🔬 mesoscale physics

Emergent electronic insulating states in a one-dimensional moiré superlattice

This study demonstrates the emergence of moiré-engineered electronic insulating states in one-dimensional armchair carbon nanotube/hexagonal boron nitride heterostructures, revealing that while single-particle effects explain gaps at full and charge neutrality fillings, interaction-driven mechanisms are likely responsible for the insulating behavior observed at half-filling.

Original authors: Jianfeng Bi, Masaki Minamikawa, Ruige Dong, DongJun Kang, Zihan Weng, Shaoqi Sun, Kenji Watanabe, Takashi Taniguchi, Ryosuke Okumura, Huizhen Wu, Naoto Nakatsuji, SeokJae Yoo, Mikito Koshino, Sihan Zh

Published 2026-08-10

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CC BY 4.0

Original authors: Jianfeng Bi, Masaki Minamikawa, Ruige Dong, DongJun Kang, Zihan Weng, Shaoqi Sun, Kenji Watanabe, Takashi Taniguchi, Ryosuke Okumura, Huizhen Wu, Naoto Nakatsuji, SeokJae Yoo, Mikito Koshino, Sihan Zhao

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 the world of electronics as a bustling city made of tiny, flat roads. For a long time, scientists have been building "moiré superlattices" on these flat roads. Think of a moiré pattern like the shimmering, wavy interference you see when you hold two fine mesh screens slightly askew over each other. In the flat, two-dimensional world of materials like graphene, twisting these screens creates a giant, repeating grid of invisible hills and valleys. This grid acts like a master switch, turning the material from a conductor into an insulator or creating exotic quantum states that behave like new kinds of matter. It's a powerful trick, but it's been stuck in two dimensions.

Now, imagine trying to do the same thing on a one-dimensional road, like a single, thin wire or a carbon nanotube. This is much harder. In the flat world, you can twist two sheets to make a pattern. But in the one-dimensional world, the "twist" is usually random and uncontrollable, like trying to align two spinning hula hoops perfectly without a guide. Without a way to control this alignment, scientists couldn't build a reliable "moiré grid" on these thin wires. This left a huge gap in our understanding: could these one-dimensional wires host the same magical, insulating quantum states as their flat cousins, or are they just boring, metallic pipes?

This paper reports a clever solution to that problem. The researchers took a single-walled carbon nanotube—a tiny, hollow cylinder made of carbon atoms—and carefully aligned it with a flat sheet of hexagonal boron nitride (hBN). Think of the nanotube as a rolling pin and the hBN as a flat dough. By rolling the pin at just the right angle, they created a perfect, repeating pattern of interaction along the length of the tube. This is their "lattice-aligned" setup.

When they tested these aligned tubes at very low temperatures, they found something surprising. Even though a single carbon nanotube should naturally act like a perfect metal (allowing electricity to flow freely), these aligned tubes suddenly turned into insulators at specific points. It's as if the road suddenly developed a series of invisible, impenetrable walls that stopped traffic completely. These "insulating states" appeared at three specific spots: when the tube was empty of extra electrons (the charge neutrality point), when it was completely full of a certain type of charge carrier, and when it was half-full. The researchers measured the energy gaps required to break through these walls, finding them to be around 22 to 26 meV at the empty point, and smaller gaps of about 11 to 13 meV at the other points.

To prove that this wasn't just a fluke or a defect in the tube, they ran a control experiment. They took another identical carbon nanotube but placed it on a standard surface without the special alignment. This tube behaved exactly as expected: it stayed a metal, letting electricity flow freely with no insulating walls. This comparison confirmed that the "magic" only happened when the tube was perfectly aligned with the hBN substrate, creating the one-dimensional moiré superlattice.

The scientists then used computer simulations to understand why this happened. They found that when the tube sits on the hBN, it slightly flattens out, like a tire pressing against the ground. This flattening, combined with the atomic mismatch, causes the atoms to rearrange into a pattern where the most stable areas (where carbon sits directly on top of boron atoms) expand. This creates a landscape with deep valleys that trap electrons, opening up a gap in the energy levels and turning the metal into an insulator.

However, there is a mystery the paper highlights. The computer simulations, which only looked at how individual electrons move in this new landscape, successfully predicted the insulating states at the "full" and "empty" points. But they failed to predict the insulating state at the "half-full" point. The simulations suggested the tube should still be a metal there. Since the experiment clearly showed an insulator at the half-full point, the authors suggest that something more complex is happening. It's likely that the electrons are interacting with each other or vibrating with the atoms in a way that the simple "one-by-one" simulation didn't catch. This suggests that in one-dimensional moiré systems, the collective behavior of electrons might create new quantum phases that we haven't seen before, opening a door to exploring a whole new frontier of physics in one dimension.

Technical Summary: Emergent Electronic Insulating States in a One-Dimensional Moiré Superlattice

Problem Statement
While two-dimensional (2D) van der Waals (vdW) moiré superlattices have become a powerful tool for engineering novel quantum states through interlayer twisting and lattice mismatch, extending this "moiré engineering" to one-dimensional (1D) vdW systems has remained a significant challenge. In 1D systems, such as carbon nanotubes, the relative twist between constituent materials is typically uncontrolled, making the deterministic creation of moiré superlattices difficult. Consequently, there is a lack of experimental evidence for moiré-induced emergent insulating states in 1D vdW materials, and it remains unknown whether interaction-induced quantum phases beyond single-particle physics exist in 1D moiré systems.

Methodology
The authors introduce a fundamentally distinct approach to realize a twist-controlled 1D moiré superlattice by crystallographically aligning an armchair single-walled carbon nanotube (SWNT) with a 2D hexagonal boron nitride (hBN) substrate.

Sample Fabrication: Individual armchair SWNTs (specifically (18,18) and (22,22) chiralities) were non-invasively identified using combined Rayleigh and Raman spectroscopy. These nanotubes were transferred onto hBN substrates using a polypropylene carbonate (PPC) dry transfer method, followed by high-temperature annealing (450°C) to induce crystallographic alignment.
Characterization: Atomic force microscopy (AFM) friction imaging was used to verify the alignment of the nanotube zigzag directions with the hBN zigzag directions, confirming the formation of lattice-aligned heterostructures with an alignment deviation of less than 1°.
Transport Measurements: Low-temperature electrical transport measurements (down to 4 K) were performed to map differential conductance ($dI/dV$) as a function of gate voltage ( $V_g$ ) and bias voltage ( $V_b$ ). Temperature-dependent conductance measurements were conducted to analyze activation gaps.
Control Experiments: Control devices consisting of armchair SWNTs on SiO $_2$ /Si substrates without hBN alignment were fabricated to isolate the moiré effect.
Theoretical Modeling: Density functional theory (DFT) and tight-binding calculations were employed to model the electronic structure. The models accounted for nanotube partial flattening and in-plane lattice reconstruction at the 1D moiré interface.

Key Results

Emergence of Insulating States: In lattice-aligned armchair SWNT/hBN heterostructures, pronounced insulating states (manifested as large, diamond-like features in $dI/dV$ maps) were observed at the charge neutrality point (CNP), full moiré fillings ( $\nu = \pm 4$ ), and half moiré fillings ( $\nu = \pm 2$ ).
Moiré Periodicity: The insulating states are separated by gate voltage intervals of $\Delta V_g \approx 5$ V. Based on extracted gate capacitance, these correspond to hole densities of approximately 0.16 and 0.32 nm $^{-1}$ , representing half ( $\nu = -2$ ) and full ( $\nu = -4$ ) moiré fillings, respectively, assuming a moiré period of $L_m \approx 14$ nm.
Thermal Activation: The insulating states vanish as temperature increases. Arrhenius analysis of the conductance at CNP yielded energy gaps of $\Delta \approx 22$ meV (Device 1) and $\Delta \approx 26$ meV (Device 2). Gaps at full fillings were estimated at $\sim 11$ and $\sim 13$ meV.
Control Verification: Armchair SWNT devices without hBN alignment exhibited metallic behavior with high conductance ( $\sim 4e^2/h$ ) and no pronounced insulating diamonds, confirming that the observed phenomena originate from the SWNT/hBN moiré interface.
Theoretical Insights:
- DFT calculations revealed that lattice relaxation leads to the expansion of the most stable AB' stacking regions (carbon on top of boron), creating a 1D periodic moiré structure.
- Single-particle tight-binding calculations predicted sizable band gaps at CNP ( $\sim 12.1$ meV) and full fillings, consistent with experimental observations.
- Crucially, the single-particle theory predicted no band gaps at half moiré fillings ( $\nu = \pm 2$ ). The experimental observation of insulating states at these fillings suggests that electron correlation and/or electron-phonon interactions (e.g., charge density wave ordering or interband hybridization) drive the emergence of these states, going beyond single-particle physics.

Significance
This work establishes a new and definite route for moiré engineering in 1D van der Waals materials by utilizing crystallographic alignment between 1D nanotubes and 2D substrates. The observation of interaction-induced insulating states at half-moiré fillings provides compelling evidence for many-body physics in 1D moiré systems, a regime where such effects were previously unverified. The study opens an avenue for exploring interaction-induced quantum phases in 1D, distinguishing the physics of 1D moiré superlattices from their 2D counterparts.

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