1D Moiré Channel: Quantum Wires & Correlated States

• One-dimensional moiré channels are quantum-confined systems emerging from twist, strain, or lattice mismatch in van der Waals heterostructures, creating a quasi-1D potential landscape.
• They exhibit unique electronic and excitonic band structures with flat bands, spin textures, and gate-tunable many-body states observable through spectroscopy and transport measurements.
• These channels facilitate device innovations such as quantum wires, Mott insulators, and spintronic applications, leveraging controlled moiré engineering in diverse material systems.

The one-dimensional (1D) moiré channel is a quantum-confined electronic or excitonic system that arises when two van der Waals layers with distinct lattice constants, orientations, or intrinsic distortions are combined under special geometric circumstances—typically via controlled twist, strain, or stacking protocols. The moiré channel forms when the otherwise two-dimensional moiré potential collapses into a quasi-1D potential landscape, leading to emergent physical phenomena such as 1D quantum wires, quantum emitters, correlated insulators, flat bands, spin textures, and gate-tunable many-body states. The formation, spectral features, and physical consequences of 1D moiré channels have been observed and theoretically characterized in systems ranging from transition metal dichalcogenides (TMDCs), carbon nanotubes, graphene, and rectangular or pseudo-square lattices.

1. Moiré Channel Formation: Geometric and Physical Principles

In van der Waals heterostructures, moiré patterns emerge from angular misalignment (twist), lattice mismatch, or strain between layers. For hexagonal lattices such as TMDCs, the moiré superlattice period is given by $a_M \simeq a_0/\sqrt{\delta^2+\Delta\theta^2}$, with $a_0$ the monolayer lattice constant, $\delta$ the lattice mismatch, and $\Delta\theta$ the twist angle (Bai et al., 2019). Under uniaxial strain, the 2D moiré potential $$V(x,y) = V_0[\cos(G_1\cdot\mathbf{r})+\cos(G_2\cdot\mathbf{r})+\cos(G_3\cdot\mathbf{r})]$$ continuously deforms into an effectively 1D form $V_{1D}(x)\simeq V_0\cos(2\pi x/a_M)$.

For rectangular lattices such as PdSe$_2$, "critical angles" $\theta_c$ are found at which one moiré reciprocal vector collapses, defining a strictly 1D channel with wavevector $g_2$. The moiré potential becomes $V_{\rm moiré}(r)=2V_G\cos(g_2\cdot r)$, leading to directionally localized electronic states (An et al., 19 Jul 2025).

In pseudo-square lattice systems like GdTe$_3$, stacking of two mirror-distorted layers generates a moiré period $d\simeq 1/[6.54\tan\alpha]$, where $\alpha$ is the distortion angle measured from electron diffraction. The 1D moiré superstructure is composed of a regular array of screw dislocations (Yeon et al., 13 Aug 2025).

In carbon nanotube superlattices and GNR/hBN systems, lattice mismatch ($\sim1.8\%$ for CNT/hBN) yields moiré periods $L_M\sim14$ nm, producing gate-tunable 1D arrays of quantum-confined states (Chen et al., 16 Nov 2025, Bi et al., 13 Nov 2025, Okumura et al., 24 Oct 2025).

2. Electronic and Excitonic Band Structure Modeling

The effective Hamiltonian for a 1D moiré channel adopts the canonical form: $$H = -\frac{\hbar^2}{2m^*}\frac{d^2}{dx^2} + V_0\cos\left(\frac{2\pi x}{a_M}\right)$$ for electronic or excitonic degrees of freedom along the channel direction (Bai et al., 2019, Bi et al., 13 Nov 2025). Tight-binding simulations in DWCNTs and atomic chains reveal periodic hybridizations, mini-band structure, and gap openings determined by the interlayer coupling strength and moiré period (Zhao et al., 2019, Vorobev et al., 10 Feb 2025). Band flattening, velocity renormalization and the appearance of "magic-angle" conditions are found in collapsed CNTs at $\theta_M^\ast\sim1.12^\circ$, with flat-band widths $W\lesssim1$ meV and strong localization in AA regions (Arroyo-Gascón et al., 2020).

For TMDC heterobilayers, strain merges 0D quantum emitters into extended 1D quantum wires with distinct band dispersion and large intensity enhancement, driven by higher bound-state density and partial delocalization (Bai et al., 2019).

In twisted $M$-valley bilayers, the moiré potential flattens dispersion strongly along one direction—with anisotropic effective mass $m_x^\ast\to\infty, m_y^\ast$ finite and coexisting 2D and 1D bands—while twist-induced Rashba spin-orbit coupling produces nontrivial spin textures and gate-tunable spin polarization (Ingham et al., 14 Mar 2025).

3. Correlations, Luttinger Liquid Physics, and Many-Body Effects

Strong electron-electron interactions are generically promoted in 1D moiré channels. Experimental measurements in CNT/hBN devices indicate Tomonaga–Luttinger-liquid behavior, with tunable Luttinger parameter $K_\rho$ extracted via power-law scaling of conductance $G(T)\propto T^\alpha$, where $\alpha=(K_\rho^{-1}-1)/4$ (Chen et al., 16 Nov 2025, Wang et al., 2021). Umklapp scattering at half-filling drives a Mott transition when $K_\rho<1/2$, observed as robust correlated gaps $E_{\rm gap}\sim15$–25 meV at quarter- and half-filling in transport (Chen et al., 16 Nov 2025). Further, the ratio $U/W$ can reach $400$ in collapsed CNT moiré channels (Arroyo-Gascón et al., 2020), pushing systems deep into the Mott regime, while gate tuning allows exploration of Luther–Emery liquids, Wigner crystallization, and unconventional superconductivity.

In 1D boundaries embedded in 2D twisted bilayer WSe$_2$, a local Hubbard chain is directly imaged via STM—with bandwidth $W\sim10$–30 meV, on-site interaction $U\sim100$–200 meV, and correlated charge filling controlled by back gate and tip bias, realising 1D Mott insulators and Luttinger liquid regimes (Ren et al., 2023).

4. Spectroscopic, Transport, and Imaging Signatures

Optical and electronic probes reveal characteristic signatures:

• For TMDC heterobilayers, photoluminescence (PL) from 1D moiré excitons appears as a single broad peak ($E_{1D}\sim1.326$ eV, FWHM$\sim$8 meV), with intensity enhancement $I_{1D}/I_{0D}>10^2$ and linear polarization $P\sim0.9$ (Bai et al., 2019).
• In tWTe$_2$, current anisotropy $R_{\rm hard}/R_{\rm easy}\sim10^3$, power-law suppression of the density of states, and scaling collapse in $dI/dV$ confirm the realization of a 2D array of 1D Luttinger liquids (Wang et al., 2021).
• In incommensurate DWCNTs, marked changes in optical transition spectra (from metallic to insulating states) emerge from strong moiré hybridization, with observed gaps $2|V_0|\sim20$–40 meV (Zhao et al., 2019, Koshino et al., 2014).
• STM/STS and DFT confirm 1D modulation of conduction-band edges across moiré period in strained CuSe monolayers, with energy tunability up to $\sim100$ meV for $7\%$ strain (Niu et al., 2022).

5. Universal Engineering Guidelines and Lattice Symmetry Effects

Universal collapse criteria for 1D moiré channel formation can be written as $\epsilon_c = 2/(\sqrt{\nu}\tan(\theta/2))$ (for hexagonal honeycomb lattices), relating critical strain and twist, with collapse resulting in strictly 1D reciprocal-space segments and real-space stripe arrays; aperiodic incommensurations are generic except in symmetry-selected configurations (Sinner et al., 2022).

For rectangular lattices, critical twist angles $\theta_c$ satisfying $$R(\theta_c)\cdot(m\,\vec a+n\,\vec b)=(m\,\vec a+n\,\vec b)$$ define the emergence of 1D channels, with moiré periods $\lambda_m=2\pi/|g_2|$ computable for arbitrary primitive vectors (An et al., 19 Jul 2025). Pseudo-square systems like GdTe$_3$ extend the design space to low-symmetry van der Waals crystals, with moiré periods tunable via stacking and strain, and electronic modulations observed via EELS (Yeon et al., 13 Aug 2025).

6. Device Implications, Topological and Spin Effects

1D moiré channels serve as platforms for novel device architectures:

• Quantum wires and interlayer excitonic circuits engineered by strain and twist (Bai et al., 2019).
• Gate-tunable single-electron and quantum-dot arrays in GNR/hBN and DWCNT/hBN, relevant for quantum computing and charge pumping (Okumura et al., 24 Oct 2025, Koshino et al., 2014).
• Spintronics applications in $M$-valley bilayers, with moiré-Rashba-induced spin-momentum locking and spin–density–wave instabilities under electric or magnetic field (Ingham et al., 14 Mar 2025).
• Topologically protected end-states and charge pumps upon adiabatic layer sliding, Berry curvature–dependent phase engineering, and possible Majorana zero modes at stripe ends when proximitized to superconductors (An et al., 19 Jul 2025).

7. Outlook: Universality, Extensibility, and Frontier Directions

The 1D moiré channel is a universal construct, applicable to any heterostructure where geometric, symmetry, or external parameters tune a 2D moiré potential into a strictly 1D periodic or quasi-periodic modulation. The full spectral, transport, and correlated behavior is tractable via tight-binding, continuum Dirac-Harper, and discrete WKB approaches (Vorobev et al., 10 Feb 2025, Timmel et al., 2020), with flat-band, chiral, and Mott insulating regimes accessible. Combined with gate, strain, and twist engineering, the 1D moiré channel framework enables the systematic realization and manipulation of exotic low-dimensional quantum phases in van der Waals materials.