Ultrathin bismuthene islands on graphite slide freely in one direction and pause unpredictably, revealing new ways to control friction in nanoscale materials.
(Nanowerk Spotlight) Friction at small scales is not merely a drag on efficiency—it defines the limits of how machines, sensors, and devices function at the surface. Its effects become especially pronounced in systems that operate without traditional lubricants, including many that use atomically thin materials. The discovery that two crystalline surfaces can exhibit vanishingly small friction when their atomic patterns do not align—known as structural superlubricity—has reshaped the approach to nanoscale motion control.
This effect has been demonstrated in two-dimensional systems such as graphene or hexagonal boron nitride, where the atomic lattices interact through weak van der Waals forces. When these layers are rotationally offset, the energy barriers to sliding collapse, allowing nearly frictionless movement across the plane.
Yet, in all known realizations, this phenomenon has been isotropic—meaning friction is minimized equally in all directions. While useful for reducing wear, isotropic superlubricity offers no means of controlling motion along defined paths. The ability to confine low-friction movement to specific crystallographic directions, while suppressing it in others, would allow engineers to design nanoscale surfaces where movement is channeled rather than free.
Theoretical models have predicted that such directional superlubricity should occur when two surfaces share a line of atomic alignment in one direction only, a condition tied to their lattice geometries. These configurations, called type-B contacts, should permit movement along one low-energy axis—akin to a nanoscopic rail system—while resisting it elsewhere.
Creating such an interface experimentally has proven difficult. It requires two materials with different surface symmetries, aligned in a way that satisfies the directional matching condition. It also requires an exceptionally clean and atomically flat interface, where even minor surface defects can pin motion entirely. These constraints have so far prevented directional superlubricity from being realized in a two-dimensional material system at the nanoscale.
This is what makes the current study significant. Using α-bismuthene—an anisotropic, two-dimensional form of bismuth—grown on graphite, researchers have observed directional structural superlubricity at room temperature. Even more unexpectedly, they report that the motion occurs in discrete, long-distance bursts governed by a statistical pattern known as a Lévy flight.
The result is a rare demonstration of both friction anisotropy and stochastic dynamics in a solid-state nanoscale system, realized without external force and observable in real time. These findings add a new dimension to nanotechnology and the concept of friction, showing that nanoscale contact interfaces can be programmed to support directionally selective motion rather than just low resistance.
Images and diffraction patterns from low-energy electron microscopy (LEEM) show how atomically thin islands of α-bismuthene form and move on a graphite surface. Panel (a) illustrates the experimental setup. Panel (b) shows a diffraction pattern from a single bismuthene island, revealing its crystal orientation relative to the graphite substrate (twist angle ~28°). Panels (c) and (d) display LEEM images taken early and late during bismuthene growth, showing islands forming on steps and flat areas of the graphite. Panels (e) to (h) are time-sequenced snapshots highlighting the spontaneous movement of one island along a straight path. Colored lines mark the island’s elongation direction and movement track. Panels (i) to (k) show how the positions of three islands change over time, revealing different types of motion including back-and-forth hopping and pinning. All measurements were taken at room temperature. (Image: Reprinted from DOI:10.1002/smll.202408349, CC BY) (click on image to enlarge)
In a study published in Small (“Evidence of Directional Structural Superlubricity and Lévy Flights in a van der Waals Heterostructure”), the research team deposited ultrathin α-bismuthene islands on a highly ordered pyrolytic graphite (HOPG) substrate using vapor-phase methods. These islands, just a few atomic layers thick, were imaged using low-energy electron microscopy (LEEM), which allowed direct observation of their growth and movement at nanometer resolution.
During deposition, and at room temperature, approximately 20% of the islands exhibited spontaneous, directional hopping. They moved back and forth in straight lines, sometimes over distances as large as 600 nanometers. These displacements occurred without applied forces or tip-induced perturbations, suggesting an intrinsic, energy-minimized pathway along the graphite lattice.
The movement was selective. Some islands remained stationary for the entire observation period, while others moved in preferred directions offset by about 60°, matching the symmetry of graphite’s hexagonal structure. This variability indicated that the underlying alignment—the twist angle between the bismuthene and the graphite substrate—played a crucial role in enabling or suppressing motion. Islands with twist angles around 28° and 32° showed the most consistent hopping behavior.
To understand the directional nature of this motion, the team conducted registry index simulations. These simulations map the degree of atomic alignment between the bismuthene and graphite lattices across different positions and twist angles. For most angular configurations, the resulting energy landscape was uniform, offering no preferred direction for motion.
However, at specific twist angles—most notably near 28° and 32°—the simulations revealed a highly anisotropic potential. In these cases, a narrow channel of minimal resistance forms along one crystallographic direction, while all other paths remain energetically unfavorable. This creates what the authors describe as “nanohighways,” one-dimensional sliding corridors embedded in a high-friction environment.
The experimental behavior of the bismuthene islands matched this prediction. When observed under LEEM, the islands spontaneously shifted along these preferred directions, consistent with the orientation of the graphite lattice. The directionality varied between islands based on their twist angle, with 60° offsets aligning with graphite’s symmetry. Importantly, the islands moved not continuously but in discrete hops—sometimes traveling hundreds of nanometers between periods of rest. This observation suggested not only directional control but a more complex form of motion driven by stochastic events.
A detailed statistical analysis revealed that both the hopping lengths and the waiting times between hops followed power-law distributions. In contrast to exponential distributions characteristic of random thermal diffusion, power-law behavior implies that large jumps and long pauses are not rare outliers but intrinsic parts of the motion dynamics.
These distributions—commonly called heavy-tailed—are signatures of Lévy flight dynamics. In this framework, a moving object performs short movements frequently, but also occasionally makes large jumps with a non-negligible probability. Lévy flights are a general model for systems that alternate between rest and bursts of activity. They have been observed in animal foraging, financial markets, and photon transport in disordered media—but rarely in solid-state materials.
What makes this system unusual is its scale. Lévy behavior has previously been observed in atomic or molecular motion, but the bismuthene islands studied here comprise tens of thousands of atoms. They are far more massive than single atoms, and yet exhibit dynamics typically associated with point particles. The implication is that their motion is not just thermally activated but channeled by the underlying lattice alignment and constrained to one-dimensional tracks by the energy landscape.
Island size also affected the hopping behavior. Larger islands were less mobile, most likely because they had a higher probability of encountering defects in the graphite surface, which pinned them in place. Statistical modeling of island area distributions supported this view. The probability of hopping decreased exponentially with island size, consistent with a simple model where randomly distributed point defects in the substrate serve as pinning sites. Still, even some large islands—up to 20,000 square nanometers—were observed to move, underscoring the efficiency of the low-friction pathways created at the correct lattice alignment.
The presence of directional superlubricity and Lévy flight dynamics in the same system is not only rare but potentially instructive. It suggests that anisotropic energy landscapes can induce not just preferred paths of motion but also stochastic patterns in how motion unfolds over time. In this context, defects, lattice twist, and thermal phonons interact to create a complex but deterministic environment for motion—where the rules are statistical but the pathways are structural.
The study points to several promising research directions. One is to explore other combinations of two-dimensional materials with mismatched surface symmetries. The growing catalogue of van der Waals materials includes compounds with rectangular, rhombic, and orthorhombic unit cells. Pairing these in controlled ways could yield further examples of directional superlubricity.
Another is to conduct force-resolved experiments using scanning probes, which could provide more quantitative measurements of the friction forces along and across these nanohighways. Molecular dynamics simulations could also help clarify how island shape, size, edge structure, and defect density affect both mobility and the emergence of Lévy statistics.
In practical terms, the work advances how nanotechnology and the concept of friction are understood in low-dimensional systems. Rather than being an unavoidable loss mechanism, friction can be modulated, oriented, or suppressed entirely along defined tracks.
The observation of Lévy-type motion in such a system also hints at possible applications in stochastic control, where engineered disorder or randomness is used deliberately to enhance performance—such as in signal amplification, molecular sorting, or probabilistic computing.
What this study ultimately demonstrates is that motion at the nanoscale is not only a question of energy minimization but also of geometry, symmetry, and statistics. By carefully aligning lattices and observing their interaction over time, researchers can tune not just how motion occurs, but where and when. This level of control could become a foundational principle for future devices operating at the intersection of mechanics, materials science, and statistical physics.
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