.1 Å. In addition, pixelated detectors capable of rapidly recording two-dimensional diffraction patterns at every scan position have become practical, enabling the acquisition of four-dimensional data (4D-STEM)—combining a two-dimensional scan position with a two-dimensional diffraction pattern. Professor Shibata and colleagues combined these two technologies to open a path toward using a crystal itself as an atomic-scale interferometer.
The Channeling Effect Creates "Two Wave Sources"
The experimental procedure was as follows. First, when a silicon crystal is viewed along the [110] direction, one sees a "dumbbell structure" in which two atomic columns are paired with a spacing of 136 pm (1.36 Å). The research group positioned the STEM electron probe precisely at the midpoint between this pair of atoms and directed the beam there.
As electrons travel through the crystal, the attractive potential of the atomic nuclei acts like a waveguide, confining the electron beam along the two atomic columns. This phenomenon is known as the channeling effect. As a result, two tiny wave sources, separated by 136 pm, form at the exit surface of the sample. These two wave sources interfere with each other, producing a fringe pattern on the detector.
From the massive amount of recorded 4D-STEM data, the researchers selected only the diffraction patterns corresponding to conditions where the electron beam entered at the midpoint of an atomic pair, and averaged the patterns over 356 crystallographically equivalent atomic pairs. This revealed clear interference fringes—up to the third order—perpendicular to the direction connecting the atomic columns. The fringe period was 0.736 Å, consistent with the value expected from the 136 pm slit spacing. In contrast, when the probe was placed directly above a single atomic column, the interference fringes vanished completely. Double-slit interference occurs only at the special "midpoint" position between neighboring atomic pairs.
Whereas the slit spacing in Young's experiment was about 1 mm, the slit spacing in this study is 136 pm. The scale ratio is roughly seven orders of magnitude—that is, ten million to one.
"Correlated Vibrations" Preserve the Coherence of the Fringes
This is the crux of the study. Atoms in a crystal vibrate thermally even at room temperature. If two neighboring atoms vibrated completely independently of one another, the slit spacing would fluctuate randomly, and higher-order interference fringes should disappear. Indeed, calculations using the Einstein model—which assumes independent, isotropic vibrations—predicted that all fringes beyond the first order would vanish, sharply contradicting the experimental results.
However, when "correlated displacements" derived from silicon phonon (lattice vibration) theory were incorporated into the model, the experiment was reproduced accurately, including fringes up to the third order. The tendency of neighboring atoms to vibrate in the same direction—correlated thermal vibration—turned out to be the physical reason atomic-scale interference is preserved.
These fringes proved robust even at high temperature. Even when heated to 900 K (about 627°C), the second-order fringe was clearly observed. Under the Einstein model, the fringes would vanish completely at 900 K, so their survival at this high temperature is itself evidence of the correlated-vibration effect.
| Condition | Fringe survival | Agreement with experiment |
|---|---|---|
| Einstein model (independent vibration, 300 K) | Only 1st order; 2nd and higher vanish | Mismatch |
| Correlated phonon model (300 K) | Survives up to 3rd order | Match |
| Einstein model (900 K) | Completely vanishes | Mismatch |
| Correlated phonon model (900 K) | Survives up to 2nd order | Match |
| Experiment (300 K) | Observed up to 3rd order | Reference |
| Experiment (900 K) | Observed up to 2nd order | Reference |
Reading "Bond Stiffness" from the Fringes
The research group also analyzed the directional dependence of the interference fringes. If the two atoms move in the same direction along the axis connecting the atomic columns (the x-direction), the 136 pm slit spacing is preserved and the higher-order fringes survive. If they move in opposite directions, the spacing fluctuates and the higher-order fringes are lost. In the perpendicular direction (the y-direction), if the atoms move in the same direction, the orientation of the double-slit axis is preserved; if they move in opposite directions, the axis tilts and the fringes blur angularly. Because the effect manifests differently in these two directions, a single interference pattern makes it possible to independently read out the degree of correlated vibration along both directions.
The correlation coefficients obtained from this analysis were along the x-direction (parallel to the bond) and along the y-direction (perpendicular to the bond). The finding that vibrations align more readily along the x-direction reflects the fact that the stiffness resisting stretching and compressing the bond is greater than the stiffness resisting lateral displacement. These correlation coefficients remained nearly unchanged even when the temperature was raised to 900 K—meaning that the degree of alignment in atomic vibration reflects an intrinsic property of the atomic bond itself, independent of temperature.
This correlation coefficient corresponds directly to the force constant, which represents the "stiffness" of the atomic bond. If neighboring atoms are connected by a stiff spring, the motion of one atom drags the other along with it, yielding a large correlation coefficient. Conversely, if the bond is soft, the two atoms move independently. Reading the correlation coefficient from the interference fringes is directly equivalent to evaluating, in real space, how stiff a given atomic bond is.
CAVIAR: Another Approach
This study is not the only effort attempting to capture correlated atomic vibrations using an electron microscope. In June 2026, Anton Gladyshev, Christoph T. Koch, and colleagues at Humboldt University published a framework called CAVIAR (Correlated Atomic Vibration Imaging with sub-Angstrom Resolution) in Nature Communications, based on electron ptychography (a phase-retrieval imaging method). CAVIAR reconstructs the sample's transmission function from 4D-STEM data and extracts the spatial correlation of atomic-position fluctuations within it, observing displacement correlations of 10–20 pm in a hexagonal boron nitride (hBN) bicrystal.
The difference between the two approaches lies in how each exploits the physics of interference. Shibata and colleagues' method uses the crystal itself as an interferometer, reading the correlation coefficient directly from the observable visibility of the interference fringes. CAVIAR, by contrast, reconstructs atomic positions through computational phase retrieval and estimates correlations from their statistical fluctuations. The former excels at local measurements focused on a single atomic bond, while the latter excels at extracting phonon dispersion within a volume of several nm. The fact that two complementary approaches emerged in the same year suggests this field has reached a critical juncture.
| Item | This study (Shibata et al.) | CAVIAR (Gladyshev, Koch et al.) |
|---|---|---|
| Journal | Nature (August 2026) | Nature Communications (June 2026) |
| Principle | Interferometric measurement using an atomic pair as a double slit | Phase retrieval via electron ptychography and extraction of displacement correlations |
| Observable | Visibility and directional dependence of interference fringes | Spatial correlation of reconstructed atomic positions |
| Spatial resolution | Single atomic-bond level | Atomic resolution within a volume of several nm |
| Demonstration sample | Si single crystal ([110] direction) | hBN bicrystal |
| Temperature dependence | Measured from 300 K to 900 K | Room temperature |
| Physical quantities obtained | Correlation coefficients (, ), force-constant ratio | Phonon frequencies, directionality of displacement correlation |
How Far Can This Go Toward Semiconductor Heat-Dissipation Design?
As semiconductor devices become more powerful and more compact, controlling heat generation has become a pressing engineering challenge. How heat propagates is governed by phonons—lattice vibrations—but at the nanoscale, conventional diffusion models (Fourier's law) break down, giving way to ballistic transport and fluid-like behavior. Near interfaces and defects in particular, phonon scattering significantly impedes heat conduction, yet until now no experiment had directly examined the microscopic mechanism at the level of a single atomic bond.
What this study demonstrates is a principle: through analysis of interference fringes, it is possible to quantitatively evaluate the stiffness of a specific atomic bond and the degree of correlation in its vibrations. If this method could be applied near interfaces and defects in semiconductor devices, it might become possible to visualize, at the atomic level, where heat flows easily and where it becomes bottlenecked.
That said, verification so far has been limited to uniform regions of high-purity silicon single crystal. Whether the channeling effect is sufficiently maintained, and whether interpretable interference fringes appear, in regions where crystal periodicity is disrupted—such as interfaces or defects—remains unverified. Extension to material systems beyond silicon, particularly compound semiconductors and oxides, is also a task for the future. The experimental condition of averaging over 356 equivalent atomic pairs to secure sufficient signal will likely require a different strategy when investigating local inhomogeneities.
An experiment devised 200 years ago to prove the wave nature of light has been transformed into an instrument for reading the "cooperation" of atoms. The information encoded in these interference fringes speaks to both an engineering challenge—thermal design in semiconductors—and a question of basic science: the physics of phonons.