One-Dimensional Electronic States in a Moiré Superlattice of Twisted Bilayer WTe2

TL;DR

The paper investigates the microscopic origin of one-dimensional moiré electronic states in a purely 1D moiré pattern formed by twisted bilayer 1T$'$-WTe$_2$ at a large twist angle. It combines DFT structural relaxation with HAADF-STEM validation to show that in-plane lattice relaxation reconstructs moiré stripes and induces a position-dependent intralayer moiré potential, $V_{ m eff}( ext{r})$, that drives quasi-1D bands dispersing along the stripe while remaining nearly flat perpendicular to it. An effective tight-binding model, using $V_{ m eff}( ext{r})$, reproduces both the band dispersion and the real-space localization of the wave functions, confirming intralayer effects as the primary mechanism. The work provides a unified framework for realizing 1D moiré physics in anisotropic 2D materials and positions twisted bilayer WTe$_2$ as a robust platform for exploring extended networks of 1D moiré channels and related many-body phenomena.

Abstract

One-dimensional (1D) moiré superlattices provide a new route to engineering reduced-dimensional electronic states in van der Waals materials, yet their electronic structure and microscopic origin remain largely unexplored. Here, we investigate the structural relaxation and electronic properties of a 1D moiré superlattice formed in twisted bilayer 1T$'$-WTe$_2$ using density functional theory calculations, complemented by high-angle annular dark-field scanning transmission electron microscopy. We show that lattice relaxation strongly reconstructs the moiré stripes, leading to stacking-dependent stripe widths that are in excellent agreement with experimental observations. The relaxed structure hosts quasi-one-dimensional electronic bands near the Fermi level, characterized by strong dispersion along the stripe direction and nearly flat dispersion in the perpendicular direction. By comparing the full bilayer with isolated relaxed layers, we establish that these 1D electronic states are governed predominantly by an intralayer moiré potential induced by in-plane lattice relaxation, rather than by interlayer hybridization. We extract this position-dependent moiré potential directly from DFT calculations and construct an effective tight-binding model that reproduces both the band dispersion and the real-space localization of the electronic wave functions. Our results identify lattice relaxation as the key mechanism underlying 1D electronic states in 1D moiré superlattices. %and establish twisted bilayer WTe$_2$ as a promising platform for exploring emergent one-dimensional moiré physics. The framework developed here provides a unified theoretical basis for realizing and exploring one-dimensional moiré physics in a broad class of anisotropic two-dimensional materials.

Figures (12)

• Figure 1: Schematic illustration of a twisted bilayer composed of an anisotropic two-dimensional lattice stacked at (a) $\theta = 5^\circ$ and (b) $\theta \approx 65^\circ$. The anisotropic monolayer lattice is constructed by uniaxially deforming an equilateral triangular lattice by a factor of 0.9 along the $x$-direction of the unrotated configuration. While the low-angle stacking in (a) produces an anisotropic two-dimensional moiré pattern, the large-angle configuration in (b) gives rise to a purely one-dimensional moiré superlattice. The lower panels show the corresponding momentum-space constructions; in the one-dimensional case, only a single moiré reciprocal lattice vector $\bm{G}_{\rm M}$ remains.
• Figure 2: Atomic structure of a 1T$'$-WTe$_2$ monolayer. (a) Top view of the in-plane structure. (b) Side view in the $y$-$z$ plane. Black dots denote W atoms, while blue and red dots denote Te atoms. The shaded rectangle indicates the unit cell spanned by the primitive lattice vectors $\bm{a}_1$ and $\bm{a}_2$.
• Figure 3: (a) One-dimensional moiré pattern formed by twisting two 1T$'$-WTe$_2$ monolayers. The top layer (transparent dots) is rotated by $\theta\approx62^\circ$ relative to the bottom layer (solid dots). (b) Periodic stacking configuration corresponding to the local structure in (a), with the period indicated by the rhombus. Periodic interlayer sliding along the $x$ direction gives rise to the repeating XX, XY, and YY stacking configurations.
• Figure 4: (a) Effective isoscales triangular lattice approximating the atomic structure of WTe$_2$. (b) Twisted stacking of the effective triangular lattices. Black and orange denotes the bottom and top layers, respectively. The two layers are rotated such that their lattice vectors parallel to the $x$ axis have the equal length but are not identical. The inset shows a magnified view of a single isoscales plaquette with an aligned baseline. (c) Zoom-out view of (b), showing a clear moiré period $L_\mathrm{trig}$. Atomic color codes are the same as in Fig. \ref{['fig:single']}
• Figure 5: Momentum-space structure of twisted bilayer WTe$_2$ for a commensurate approximant. Three levels of Brilloiuin zones are indicated, corresponding to the effective triangular lattice, the WTe$_2$ monolayers, and the commensurate bilayer supercell.