🔬 condensed matter

Electronic procrystalline state in moire structures

This study reports the first experimental observation of an electronic procrystalline state in a NiTe2/NbSe2 moire superstructure, characterized by long-range periodic charge modulation with embedded short-range irregular orders that coexist with superconductivity and can be precisely tuned by NiTe2 thickness.

Original authors: Hui Guo, Zihao Huang, Yixuan Gao, Haowei Chen, Hao Zhang, Qian Fang, Yuhan Ye, Xianghe Han, Zhongyi Cao, Jiayi Wang, Runnong Zhou, Zhilin Li, Chengmin Shen, Haitao Yang, Hui Chen, Wang Yao, Ziqiang Wa

Published 2026-01-15

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CC BY 4.0

Original authors: Hui Guo, Zihao Huang, Yixuan Gao, Haowei Chen, Hao Zhang, Qian Fang, Yuhan Ye, Xianghe Han, Zhongyi Cao, Jiayi Wang, Runnong Zhou, Zhilin Li, Chengmin Shen, Haitao Yang, Hui Chen, Wang Yao, Ziqiang Wang, Hong-Jun Gao

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a world made of tiny, dancing atoms. Usually, these atoms line up in perfect, repeating rows, like soldiers in a parade or tiles on a bathroom floor. This is a crystal. Sometimes, they are completely messy, like a pile of sand; this is an amorphous material.

Recently, scientists discovered a third, weird option called a procrystal. Think of a procrystal like a perfectly organized apartment building (the long-range order), but inside every single apartment, the furniture is thrown around randomly (the short-range disorder). The building has a strict address system, but the rooms inside are chaotic.

Until now, scientists had only seen this "apartment building with messy rooms" in the physical arrangement of atoms. They wondered: Do electrons (the tiny particles that carry electricity) do the same thing?

This paper says: Yes, they do. The researchers found a new state of matter they call an Electronic Procrystalline (EPC) state.

Here is how they found it and what it looks like, using simple analogies:

1. The Setup: A Mismatched Dance Floor

The scientists created a special "sandwich" using two different metals:

The Floor: A superconductor called NbSe2 (which lets electricity flow without resistance).
The Dancers: A single, ultra-thin layer of NiTe2 placed on top.

Because the atoms in the top layer and the bottom layer are slightly different sizes, they don't line up perfectly. Instead, they create a giant, repeating pattern called a moiré pattern. Imagine holding two window screens with slightly different grid sizes over each other; you see a new, larger pattern of light and dark spots appear. That is the moiré pattern.

2. The Discovery: The "Bubbly" Neighborhood

When they looked closely at this pattern with a super-powerful microscope (STM), they saw something strange:

The Neighborhood (Long-Range Order): The electrons formed a giant, repeating map of "bubbles" (bright spots) and "valleys" (dark spots) across the whole surface. This is the "apartment building" part—it's perfectly organized and repeats over and over.
The Rooms (Short-Range Disorder): Inside each of those "bubbles," the electrons weren't just sitting still. They were forming tiny, messy, short-lived patterns. It's like looking inside one of those bubbles and seeing a mini-mess of furniture that looks a bit like a hexagon (six-sided shape), but it's not perfect. It's "quasi-ordered."

This combination—a perfectly organized map of giant bubbles, where each bubble contains its own unique, messy internal pattern—is the Electronic Procrystalline state.

3. The Magic Trick: Superconductivity

Even cooler? This messy electronic state doesn't stop the material from being a superconductor. Usually, when things get messy, electricity struggles. But here, the electrons managed to be both superconducting (flowing perfectly) and procrystalline (messy inside) at the same time.

It's like a highway where the cars are driving in perfect lanes (superconductivity), but inside every single car, the passengers are playing a chaotic game of musical chairs (the procrystalline state).

4. The Control Knob: Changing the Thickness

The researchers found they could control this "messiness" by changing how thick the top layer of NiTe2 was:

1 Layer (Monolayer): The messy "procrystalline" state is strong and clear.
2 Layers: The messiness inside the bubbles gets weaker and disappears, though the big "bubble" map remains.
3 or 4 Layers: The whole effect fades away.

They even built a tiny "junction" where the 1-layer part (messy) meets the 2-layer part (clean). At the boundary where they meet, a special "edge state" appeared, like a ripple forming exactly where the two different worlds touch.

Why This Matters

This discovery is important because it proves that electrons can form this unique "ordered chaos" state. Before this, we only knew about this in the physical atoms. Now we know electrons can do it too.

The paper suggests that by using these "mismatched" metal layers (moiré structures), scientists can now build new types of quantum materials where they can tune how "messy" or "ordered" the electrons are, just by changing the thickness of the layers. It opens a door to understanding a whole new class of quantum behaviors that we couldn't see in simpler materials like graphene.

In short: The scientists found a way to make electrons dance in a giant, perfect pattern, where every step of the dance has its own unique, messy improvisation, and they can turn this "messy dance" on or off by adding more layers to their material.

Technical Summary: Electronic Procrystalline State in Moiré Structures

Problem Statement
Solid-state materials exhibit a spectrum of atomic structural orders, ranging from crystalline to amorphous, which dictate their physical properties. Recently, "procrystals"—solids featuring a long-range ordered lattice framework tiled with disordered atomic or molecular structures—have emerged as a distinct category of matter. While the structural concept of a procrystal is established, its electronic analogue, the electronic procrystalline (EPC) state, has not been experimentally observed. The EPC state is theoretically defined as a quantum electronic phase where irregularly short-range-ordered electronic states act as random building blocks within a long-range periodic lattice, breaking the translational symmetry of the underlying crystal and precluding a standard Bloch description. The challenge lies in realizing and characterizing this hybrid state of long-range order and short-range disorder in a controllable quantum system.

Methodology
The authors constructed a moiré superstructure by epitaxially growing a monolayer of metallic NiTe₂ onto a superconducting NbSe₂ substrate. This system utilizes the incommensurate lattice wavevectors between the two metallic transition-metal dichalcogenides (TMDs) to generate a moiré potential.

Sample Preparation: High-quality NbSe₂ single crystals were cleaved and annealed under ultra-high vacuum (UHV). Monolayer, bilayer, and trilayer NiTe₂ films were grown via molecular beam epitaxy (MBE) using electron-beam evaporation of Ni and atomic Te.
Characterization: The study employed low-energy electron diffraction (LEED) to confirm large-scale ordering and scanning tunneling microscopy/spectroscopy (STM/STS) at ultra-low temperatures (down to 0.4 K) to resolve atomic structures and local density of states (LDOS).
Analysis Techniques: The authors utilized fast Fourier transform (FFT) analysis to identify wavevectors, two-dimensional lock-in techniques to extract amplitude and phase of charge modulations, and density functional theory (DFT) calculations to model strain, charge transfer, and electronic susceptibility.

Key Contributions and Results

Observation of the EPC State:
The study reports the first experimental observation of an EPC state in the NiTe₂/NbSe₂ moiré system. The system exhibits a long-range periodic charge modulation at the moiré scale, characterized by three inequivalent local regions within the moiré unit cell: bright (ABHollow), dark (AA), and intermediate (ABSe).
Short-Range Irregular Orders:
Inside the moiré unit cells, specifically within the ABHollow regions, the authors identified short-range charge orders with a quasi-period of approximately $\sqrt{3} \times \sqrt{3}$ relative to the pristine NiTe₂ lattice. Crucially, these short-range orders are irregular:
- They lack long-range phase coherence.
- They exhibit quasi-sixfold rotational symmetry but vary in rotation angle and periodicity between different moiré cells.
- This combination of a long-range moiré lattice and disordered short-range internal structures constitutes the EPC state.
Coexistence with Superconductivity:
The EPC state was observed to coexist with proximity-induced superconductivity in the monolayer NiTe₂. The superconducting gap size and coherence peak height showed strong spatial modulation across the ABHollow regions. The inhomogeneity of the superconducting state, including the formation of a "paired electronic procrystalline state," reinforces the disordered nature of the electronic environment.
Thickness-Dependent Modulation:
The emergence of the EPC state and the specific $\sqrt{3} \times \sqrt{3}$ short-range order are highly sensitive to the thickness of the NiTe₂ film:
- Monolayer (1L): Exhibits the full EPC state with distinct short-range $\sqrt{3} \times \sqrt{3}$ charge orders.
- Bilayer (2L): The moiré modulation persists, but the short-range charge order is suppressed. The electronic state remains disordered but lacks the specific quasi-periodic order.
- Trilayer (3L) and Four-layer (4L): The charge modulation is further suppressed and eventually disappears.
- Junctions: A lateral heterostructure between 1L and 2L regions revealed a distinct charge edge state at the interface (~45 meV), which is absent in 2L-3L junctions, highlighting the tunability of the phase.
Mechanism:
DFT calculations suggest that the short-range charge order originates from enhanced electron correlations driven by a cooperative effect of moiré-confined strain, charge transfer, and electron density localization within the ABHollow regions. The strain in the monolayer shifts the Fermi surface nesting vector, promoting the $\sqrt{3} \times \sqrt{3}$ order, an effect that diminishes in thicker layers due to reduced strain and localization.

Significance
The paper claims to uncover a new class of correlated electronic states that can exist in moiré systems formed by metallic layers with pronounced carrier density. This work extends the understanding of emergent quantum phases beyond the extensively studied twisted semimetallic graphene and semiconducting TMDs systems, where low-energy states are typically described by translation-invariant Hamiltonians.

The discovery of the EPC state demonstrates that moiré superlattices with incommensurate lattice wavevectors can host electronic phases where conventional periodic Hamiltonian models fail due to the breakdown of translational symmetry. The authors posit that this platform offers a unique opportunity to explore the interplay between exotic procrystalline charge orders and other correlated phenomena, such as superconductivity, spin density waves, and pair density waves, providing a new avenue for tuning novel quantum phases through structural parameters like film thickness.