Sliding Crystal Phenomena

• Sliding crystal is a phenomenon where ordered states (charge, spin, or layered structures) move collectively under external drives through elastic, plastic, or solitonic mechanisms.
• Experiments and simulations reveal that commensurability, substrate strength, and temperature govern depinning thresholds and transition between pinned and moving phases.
• These sliding systems underpin advances in electronic transport, superconductivity, and lubrication by linking material microstructure to nonlinear dynamic responses.

“Sliding crystal” denotes a class of phenomena in which a crystalline, charge-ordered, spin-ordered, or layer-registered state moves collectively under a drive, shear, or pressure. In the literature represented here, the term is used in several distinct but related senses: rigid or defect-mediated translation of generalized Wigner crystals on moiré substrates, quantized motion of crystalline lubricants via soliton transport, gyrotropic flow of skyrmion crystals, depinning of colloidal monolayers, and interlayer registry changes in van der Waals solids that themselves generate ferroelectric, charge-density-wave, or superconducting responses (Reichhardt et al., 2024, Vigentini et al., 2014, Xie et al., 2023, Mandelli et al., 2015, Zhou et al., 2024, Liu et al., 2 Aug 2025). A common thread is the competition among elasticity, commensurability, disorder or corrugation, and collective coordinates, which determines whether the crystal remains pinned, slides as an ordered solid, or moves through solitons, anti-kinks, fluids, or other defect-dominated channels.

1. Definitions and principal usages

In charge-ordered moiré systems, a sliding crystal is a generalized Wigner crystal on a two-dimensional hexagonal periodic substrate that loses pinning and moves collectively as a solid or through defects under a dc drive; the relevant control parameters are filling factor $\nu=N/N_p$, substrate strength $F_p$, drive $F_D$, and temperature (Reichhardt et al., 2024). In tribological solid-state models, the same expression can mean a rigid crystal sliding over a thin solid crystalline film, where the lubricant crystal acquires a geometry-controlled mean velocity through the motion of soliton or antisoliton lines (Vigentini et al., 2014). In chiral magnets, the skyrmion crystal is treated as a sliding density wave with a collective displacement field and a gyrotropic transverse response set by the skyrmion number (Xie et al., 2023). In vdW ferroics and superconductors, “sliding” can instead refer to lateral interlayer registry changes: CuInP$_2$S$_6$ undergoes a pressure-driven interlayer-sliding-mediated phase transition, and bulk 3R-NbSe$_2$ realizes interlayer sliding that suppresses interlayer coupling and stabilizes Ising-type superconductivity together with an unconventional CDW state (Zhou et al., 2024, Liu et al., 2 Aug 2025).

A recurring misconception is that a sliding crystal must translate as a perfectly rigid lattice. The cited literature shows a broader taxonomy. Sliding may be elastic, as in a moving crystal that preserves topology; plastic, as in moving fluids; solitonic, as in anti-kink or antisoliton flow; gyrotropic, as in skyrmion crystals; or purely interlayer, where the relevant “crystal” coordinate is stacking registry rather than center-of-mass translation (Reichhardt et al., 2024, Xie et al., 2023, Miao et al., 2023). This suggests that “sliding crystal” is best treated as a family of driven ordered states rather than a single dynamical phase.

2. Generic mechanisms and theoretical descriptions

Representative descriptions emphasize collective coordinates and stress redistribution. For generalized Wigner crystals in moiré systems, the overdamped dynamics is

$$\eta \frac{d {\bf R}_i}{dt} = -\sum_{j\neq i}^{N} \nabla V(R_{ij}) + {\bf F}^s_i + {\bf F}_D + {\bf F}^T,$$

with long-range Coulomb interactions, a hexagonal periodic substrate, dc drive, and thermal Langevin noise; the central transport observable is the average velocity $\langle V\rangle(F_D)$, interpreted as an I–V curve, with $d\langle V\rangle/dF_D$ as differential conductivity (Reichhardt et al., 2024). For skyrmion crystals, the collective dynamics is cast in Thiele form,

$$\mathbf{G}\times(\mathbf{v}_s-\mathbf{v}_d) + \mathbf{D}(\beta\mathbf{v}_s-\alpha\mathbf{v}_d) + \mathbf{F} = 0,$$

so pinning, elasticity, and the gyrocoupling $F_p$0 jointly determine longitudinal and transverse sliding (Xie et al., 2023). For Berry-phase dynamics of sliding electron crystals, the relevant variables are the center-of-mass position $F_p$1 and momentum $F_p$2, with effective semiclassical equations

$F_p$3

so the sliding crystal acquires an anomalous transverse velocity governed by a Berry curvature in $F_p$4-space (Zeng et al., 2024).

A different but structurally analogous formulation appears in metallic glasses, where no glide planes or dislocations exist. There the sliding object is a planar layer with a homogeneous distribution $F_p$5 of local critical stresses, and the macroscopic athermal threshold is obtained from

$F_p$6

with the instability condition $F_p$7 yielding the threshold of athermal sliding (Lazarev et al., 2011). Across these settings, the same formal ingredients recur: a collective coordinate, an elastic or interaction energy, a periodic or random pinning landscape, and a nontrivial rule for how local motion redistributes stress or phase.

3. Electronic sliding crystals

In moiré generalized Wigner systems, sliding is strongly filling dependent. Commensurate fillings $F_p$8, $F_p$9, and $F_D$0 are strongly pinned, with $F_D$1 for $F_D$2 and $F_D$3; at $F_D$4, depinning is elastic with $F_D$5 and $F_D$6, while near $F_D$7 hole doping produces a two-step process in which anti-kinks first slide at $F_D$8 and the full crystal or a moving fluid appears only near $F_D$9. At $_2$0, the pinned honeycomb lattice depins discontinuously into a moving hexagonal “floating solid,” and nearby incommensurate states can show 2D zig-zag anti-kink flow. Finite temperature lowers the effective depinning or melting scale at commensurate fillings and enhances creep in incommensurate states (Reichhardt et al., 2024).

Disorder and magnetic field add a distinct transverse-response problem. For a sliding Wigner crystal with quenched disorder, the Hall angle is not fixed at the intrinsic value $_2$1; instead it is near zero at depinning, increases approximately linearly with drive over a broad regime, and saturates close to the disorder-free value only at high drives. The mechanism is a velocity-dependent side jump when electrons traverse pinning sites, opposite to the Hall direction and decreasing in magnitude as the drive increases (Reichhardt et al., 2020). In AB-stacked bilayer graphene, transport signatures consistent with a sliding Wigner crystal were reported in a low-density phase near an ultra-low-density van Hove singularity: in phase II, low-frequency noise is enhanced by several orders of magnitude, broad noise bulges appear at a characteristic $_2$2, and the extracted $_2$3 increases approximately linearly with $_2$4, matching the expectation $_2$5 for a sliding electron crystal (Seiler et al., 2024).

Electron crystals on superfluid helium supply a finite-size realization of the same depinning logic. In a 10 $_2$6m-wide microchannel, the threshold electric field for decoupling of a finite Wigner crystal from its ripplonic dimple lattice significantly decreases when the crystal length becomes shorter than 25 $_2$7m. The effect is described by

$_2$8

with $_2$9 and $_6$0, and is attributed to radiative loss of resonantly excited ripplons from a finite crystal (Lin et al., 2018). In a more recent Berry-phase formulation of sliding anomalous Hall crystals, acceleration modifies both center-of-mass and internal currents, so the net Hall conductance is, in general, not quantized; this explicitly departs from a rigid “Chern crystal” picture and ties sliding transport to quantum geometry and Galilean non-invariance (Zeng et al., 2024).

4. Colloidal, atomic, and lubricated interfaces

The cleanest realization of a structural superlubric–pinned transition is the incommensurate colloidal monolayer over a laser-induced triangular optical lattice. For mutually commensurate lattices, the monolayer is always pinned by static friction, whereas in the incommensurate case the simulations show a sharp transition from a superlubric state to a pinned state as the corrugation strength $_6$1 is increased. The transition is the 2D analogue of the Aubry transition, but unlike the 1D case it is first order: $_6$2 jumps upward, $_6$3 jumps downward, static friction appears abruptly, and the fraction of colloids in repulsive regions above the saddle-point energy collapses (Mandelli et al., 2015). Earlier simulations of sliding colloidal monolayers had already established the dynamical distinction between free motion of solitons and antisolitons in hard incommensurate crystals and soliton–antisoliton pair nucleation at the large static friction threshold $_6$4 when the two lattices are commensurate and pinned (1208.09050).

In crystalline lubrication, the moving object is not the substrate or the sliders alone but the solid lubricant trapped between them. In a realistic three-dimensional crystal–lubricant–crystal geometry, the lubricant center-of-mass velocity locks to the geometric ratio

$_6$5

because the flux of particles is controlled by soliton lines generated by lattice mismatch. The same mechanism predicts forward motion for $_6$6 and backward motion for $_6$7, and the quantized plateau persists over finite ranges of speed, load, temperature, and lubricant thickness before dynamical depinning occurs (Vigentini et al., 2014).

At the nanoscale, the effective rigidity of the sliding crystal becomes decisive. For Au(111) on graphite, a monolayer island is soft enough to deform into near commensurability and is therefore easily pinned, whereas thicker clusters remain incommensurate, develop a solitonic pattern, and exhibit much lower static friction. For fixed contact area $_6$8, going from a monolayer to a bilayer reduces the static friction per contact atom by almost a factor of 5. The critical contact size for accommodating the soliton pattern is $_6$9 atoms for a monolayer but $_2$0 atoms for a thick cluster, so thickness promotes lubricity by increasing effective rigidity and reducing interdigitation with the substrate (Guerra et al., 2016).

5. Spin, ferroic, and superconducting forms

For spin textures, the skyrmion crystal and the helix phase are both treated as sliding density waves, but topology makes their dynamics sharply different. In the flow regime at large current density, both obey $_2$1, as in classical CDWs, yet impurity pinning is much weaker in the skyrmion crystal: $_2$2 Moreover, the velocity correction in the skyrmion crystal is mostly in the transverse direction to the current because of the gyrotropic term, whereas the helix behaves as a topologically trivial density wave with much stronger longitudinal pinning (Xie et al., 2023).

In vdW ferroics, sliding can be the phase-transition coordinate itself. Under hydrostatic pressure, CuInP$_2$3S$_2$4 first shows a tendency towards a high polarization state and then undergoes an interlayer-sliding-mediated phase transition from monoclinic Cc to trigonal $_2$5. The structural change corresponds to a lateral shift of $_2$6, converting sulfur stacking from ABC-type to AB-type. Along this path, the displacive-instable Cu ion acts as a pivot point that regulates the interlayer interaction, while the room-temperature transition occurs near 4 GPa and the 0 K enthalpy crossing between Cc and P31c appears near 5.8 GPa in DFT (Zhou et al., 2024).

A direct electrical realization of sliding ferroelectricity was reported in the amphidynamic crystal (15-Crown-5)Cd$_2$7Cl$_2$8. Below $_2$9 K, freezing of the crown-ether rotators generates a geometric dipole in each layer, and DFT decomposes the resulting bulk polarization into a geometric component $$\eta \frac{d {\bf R}_i}{dt} = -\sum_{j\neq i}^{N} \nabla V(R_{ij}) + {\bf F}^s_i + {\bf F}_D + {\bf F}^T,$$0 and a sliding component $$\eta \frac{d {\bf R}_i}{dt} = -\sum_{j\neq i}^{N} \nabla V(R_{ij}) + {\bf F}^s_i + {\bf F}_D + {\bf F}^T,$$1, yielding $$\eta \frac{d {\bf R}_i}{dt} = -\sum_{j\neq i}^{N} \nabla V(R_{ij}) + {\bf F}^s_i + {\bf F}_D + {\bf F}^T,$$2. The sliding contribution is therefore about $$\eta \frac{d {\bf R}_i}{dt} = -\sum_{j\neq i}^{N} \nabla V(R_{ij}) + {\bf F}^s_i + {\bf F}_D + {\bf F}^T,$$3 of the total and can be directly accessed because the material is a large-band-gap insulator that supports macroscopic P–E hysteresis (Miao et al., 2023).

Interlayer sliding can also stabilize two-dimensional superconducting phenomena in a bulk crystal. In sliding 3R-NbSe$$\eta \frac{d {\bf R}_i}{dt} = -\sum_{j\neq i}^{N} \nabla V(R_{ij}) + {\bf F}^s_i + {\bf F}_D + {\bf F}^T,$$4, deliberately engineered interlayer shifts break [001] mirror symmetry and suppress interlayer coupling, yielding Ising-type superconductivity coexisting with an unconventional CDW state akin to monolayer 2H-NbSe$$\eta \frac{d {\bf R}_i}{dt} = -\sum_{j\neq i}^{N} \nabla V(R_{ij}) + {\bf F}^s_i + {\bf F}_D + {\bf F}^T,$$5. The in-plane upper critical field follows a 2D GL form with $$\eta \frac{d {\bf R}_i}{dt} = -\sum_{j\neq i}^{N} \nabla V(R_{ij}) + {\bf F}^s_i + {\bf F}_D + {\bf F}^T,$$6 T and an effective superconducting thickness $$\eta \frac{d {\bf R}_i}{dt} = -\sum_{j\neq i}^{N} \nabla V(R_{ij}) + {\bf F}^s_i + {\bf F}_D + {\bf F}^T,$$7 nm, while thin devices show BKT behavior with $$\eta \frac{d {\bf R}_i}{dt} = -\sum_{j\neq i}^{N} \nabla V(R_{ij}) + {\bf F}^s_i + {\bf F}_D + {\bf F}^T,$$8 at $$\eta \frac{d {\bf R}_i}{dt} = -\sum_{j\neq i}^{N} \nabla V(R_{ij}) + {\bf F}^s_i + {\bf F}_D + {\bf F}^T,$$9 K. The low-temperature suppression of $\langle V\rangle(F_D)$0 is attributed to competition between Ising and Rashba SOC, and in-plane magnetotransport exhibits a robust two-fold superconducting anisotropy (Liu et al., 2 Aug 2025).

6. Microstructural and non-rigid meanings

Some usages shift the emphasis from whole-crystal translation to interfacial or internal sliding. In high-temperature creep of Type 316 stainless steel, grain-boundary sliding is modeled with interface elements and special triple-line constraints within a crystal-plasticity finite-element framework. The calibrated 39-grain aggregate reproduces a grain-boundary-sliding fraction $\langle V\rangle(F_D)$1 at 625 $\langle V\rangle(F_D)$2C and 220 MPa with $\langle V\rangle(F_D)$3 mm/s and $\langle V\rangle(F_D)$4; even under these modest sliding levels, transverse boundaries can carry normal stresses of the order of 100–180 MPa when neighboring grains are plastically harder, and boundaries normal to the applied load still slide, albeit at rates 1–3 orders of magnitude lower than inclined boundaries (Petkov et al., 2021). Here the “sliding crystal” is a polycrystal whose interfaces, rather than its lattice as a whole, supply the relevant sliding degree of freedom.

In metallic glass, the same phrase denotes an amorphous sliding layer with a distribution of local critical stresses rather than a periodic lattice. The exactly solvable model recovers the hierarchy $\langle V\rangle(F_D)$5, $\langle V\rangle(F_D)$6, and $\langle V\rangle(F_D)$7, and predicts a sliding activation volume obeying $\langle V\rangle(F_D)$8 with $\langle V\rangle(F_D)$9. The proposed interpretation is that intercluster boundaries of a polycluster metallic glass are natural sliding layers of the modeled type (Lazarev et al., 2011).

Tribological loading of a copper bicrystal reveals yet another meaning: the crystal under a moving contact does not merely translate but rotates kinematically. EBSD performed directly on wear tracks shows lattice rotations predominantly around the transverse direction, approximately up to 35$d\langle V\rangle/dF_D$0 for most indexed points and roughly up to 90$d\langle V\rangle/dF_D$1 for a smaller population, with a superimposed rotation around $d\langle V\rangle/dF_D$2SD; reversing the sliding direction reverses the sense of rotation while preserving its principal character (Haug et al., 2021). In a still more localized usage, “sliding” may refer to electronic redistribution rather than motion of the lattice at all: in a Cu–O–Cu–O cluster model for La$d\langle V\rangle/dF_D$3Sr$d\langle V\rangle/dF_D$4CuO$d\langle V\rangle/dF_D$5, a displacement of the nearest-neighbor La(Sr)O plane lattice atoms by as little as $d\langle V\rangle/dF_D$6 \AA\ can trigger electron pairs’ concerted sliding over distances about 2 \AA, through avoided crossings between electronic states (1904.02551).

Taken together, these works show that sliding crystal physics is not defined by a unique microscopic carrier. It may be carried by whole lattices, domain walls, kinks, antisolitons, skyrmion textures, interlayer registries, grain boundaries, or even paired electronic charge distributions. The unifying content is the driven motion of an ordered or partially ordered structure through a pinning landscape, with depinning thresholds, symmetry constraints, and nonlinear transport or mechanical signatures that encode the nature of the sliding state (Reichhardt et al., 2024, Vigentini et al., 2014, Zeng et al., 2024).