- The paper demonstrates that 1D moiré potentials explicitly break the threefold symmetry of CDW order in misfit van der Waals heterostructures.
- It employs advanced STM/STS, nc-AFM, DFT, and REMD analyses to reveal nanometer-scale anisotropic coherence lengths and nonlinear shifts in CDW wave vectors.
- Superconductivity remains robust and isotropic with BCS s-wave behavior, contrasting sharply with the deformable and tunable CDW order under symmetry breaking.
Moiré-Induced Symmetry Breaking of Charge Order in van der Waals Heterostructures
Introduction and Context
Misfit layered chalcogenides, which intrinsically stack monolayers with distinct lattice symmetries, represent a unique natural platform for examining how explicit symmetry breaking shapes collective electronic phases such as charge density wave (CDW) order and superconductivity. In these systems, the incommensurability of the components—typically square rocksalt monochalcogenide bilayers (MS, with M = Pb, Sn) and hexagonal transition-metal dichalcogenide monolayers (1H-TaS₂)—generates a one-dimensional (1D) moiré superlattice at the interface. This symmetry mismatch fundamentally alters electronic ground states by lowering rotational symmetry and introducing spatially anisotropic potentials. The paper addresses the response of collective electronic orders, specifically CDW and superconductivity, in misfit compounds (PbS)₁.₁₃TaS₂ and (SnS)₁.₁₅TaS₂ to such moiré-induced symmetry breaking.
Experimental Methodology
High-quality single crystals of the target misfit compounds were synthesized by chemical vapor transport. Scanning tunneling microscopy/spectroscopy (STM/STS) and non-contact atomic force microscopy (nc-AFM) provided high-resolution real and reciprocal space access to the local structure and electronic order at cryogenic temperatures (down to 0.34 K). The electronic band structure and collective electronic instability landscape were analyzed through DFT, Wannier downfolding approaches, and replica-exchange molecular dynamics (REMD) for an 18×18 supercell, with particular emphasis on the interplay of interlayer charge transfer and a spatially modulated moiré potential.
Moiré-Induced Breakdown of CDW Symmetry
The presence of a rocksalt MS (001) layer epitaxially aligned with the hexagonal 1H-TaS₂ produces a commensurate registry along one axis (y), while introducing 1D incommensurability along the orthogonal direction (x), driving the formation of a long-wavelength moiré potential. STM topographies of TaS₂ reveal a 2D incommensurate superlattice, in stark contrast to the nearly commensurate, threefold symmetric CDW typically reported for both bulk and isolated monolayer 1H-TaS₂.
Fourier analysis of atomically-resolved topographies demonstrates several key features:
- The usual threefold (C₃) rotational symmetry of the CDW is explicitly lifted, with the three primary ordering wave vectors (Q_B) displaying distinct intensities and coherence lengths.
- The CDW is incommensurate, with domain sizes at the nanometer scale and anisotropic coherence lengths (e.g., L₁ ≈ 45 Å; L₂,₃ ≈ 13 Å).
- The maximum Fourier intensity positions shift to rational fractions of the principal Bragg vector (Q_B/2 for one direction, 3Q_B/8 and 5Q_B/8 for the others), evidencing strong nonlinear and anharmonic coupling between the intrinsic CDW instability and the uniaxial moiré potential.
These deformations are not compatible with simple locking scenarios but arise via the explicit symmetry-breaking field imposed by the moiré interface.
Microscopic Modeling: Charge Transfer and Moiré Potential
Model relaxations for pristine, undoped 1H-TaS₂ predict the expected commensurate 3×3 CDW. However, experimentally the CDW is not only incommensurate but strongly deformed. Simulations with up to 0.2e per Ta unit cell electron doping—commensurate with ARPES and STS observations—shift the CDW instability away from the typical Q_B, reduce coherence lengths, and generate a variety of incommensurate or near-2×2-like states. The introduction of a 1D moiré potential, modeled as a periodically modulated energy term, further lifts the degeneracy among the Q_B directions and stabilizes the anisotropically deformed CDW observed in experiment.
The results conclusively show that the CDW’s internal degrees of freedom (wave vector magnitude, coherence length, and amplitude) are highly susceptible to external symmetry-breaking and charge transfer. The CDW order remains robust in its favored ordering directions, but is intrinsically “soft” along other collective variables, being readily shifted by small symmetry-breaking perturbations.
Superconductivity: Robustness Against Moiré Symmetry Breaking
In contrast to the pronounced susceptibility of the CDW, superconductivity in 1H-TaS₂ appears largely insensitive to the symmetry-breaking moiré potential. High-resolution STS reveals a fully isotropic, single-gap spectrum well-captured by BCS s-wave theory, with gap values Δ_TaS₂ = 0.38 ± 0.03 meV ((PbS)₁.₁₃TaS₂) and 0.33 ± 0.03 meV ((SnS)₁.₁₅TaS₂). Critical temperatures are in the range 2.7–3 K, yielding gap ratios 2Δ/k_B T_c < 3.53 (the weak-coupling BCS limit). Induced gaps of commensurately smaller size appear uniformly in the monochalcogenide layers, consistent with proximity-coupled superconductivity at a structurally and electronically transparent interface.
No signatures of unconventional or multi-gap superconducting order are detected. The observed isotropy and homogeneity, including the mutual response to out-of-plane magnetic fields, imply the superconducting instability is decoupled from both the moiré and incommensurability-driven CDW degeneracy lifting.
Implications and Perspective
This study provides strong evidence for a hierarchy of susceptibility among correlated electronic ground states in van der Waals heterostructures. While superconductivity is robust to moiré-induced symmetry breaking, CDW order is highly deformable, even at the level of microscopic domains and wavevector selection. These findings challenge prior assumptions that collective orders in 2D materials track uniformly under external symmetry reduction and demonstrate that targeted symmetry engineering—for instance, controlled stacking of heterosymmetric lattices—offers a unique route for the manipulation of broken symmetry phases without strongly perturbing the underlying electronic band structure.
Looking forward, the demonstrated sensitivity of CDW order to moiré potentials opens avenues for programmable control of charge-ordered domains, wave vector selection, and the examination of actively tunable quantum phase competition in 2D materials. The relative insensitivity of s-wave superconductivity, even in the highly anisotropic and incommensurate limit, raises further questions about the interplay between lattice symmetry, electronic topology, and emergent collective phenomena in engineered quantum materials.
Conclusion
The explicit symmetry breaking induced by one-dimensional moiré potentials in misfit van der Waals heterostructures—realized in (PbS)₁.₁₃TaS₂ and (SnS)₁.₁₅TaS₂—was shown to fragment and anisotropically deform CDW order without substantially altering conventional s-wave superconductivity. The emergent picture is one where CDW order is strongly nonlinear and soft against symmetry-breaking perturbations, while the superconducting order remains robust. These findings establish symmetry-mismatched stacking as a tool for manipulating correlated phases in 2D materials and suggest rich prospects for further exploration and control of interaction-driven orders in atomically layered systems (2603.05759).
