- The paper demonstrates through equivariant machine-learning molecular dynamics that twisted 3R-MoS₂ undergoes thermally driven, long-range interlayer sliding at about 1 m/s and moiré-texture drift near 40 m/s at 300 K.
- The paper finds that sliding occurs through local domain-wall migration and collective reconstruction, lowering the effective barrier by nearly two orders of magnitude compared with rigid layer translation.
- The paper shows that sulfur vacancies induce pinning at roughly 0.1% concentration, identifying defect density rather than twist angle as the key control over freely sliding versus localized moiré textures.
Overview and motivation
Sliding ferroelectrics, in which out-of-plane polarization arises from interlayer charge redistribution at a van der Waals interface and can be reversed by in-plane layer sliding, are candidates for fatigue-free, high-endurance memory devices. The prevailing microscopic picture treats polarization switching as a collective, rigid, synchronized translation of the two layers. However, experiments increasingly indicate that switching proceeds through domain-wall (DW) nucleation and propagation, and recent theory has reported superlubric, soliton-like DW dynamics in sliding ferroelectrics. This paper addresses the unresolved question of the actual microscopic sliding dynamics by studying twisted bilayer 3R-MoS2 — a ferroelectric moiré superlattice with a dense network of stacking domains separated by DWs — using machine-learning molecular dynamics (MLMD) (2604.20277).
The central claims are threefold: (i) ferroelectric MoS2 moiré superlattices exhibit spontaneous, thermally driven, long-range interlayer sliding at 300 K with velocities on the order of 1 m/s, manifested as a phason-like global drift of the moiré texture; (ii) this sliding proceeds along a nearly barrierless domain-wall-mediated collective reconstruction pathway rather than rigid layer translation; and (iii) dilute sulfur vacancies, at concentrations as low as ~0.1%, convert the sliding into localized pinning, which reconciles these simulations with the absence of freely drifting moiré textures in experiments.
Machine-learning potential for bilayer MoS2
Because moiré supercells contain thousands of atoms — the 2.4° structure studied here has 10,038 atoms — direct density functional theory (DFT) molecular dynamics is intractable. The authors trained an E(3)-equivariant graph neural network potential on DFT trajectories of a 3×3×1 supercell of 3R-MoS2, incorporating biaxial strain (±2%), sliding configurations along the full sliding path, variable interlayer distances (2.745 Å and 3.945 Å), and Mo/S vacancies. Two architectural modifications — chemically resolved edge-wise gating and a trainable anisotropic distance-decay factor — were introduced to capture the anisotropic, stacking-dependent interlayer coupling.
The model achieves mean absolute errors of 0.11 meV/atom in energy and 13.7 meV/Å in forces, comparable to state-of-the-art interatomic potentials, and faithfully reproduces the DFT potential energy surface (interlayer distance dependence, lattice constant dependence, sliding profile, and phonon spectrum). Validation on moiré supercells with defects confirms transferability to the large structures used in the dynamics simulations.
Thermally driven long-range sliding
For the 2.4° twisted structure (13 nm moiré period), structural relaxation produces the expected reconstruction into triangular MX/XM ferroelectric domains separated by compressed SP regions, with the domain pattern matching prior reports for twisted transition-metal dichalcogenide bilayers. MLMD at 300 K — with zero initial relative interlayer velocity, ruling out the "flying-ice-cube" artifact — reveals that the moiré texture drifts globally over hundreds of picoseconds while preserving its topology. The relative interlayer center-of-mass displacement grows continuously, corresponding to an interlayer sliding velocity on the order of 1 m/s, amplified into a moiré-texture drift velocity on the order of 40 m/s. The sliding direction is not fixed; it varies with random seed and temperature.
Notably, this behavior is not restricted to small twist angles. Comparable long-range drift appears at 10.4° and 15.2°, where well-defined small-angle moiré patterns and strong reconstruction are absent, while the untwisted bilayer remains essentially static. The paper draws the important conclusion that the essential ingredient is the twisting-induced multidomain structure with its DW network, not a large moiré period per se.
Barrier lowering by domain-wall motion
The rigid-sliding barrier — obtained by displacing the upper layer while freezing in-plane atomic coordinates — is approximately 3.8 meV/atom for the 2.4° structure, comparable to the ~3 meV/atom barrier of untwisted 3R-MoS2. The authors argue this rigid barrier is inconsistent with the observed dynamics on three grounds: it is too large to be overcome thermally at room temperature (the untwisted bilayer, with a similar barrier, shows no drift); rigid sliding strongly distorts the moiré texture, whereas MLMD shows global translation of an intact texture; and it suppresses the domain reconstruction that defines the moiré superlattice.
When the barrier is instead computed by constrained relaxation — allowing full atomic relaxation while imposing zero net in-plane force on each layer so that the global interlayer shift is retained — the barrier is reduced by nearly two orders of magnitude to an almost barrierless level. Along this relaxed pathway, the moiré texture translates nearly as a rigid whole while the microscopic rearrangement occurs locally at the DWs. This establishes the DW-mediated collective reconstruction pathway as the operative mechanism: macroscopically a global interlayer slide, microscopically DW migration assisted by local atomic rearrangement. This picture unifies prior observations of superlubric DW motion in sliding ferroelectrics, fast polarization switching, and thermally driven moiré distortion and twist relaxation.
Vacancy-induced sliding-to-pinning transition
Interfacial sulfur vacancies, ubiquitous in synthesized MoS2, act as pinning centers because their formation energy is stacking-dependent: a vacancy is ~50 meV lower in energy in the SP regions than in MX/XM domains. As the moiré texture drifts, the local stacking environment of each vacancy changes, generating an additional barrier that grows approximately with vacancy concentration.
The MLMD results show a sharp defect-dependent transition. The defect-free 4.1° structure exhibits unbounded continuous sliding; a single vacancy (0.042%) does not yet pin it, but three vacancies (0.126%) arrest the long-range motion. Single vacancies already pin the 5.1° (0.066%) and 10.4° (0.28%) structures, converting unbounded sliding into bounded oscillations about the origin. From the crossover, the pinning threshold is estimated at roughly 0.1% vacancy concentration — close to the experimentally reported lower limit for sulfur vacancies in MoS2. This result directly explains why freely drifting moiré textures are not observed experimentally, and why earlier defect-free simulations could show nearly dissipationless DW motion. The authors are careful to note that this thermal pinning does not imply complete suppression of DW motion: electric-field-driven DW motion can remain active in the presence of defects, consistent with the fatigue-resistant, fast-switching behavior of sliding ferroelectric devices.
Limitations and open questions
Several limitations are acknowledged or evident. The full long-time dynamics of the largest (2.4°) structure was not explicitly resolved because of the computational cost of MLMD on 10,038 atoms; its oscillation period in the pinned regime is only expected to reach hundreds of picoseconds. The pinning threshold is inferred from a crossover in smaller twist-angle structures rather than directly demonstrated at 2.4°, and the linear scaling of the vacancy-induced barrier with concentration is stated as an expectation in the dilute limit rather than derived. The simulations are performed on freestanding bilayers; the authors argue qualitatively that substrates, boundaries, and other extrinsic perturbations should further suppress drift, but these effects are not modeled. Open questions include the quantitative dependence of the sliding velocity and pinning threshold on temperature, the interplay between vacancy pinning and field-driven switching dynamics, and whether the same DW-mediated pathway governs polarization reversal in untwisted sliding ferroelectrics where DWs must first be nucleated.
Conclusion
Using a high-accuracy equivariant machine-learning potential, this work demonstrates that interlayer sliding in ferroelectric MoS2 moiré superlattices is governed by a domain-wall-mediated collective reconstruction pathway with an effectively vanishing barrier, rather than by rigid layer translation. Thermally driven sliding at ~1 m/s at 300 K, its reduction to bounded oscillations by ~0.1% sulfur vacancies, and the persistence of both behaviors across a broad range of twist angles collectively revise the microscopic picture of sliding dynamics. The results connect the superlubric DW physics of sliding ferroelectrics with the phason and soliton physics of moiré superlattices, and identify defect density — not twist angle — as the key parameter controlling whether moiré textures slide or remain pinned.