Modulation of charge density waves in a twisted vortex moire superlattice

This study demonstrates that a twisted vortex moire superlattice formed between monolayer VTe2 and NbSe2 enables nanoscale manipulation of charge density waves through strain-induced reconstruction of the CDW landscape, creating inequivalent local phases that compete with proximity-induced superconductivity.

The Gist

Imagine you have two layers of honeycomb-patterned wallpaper. One layer is made of a material called VTe2, and the other is a superconductor called NbSe2. Normally, if you stack these two perfectly aligned, they just sit there. But in this experiment, the scientists twisted the top layer slightly (by about 1.4 degrees) and let them settle.

Because the patterns are almost, but not quite, the same size, they don't just sit on top of each other like rigid tiles. Instead, they "relax" and stretch to fit together, creating a giant, swirling pattern on the surface called a vortex moiré superlattice. Think of it like swirling two different colored sands together; instead of a uniform mix, you get distinct swirls and eddies where the grains bunch up or spread out.

Here is what the scientists discovered about this swirling landscape:

1. The "Traffic Jam" of Electrons (Charge Density Waves)

In the top layer (VTe2), electrons naturally like to form a regular, repeating pattern, almost like cars getting stuck in a synchronized traffic jam. This is called a Charge Density Wave (CDW). Usually, this jam stretches across the whole material in a straight, orderly line.

However, the swirling "vortex" pattern created by the twist acts like a bumpy, uneven road.

• The Result: The orderly traffic jam breaks apart. In some parts of the swirl (the "compressed" areas where the atoms are squeezed together), the electrons form a tight, short-lived cluster. In the very center of the swirl (the "vortex core"), where the atoms are stretched apart, the traffic jam completely dissolves, and the electrons flow freely.
• The Analogy: Imagine a marching band. Usually, they march in a perfect, long line. But if the ground suddenly has deep potholes in some spots and tight squeezes in others, the band breaks formation. In the tight spots, they huddle together; in the potholes, they scatter.

2. The Room-Temperature Surprise

Usually, these electron "traffic jams" (CDWs) fall apart and disappear when things get warm. But the scientists found something special in the "squeezed" parts of the swirl. Even at room temperature (which is very hot for these tiny quantum materials), the electrons still managed to hold onto a short-range, huddled pattern. The local squeezing of the atoms acted like a strong glue, keeping the order alive even when it was supposed to melt away.

3. The Tug-of-War with Superconductivity

The bottom layer (NbSe2) is a superconductor, meaning electricity flows through it with zero resistance. When you put the top layer on it, this superconductivity "leaks" up into the top layer.

The scientists found a fascinating tug-of-war happening inside the swirl:

• Where the electron traffic jam (CDW) is strong and huddled (in the compressed areas), the superconductivity gets weak.
• Where the traffic jam dissolves (in the stretched vortex core), the superconductivity gets stronger.

It's like a seesaw: when one side goes up, the other goes down. The swirling pattern of the moiré superlattice creates a map where superconductivity and electron ordering constantly battle for dominance, changing from spot to spot within a single tiny unit.

The Big Picture

The main takeaway is that by twisting these two materials just right, the scientists created a landscape where the rules of physics change from place to place within a single tiny square. They didn't just change the material globally; they created a "patchwork quilt" of different electronic behaviors right next to each other.

This proves that we can use these twisted, swirling patterns to manually sculpt and control how electrons behave at the nanoscale, turning a uniform material into a complex, customizable playground for quantum states.

Technical Summary

Technical Summary: Modulation of Charge Density Waves in a Twisted Vortex Moiré Superlattice

Problem and Motivation
Twisted van-der-Waals heterostructures have established a paradigm for engineering electronic structures through moiré-band reconstruction, enabling the emergence of correlated phases such as superconductivity and charge ordering. While global band engineering is well-explored, the continuous nanoscale manipulation of globally coherent electronic orders remains largely unexplored. Specifically, it is unclear how reconstructed moiré structures in the small-angle and near-commensurate regimes, which feature continuously varying local environments (strain, stacking, and coupling), can deterministically reshape intertwined collective electronic states like charge density waves (CDW) and superconductivity within a single moiré unit cell.

Methodology
The authors constructed a twisted vortex moiré superlattice by epitaxially growing monolayer 1T-VTe2 on bulk 2H-NbSe2 substrates with a small twist angle (1.4°) using molecular beam epitaxy (MBE). The near lattice commensurability between VTe2 (3.55 Å) and NbSe2 (~3.46 Å) in this regime prevents simple rigid moiré modulation, instead inducing substantial lattice relaxation and strain reconstruction.

The study employed a multi-modal approach:

• Structural Characterization: Low-energy electron diffraction (LEED) confirmed crystallinity, while scanning tunneling microscopy (STM) and spectroscopy (STS) were used to visualize the real-space vortex textures and atomic lattice reconstruction.
• Electronic Probing: Spatially resolved STS and dI/dV mapping were performed at temperatures ranging from 0.4 K to 300 K to investigate the stability and coherence of CDW and superconducting states.
• Data Analysis: A two-dimensional lock-in technique was utilized to extract amplitude and phase maps of the CDW modulations from STM data.
• Theoretical Modeling: First-principles calculations based on Density Functional Theory (DFT) and deep-learning-based interatomic potentials (DeePMD-kit) were used to simulate the relaxed atomic structures and calculate the strain dependence of CDW stability.

Key Results

1. Formation of Vortex Moiré Superlattices: The system exhibits a vortex-like moiré texture with a periodicity of ~9.8 nm, distinct from conventional rigid moiré patterns. This structure arises from strong lattice relaxation, creating a continuously varying strain field within a single moiré unit cell.
2. Intra-Moiré CDW Reconstruction: The intrinsic long-range 4×4 CDW of monolayer VTe2 (stable below ~190 K) is fragmented into inequivalent local phases within the vortex unit cell:
   • Regions A and B (Distorted Triangular Domains): These regions exhibit enhanced short-range CDW correlations that persist up to room temperature.
   • Region H (Vortex Core): This region shows a strong suppression of CDW order.
   • The CDW periodicity in the surviving regions shifts to a quasi-periodicity of ~3.8 times the lattice constant, deviating from the commensurate 4×4 order.
3. Strain-Driven Mechanism: Statistical analysis of local lattice constants and theoretical strain mapping reveal that the vortex core (Region H) experiences significant tensile strain (3.65 Å lattice constant), while the triangular domains (Regions A and B) experience compressive strain (3.42 Å and ~3.51 Å). First-principles calculations confirm that compressive strain substantially stabilizes the CDW phase, whereas tensile strain suppresses it.
4. Competing Interplay with Superconductivity: The proximity-induced superconductivity from the NbSe2 substrate exhibits an anti-correlated spatial modulation with the CDW. Regions with suppressed CDW (vortex core) display stronger superconducting signatures (higher coherence peaks and gap depth), while CDW-stabilized regions show reduced superconducting spectral weight.

Significance and Claims
The paper establishes that reconstructed vortex moiré superlattices serve as a versatile platform for the deterministic nanoscale manipulation of correlated electronic orders. The authors demonstrate that the continuously varying local strain landscape in these near-commensurate systems can fragment global electronic orders into distinct local phases with different stabilities and coherence lengths. Specifically, the work shows that:

• Local strain can be used to tune the stability of charge order, enabling the survival of short-range CDW correlations at room temperature in specific sub-regions of a single unit cell.
• The interplay between competing orders (CDW and superconductivity) can be spatially reconstructed on the nanoscale, creating a continuously modulated landscape of intertwined electronic phases.

This approach moves beyond conventional global moiré band engineering, offering a method to engineer complex, spatially varying quantum states in low-dimensional materials through structural reconstruction rather than just twist-angle tuning.