⇦Chinese Physics Letters, 2023, Vol. 40, No. 6, Article code 067801 Optical Tunable Moiré Excitons in Twisted Hexagonal GaTe Bilayers Jinsen Han (韩锦森)1,2, Kang Lai (赖康)1,2, Xiaoxiang Yu (余晓翔)1,2, Jiahao Chen (陈家浩)1,2, Hongli Guo (郭宏礼)3*, and Jiayu Dai (戴佳钰)1,2* Affiliations 1Department of Physics, National University of Defense Technology, Changsha 410073, China 2Hunan Key Laboratory of Extreme Matter and Applications, National University of Defense Technology, Changsha 410073, China 3Department of Physics and Astronomy, California State University, Northridge, CA 91330-8268, USA Received 5 April 2023; accepted manuscript online 5 May 2023; published online 11 May 2023 *Corresponding authors. Email: hongli.guo@csun.edu; jydai@nudt.edu.cn Citation Text: Han J S, Lai K, Yu X X et al. 2023 Chin. Phys. Lett. 40 067801    Abstract Optical fine-tunable layer-hybridized Moiré excitons are highly in demand for emerging many-body states in two-dimensional semiconductors. We report naturally confined layer-hybridized bright Moiré excitons with long lifetimes in twisted hexagonal GaTe bilayers, using ab initio many-body perturbation theory and the Bethe–Salpeter equation. Due to the hybridization of electrons and holes between layers, which enhances the brightness of excitons, the twisted bilayer system becomes attractive for optical applications. We find that in both R and H-type stacking Moiré superlattices, more than 200 meV lateral quantum confinements occur on exciton energies, which results in two scenarios: (1) The ground state bright excitons $\mathrm{X}_\mathrm{A}$ are found to be trapped at two high-symmetry points, with opposite electric dipoles in the R-stacking Moiré supercell, forming a honeycomb superlattice of nearest-neighbor dipolar attraction. (2) For H-stacking case, the $\mathrm{X}_\mathrm{A}$ is found to be trapped at only one high-symmetry point exhibiting a triangular superlattice. Our results suggest that twisted h-GaTe bilayer is one of the promising systems for optical fine-tunable excitonic devices and provide an ideal platform for realizing strong correlated Bose–Hubbard physics.
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 DOI:10.1088/0256-307X/40/6/067801 © 2023 Chinese Physics Society Article Text Two-dimensional (2D) materials, such as graphene,[1,2] transition metal dichalcogenide (TMD),[3-6] and other xenes[7-9] exhibit intriguing properties and attract considerable attention for a broad range of applications. Recently, twisted bilayer van der Waals structures have shone a spotlight on amazing Mott physics,[10-13] unconventional superconductivity,[14-16] orbital magnetic moment,[17] anomalous Hall effect,[18] and topological phases transition.[19,20] The exciton properties in Moiré superlattices are of particular interest due to their long-range periodic potential and reduced screening in the systems. Novel phenomena, such as interlayer excitons,[21-24] topological phase transitions,[25] orbital-selective indirect excitons,[26] high-temperature Bose-Einstein condensation,[27,28] and valley-dependent excitons,[29-31] have been observed in Moiré superlattices. However, in twisted TMD heterostructures, the Moiré exciton generally exhibits dark exciton properties. Unlike bright excitons that can strongly couple with light, dark excitons usually have negligible oscillator strength and thus tiny optical signals, limiting their applications.[32] A layer hybridized action with both large oscillator strength and long lifetime is highly demanded in Moiré materials. The post-transition-metal chalcogenides (PTMCs), such as InSe, GaSe, GaTe, and GaS, emerge as competitive 2D materials in recent years. A wide range of tunable band gap[33] and photoluminescence,[34] high electron mobility,[35-37] long exciton lifetime have been reported for PTMCs. Tuning the prominent electronic and optical properties can facilitate PTMCs-based optoelectronics and twistronics. Twist has emerged as a new knob to engineer the electronic and optical properties and correlated states of matter in a controlled manner. However, it remains unknown how these properties are spatially modulated in the presence of a Moiré superlattice. Due to a large number of atoms in a Moiré supercell, analyzing its electronic and excitonic properties with recent ab initio calculations can be quite challenging. Fortunately, some pioneers in the field have developed interpolation techniques that allow us to study only high-symmetry sites in the small twisting angle Moiré supercell lattices.[38-40] This makes it possible to use first-principles calculations with the Bethe–Salpeter equation to study the exciton behavior in Moiré superlattices. In this Letter, we report on the electronic, optical, and excitonic properties of twisted hexagonal GaTe bilayers with two typical stacking configurations (R-type and H-type) using the ab initio many-body perturbation theory and the Bethe–Salpeter equation (BSE). There are three high-symmetry sites in each Moiré supercell, which exhibits five irreducible stacking configurations. For different stacking types, the interlayer coupling strength affects the electronic bands and the hybridization of valence bands. Correspondingly, the excitonic energy, oscillator strength, and exciton lifetime change. We find bright hybridized interlayer and intralayer excitons with large binding energy and long radiative lifetime that are confined in deep Moiré potential ($> 200$ meV) in both R- and H-type Moiré superlattices. In addition, the oscillator strength and radiative lifetime of the hybridized excitons are spatially modulated in the Moiré supercell. Our work supplies a way for the application of PTMCs in realizing layer-hybridized Moiré excitons. It promises to be a compelling platform for optically tunable, strongly correlated excitonic devices. Computational Methods. The density-functional theory (DFT)[41] calculations are carried out by the Quantum-ESPRESSO package.[42,43] The Optimized Norm-Conserving Vanderbilt pseudopotential[44,45] is used. The Perdew–Burke–Ernzerhof (PBE) exchange-correlation[46] and OptBK88-vdW[47-53] functionals are implemented in DFT calculations to get the optimized atomic structures. A plane-wave basis setup with a kinetic energy cutoff of 90 Ry for the wavefunction is used. At least $16$ Å vacuum space and $20\times20\times1$ Monkhorst–Pack grid[54] with fixed electron distribution are implemented. A single-shot $G_0W_0$[55,56] and the BSE[57] are solved in a unit cell to consider the many-body screening effects and electron–hole (e–h) interactions via the Yambo code.[58,59] The wavefunction of exciton $|\lambda\rangle $ can be obtained by diagonalizing the BSE, \begin{align} |\lambda\rangle =\sum_{e,h} A_{eh} \langle h|e\rangle , \tag {1} \end{align} where $\langle h|$ and $|e\rangle$ are hole and electron wave functions, and $A_{eh}$ indicates the weights of electron and hole pairs composting the excitons. The excitonic oscillator strength is defined by $|\sum_{e,h} A_{eh}\langle h| {\boldsymbol D} |e\rangle|^2$ with ${\boldsymbol D}$ being the dipole operator. A box-shape truncated Coulomb potential in the non-periodic direction[60,61] is used to avoid numerical divergences. We select $20 \times 20 \times 1$ $k$-grid in $G_0W_0$ calculations, and a denser $40 \times 40 \times 1$ $k$-grid is used to ensure the convergence of optical properties. There are 600 bands employed in the calculations of dielectric function and self-energy based on plasmon-pole approximation.[62,63] Since we only care about the first several excitonic states, 12 conduction bands and 12 valence bands are considered to build the BS kernel. The spin-orbit coupling is included in the calculations. Atomic Structure and Quasiparticle Properties. As depicted in Fig. 1, we investigate two typical twisting configurations, R-type and H-type, of h-GaTe bilayer in a small angle ($\sim$ $3^{\circ}$). Both the R- and H-type twisted styles preserve the $C_3$ symmetry, with three high-symmetry sites in a single Moiré supercell. In this way, the stacking structures at the six high-symmetry sites can be treated as six different types of stacked h-GaTe bilayers, named as $\mathrm{R}_\mathrm{h}^\mathrm{h}$ (AA), $\mathrm{R}_\mathrm{h}^\mathrm{X}$, $\mathrm{R}_\mathrm{h}^\mathrm{M}$ and $\mathrm{H}_\mathrm{h}^\mathrm{h}$ (AA$'$), $\mathrm{H}_\mathrm{h}^\mathrm{X}$, $\mathrm{H}_\mathrm{h}^\mathrm{M}$. Here we use the same notations as that in twisted TMDs.[40] R$_\mathrm{h}^\mathrm{u}$ ($\mathrm{H}_\mathrm{h}^\mathrm{u}$, $\mathrm{u} = \mathrm{h}, \mathrm{X}, \mathrm{M}$) means that the hollow center, chalcogen, and post-transition-metal elements in the upper layer is vertically overlapped with the hollow center in the lower layer. Among all these stacking configurations, only five of them are irreducible, where the $\mathrm{R}_\mathrm{h}^\mathrm{X}$ and $\mathrm{R}_\mathrm{h}^\mathrm{M}$ shares the same configuration with opposite out-of-plane dipoles as shown by the arrows in Fig. 1. The h-GaTe monolayer has two sublayers bounded by Ga–Ga covalent bond. The h-GaTe bilayers can be created by the symmetry operation on the h-GaTe monolayer. The symmetry operations are given in Table 1, where the $m$ means the mirror operation along the $x$–$y$ plane, $T=[\frac{1}{2},0,0]$ ($T'=[-\frac{1}{2},0,0]$) indicates the slide operation along the $x$ axis with $\frac{1}{2}$ ($-\frac{1}{2}$) cell parameter. The R-type twisted h-GaTe bilayer can be generated by rotating from $\mathrm{R}_\mathrm{h}^\mathrm{h}$ stacking structure [Fig. 1(a)] while the H-type emerges by a rotating from $\mathrm{H}_\mathrm{h}^\mathrm{h}$ stacking mode [Fig. 1(b)]. In R-type twisted h-GaTe, there are two irreducible stacked structures at three high-symmetry sites, as depicted in Fig. 1(a), while three irreducible types of stacking modes are observed in H-type.
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Fig. 1. Atomic configurations for two types of twisting h-GaTe bilayer. Gallium atoms are denoted by purple, and tellurium atoms are labelled as gray. (a) The R-type twisted structure and (b) the H-type structure with the twist angle of about $3^{\circ}$. The unit cell is marked in red rhombus. There are six high-symmetry sites, labeled as (I–VI), in the two types of Moiré supercells. Six stacking configurations, $\mathrm{R}_\mathrm{h}^\mathrm{h}$, $\mathrm{R}_\mathrm{h}^\mathrm{X}$, $\mathrm{R}_\mathrm{h}^\mathrm{M}$ and $\mathrm{H}_\mathrm{h}^\mathrm{h}$, $\mathrm{H}_\mathrm{h}^\mathrm{X}$, $\mathrm{H}_\mathrm{h}^\mathrm{M}$ at six high-symmetry sites are illustrated in the bottom panel. The gray dashed line is a guide for the alignment of atoms in different layers. The black arrows in $\mathrm{R}_\mathrm{h}^\mathrm{X}$ and $\mathrm{R}_\mathrm{h}^\mathrm{M}$ indicate the dipole directions ${\boldsymbol D}$.
Due to the buckled structure of h-GaTe monolayer, different stacking configurations give different interlayer couplings and thus different interlayer distances. For $\mathrm{R}_\mathrm{h}^\mathrm{h}$ and $\mathrm{H}_\mathrm{h}^\mathrm{M}$ stackings, the outward Te atoms in the upper and lower layers are aligned. The repulsive interaction between Te–Te atoms leads to relatively large interlayer distances. In comparison, the $\mathrm{H}_\mathrm{h}^\mathrm{h}$, $\mathrm{R}_\mathrm{h}^\mathrm{X}$ ($\mathrm{R}_\mathrm{h}^\mathrm{M}$), and $\mathrm{H}_\mathrm{h}^\mathrm{X}$ stacking configurations show alignment between outward Te atoms and inward Ga atoms, and hence have relatively strong interactions and small interlayer distances. Among five stacking configurations, $\mathrm{R}_\mathrm{h}^\mathrm{X}$ ($\mathrm{R}_\mathrm{h}^\mathrm{M}$) stacking shows the smallest interlayer distance and the strongest interlayer interactions while $\mathrm{H}_\mathrm{h}^\mathrm{M}$ stacking shows the largest interlayer distance and the weakest interlayer interactions. Thus, in the Moiré supercells, the interlayer distances vary at different high-symmetry sites. The in-plane local strain results from the mismatch of the lattice constant and is negligible in systems with matched lattice constants.[64] In twisted h-GaTe bilayers, interlayer coupling rather than the local strain is the key factor affecting the Moiré potential and the A exciton.
Table 1. Geometric parameters and band gaps of h-GaTe bilayers, including interlayer distance ($d_\mathrm{L}$), symmetry operator, and direct band gap at $\varGamma$ point ($E^\varGamma_\mathrm{g}$). The brackets denote the calculation methods.
Stacking $d_\mathrm{L}$
(${\rm {Å}}$)		 Symmetry $E^\varGamma_\mathrm{g}$ (PBE)
(eV)		 $E^\varGamma_\mathrm{g}$ ($G_{0}W_{0}$)
(eV)
R-type R$_{\rm h}^{\rm h}$ 4.48 $m$ 1.23 2.63
R$_{\rm h}^{\rm X}$ (R$_{\rm h}^{\rm M}$) 3.60 $m+T$ 1.05 2.39
H-type H$_{\rm h}^{\rm h}$ 3.68 $\bar{1}$ 1.07 2.42
H$_{\rm h}^{\rm M}$ 4.56 $\bar{1}+T$ 1.26 2.66
H$_{\rm h}^{\rm X}$ 3.68 $\bar{1}+T'$ 1.07 2.41
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Fig. 2. Orbital-resolved band structures of $\mathrm{R}_\mathrm{h}^\mathrm{h}$ stacked h-GaTe bilayer calculated by DFT. The VBM is shifted at 0 eV, as indicated by the gray dashed horizontal lines. Here (a), (b), and (c) correspond to the $s$, $p_x \pm p_y$, and $p_z$ orbitals, respectively.
The h-GaTe bilayer shows an indirect gap for five stacking configurations, with the conduction band minimum located at the $M$ point and the valence band maximum (VBM) located near the $\varGamma$ point. We take the $\mathrm{R}_\mathrm{h}^\mathrm{h}$ stacked h-GaTe as an example, as shown in Fig. 2. The first valence band (VB$_1$) of h-GaTe bilayer has a “Mexican Hat”-like shape, which mainly attributes to the $p_z$ orbitals. The conduction band (CB) is contributed by the $s$ and $p_z$ hybridized orbitals at $\varGamma$ point. The $p_z$ orbitals are sensitive to the interlayer distances. Thus, the bandgap at $\varGamma$ point ($E_{\mathrm{g}}^\varGamma$) varies from different stacking configurations, as listed in Table 1. As a result, $\mathrm{R}_\mathrm{h}^\mathrm{X}$ ($\mathrm{R}_\mathrm{h}^\mathrm{M}$) stacking shows the smallest $E_{\mathrm{g}}^\varGamma$, while $\mathrm{H}_\mathrm{h}^\mathrm{M}$ shows the largest $E_{\mathrm{g}}^\varGamma$. To accurately calculate the band structures of 2D materials, the screening effects induced by the natural confinement in the non-periodic direction are inevitable. Hence, we employ the many-body perturbation theory on top of PBE. When considering the quasiparticle corrections, the direct band gap would increase up to 1.34–1.4 eV for h-GaTe bilayers with five stacking configurations, as shown in Table 1. In the R-type twisted h-GaTe, the $E^\varGamma_\mathrm{g}$ varies at the three high-symmetry points and is about 240 meV, with the same energy at $\mathrm{R}_\mathrm{h}^\mathrm{X}$ and $\mathrm{R}_\mathrm{h}^\mathrm{M}$. However, in the H-type, the $E^\varGamma_\mathrm{g}$ is about 250 meV, with three different gap energies at three high-symmetry points. The large band-gap-energy difference indicates that the two-type Moiré structures are ideal potential fields to confine the free carriers and promise a good platform to realize strongly correlated systems.
Table 2. Properties of the first excitons (${\mathrm{X}_\mathrm{A}}$) for different stacking styles in twisted h-GaTe bilayers, including excitonic energy ($E_{\mathrm{X}_\mathrm{A}}$), exciton binding energy ($E^{\rm b}_{\mathrm{X}_\mathrm{A}}$), oscillator strength (OS$_{\mathrm{X}_\mathrm{A}}$), and lifetime ($\tau_{_{\scriptstyle \mathrm{X}_\mathrm{A}}}$).
$E_{\mathrm{X}_\mathrm{A}}$
(eV)		 $E^{\rm b}_{\mathrm{X}_\mathrm{A}}$
(eV)		 OS$_{\mathrm{X}_\mathrm{A}}$
($10^{-3}{\rm Bohr}^{2}$)		 $\tau_{_{\scriptstyle \mathrm{X}_\mathrm{A}}}$
(ps)
R-type R$_{\rm h}^{\rm h}$ 2.16 0.47 7.02 12.4
R$_{\rm h}^{\rm X}$ (R$_{\rm h}^{\rm M}$) 1.95 0.44 0.12 835.4
H-type H$_{\rm h}^{\rm h}$ 2.03 0.40 1.45 66.5
H$_{\rm h}^{\rm M}$ 2.26 0.40 9.94 8.9
H$_{\rm h}^{\rm X}$ 2.02 0.40 12.60 8.2
cpl-40-6-067801-fig3.png
Fig. 3. The optical absorption spectra of h-GaTe bilayer, i.e., the results of five different stacking modes. The blue lines represent the absorption spectra. The first excitons are labeled as $\mathrm{X}_\mathrm{A}$. The dashed grey vertical lines indicate the direct band gaps at the $\varGamma$ point.
Optical Absorptions and Excitonic Properties. The optical absorption spectra of six local stacked h-GaTe bilayers are compared in Figs. 3(a)–3(e). Like other 2D materials, excitons enhance optical absorption in all five stacking modes. The first exciton $\mathrm{X}_\mathrm{A}$ leads to a pre-edge in the absorption. As a result, the absorption edge lies before the quasiparticle band gaps, indicating strong coupling between electron-hole pairs and light. For $\mathrm{H}_\mathrm{h}^\mathrm{h}$, $\mathrm{R}_\mathrm{h}^\mathrm{X}$ ($\mathrm{R}_\mathrm{h}^\mathrm{M}$), and $\mathrm{H}_\mathrm{h}^\mathrm{X}$ stackings with stronger interlayer interactions, the energies of lower absorption edges are smaller than those of $\mathrm{R}_\mathrm{h}^\mathrm{h}$ and $\mathrm{H}_\mathrm{h}^\mathrm{M}$ stackings. Consequently, the spatially varied absorption can be realized in the twisted h-GaTe bilayers. Compared with the quasiparticle band gap and optical gap, we can get the exciton binding energy, as listed in Table 2. For the R- and H-type twisted h-GaTe, the exciton binding energies in different high-symmetry sites show the negligible difference. Furthermore, we investigate the local exciton spatial distributions of twisted h-GaTe bilayers. Because the first exciton in Moiré lattice is of vital importance, we only care about $\mathrm{X}_\mathrm{A}$'s behaviors. We use $\mathrm{R}_\mathrm{h}^\mathrm{h}$ stacked h-GaTe as an example. The $\mathrm{X}_\mathrm{A}$ for five stacking configurations correspond to the electronic transitions from VB$_1$ to CB and these transitions mainly locate near the $\varGamma$ point in reciprocal space, as shown in Fig. 4(a). From Fig. 2, VB$_1$ is mainly contributed by $p_z$ orbital and CB is prominent by $s$ and $p_z$ hybridized orbitals. Thus, the electron-hole pair transition is tightly associated with the interlayer coupling.
cpl-40-6-067801-fig4.png
Fig. 4. The diagram of the $\mathrm{X}_\mathrm{A}$ in $\mathrm{R}_\mathrm{h}^\mathrm{h}$ stacked h-GaTe bilayer. (a) Electron-hole transition illustrated in reciprocal space. [(b), (c)] Real space distribution for $\mathrm{X}_\mathrm{A}$: (b) top view, (c) side view. The hole position is highlighted by the black point.
In real space, the $\mathrm{X}_\mathrm{A}$ in five stacking modes shows a Wannier–Mott type exciton, with the radius up to 3 nm, as shown in Fig. 4(b). Interestingly, all five stacking modes witness a hybridized inter-layer and intra-layer exciton. In h-GaTe monolayer, the excitons are the mixture of inter- and intra-sublayer excitons. The h-GaTe bilayer has two layers coupled by van der Waals interaction and each layer has two sublayers bonded by Ga–Ga covalent bond. As illustrated in Fig. 4(c), when placing the hole position at the gallium atom in the bottom sublayer of the upper layer, the $\mathrm{X}_\mathrm{A}$ excitons in the h-GaTe bilayer are distributed across four sublayers for all stacking configurations. Therefore, the excitons in the h-GaTe bilayer are a mixture of intra-sublayer, inter-sublayer, and interlayer excitons. The interlayer excitons are linked together by crossing different layers, which indicates that the electrons are easy to excite and recombine through van der Waals interactions. Due to the different spatial separations, the excitons in the h-GaTe bilayer exhibit different lifetimes for different stackings. The exciton radiative lifetime is determined by the radiative rate at zero temperature,[65] \begin{align} \tau(0) = \gamma_{\rm s}^{-1}(0) = \frac{\hbar^2 c A_{\rm uc}}{8 \pi e^2 E_{\rm S}(0) \mu_{_{\scriptstyle \rm S}}^2(0)}, \tag {2} \end{align} where $A_{\rm uc}$ is the area of the unit cell, $E_{\rm S}(0)$ is the exciton energy, and $\mu_{_{\scriptstyle \rm S}}^2(0)$ denotes the oscillator strength. The lifetimes of $\mathrm{X}_\mathrm{A}$ in h-GaTe bilayers increase slightly compared with those in h-GaTe monolayer. The separate inter-sublayer excitons play the dominant roles in slow recombination. In different high-symmetry sites in the Moiré supercell, the lifetime of $\mathrm{X}_\mathrm{A}$ can be dramatically different. For example, in the R-type twisted h-GaTe, the lifetime of $\mathrm{X}_\mathrm{A}$ is about 835 ps in the $\mathrm{R}_\mathrm{h}^\mathrm{X}$ ($\mathrm{R}_\mathrm{h}^\mathrm{M}$) stacking mode. This is 70 times longer than the lifetime in the $\mathrm{R}_\mathrm{h}^\mathrm{h}$ stacking mode (12.4 ps). These results suggest that the twisted h-GaTe bilayer is a promising material for studying exciton-exciton interactions. In the H-type, the same phenomena are observed. Therefore, the layer hybridized excitons play crucial roles in the high-symmetry sites in the Moiré supercells. The inherent spatial separation properties suggest that the Moiré exciton could have a longer lifetime and a finite optical absorption amplitude, making it optically measurable.
cpl-40-6-067801-fig5.png
Fig. 5. The two-dimensional distribution of the Moiré potential for R-type (a) and H-type (b) h-GaTe bilayer, generated by interpolation method. The black rhombus region depicts the unit cell in Moiré superlattices.
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Fig. 6. The two-dimensional distribution of the excitonic oscillator strength of $\mathrm{X}_\mathrm{A}$ at six high symmetry points in R-type (a) and H-type (b) twisted h-GaTe bilayer.
The Moiré potential is given in Fig. 5 by interpolating the local $\mathrm{X}_\mathrm{A}$ exciton energies. Both R- and H-types exhibit Moiré potential with a magnitude of approximately 240 meV. As structures equivalent in shape but with opposite dipoles, the Moiré potentials at sites $\mathrm{R}_\mathrm{h}^\mathrm{X}$ and $\mathrm{R}_\mathrm{h}^\mathrm{M}$ have the same value. Exciton $\mathrm{X}_\mathrm{A}$ will be trapped at these two sites with opposite electric dipoles, forming a honeycomb superlattice of nearest-neighbor dipolar attraction in the R-stacking Moiré supercell. Differently, in the H-stacking Moiré supercell, $\mathrm{X}_\mathrm{A}$ will be trapped at the $\mathrm{H}_\mathrm{h}^\mathrm{X}$ site, forming a triangular lattice. We further interpolate the local exciton oscillator strength in the Moiré supercell, as shown in Fig. 6. In the R-type twisted h-GaTe, the brightest exciton oscillator strength forms triangular lattices. The large oscillator strengths lead to strong optical absorption and photoluminescence. Thus, in the R-type twisted bilayer, the optical-related signals would be detected in the $\mathrm{R}_\mathrm{h}^\mathrm{h}$ sites. The H-type twisting style shows a hexagonal lattice characteristic, with the brighter exciton located at $\mathrm{H}_\mathrm{h}^\mathrm{X}$ and $\mathrm{H}_\mathrm{h}^\mathrm{M}$. As a result, the different types of Moiré patterns can be distinguished by optical measurement. Together with the Moiré potential in Fig. 5(a), the exciton at $\mathrm{R}_\mathrm{h}^\mathrm{X}$ and $\mathrm{R}_\mathrm{h}^\mathrm{M}$ high-symmetry sites can be confined with longer lifetime, which is the key to strongly correlated physics. The R-type twisted h-GaTe provides us with a desirable platform to study the strongly exciton-exciton interaction or a bosonic Haldane model. Meanwhile, the H-type twisting styles form inequivalent hexagonal superlattices, and only $\mathrm{H}_\mathrm{h}^\mathrm{h}$ site can trap the longer lifetime excitons. In summary, we have utilized ab initio calculations to investigate exotic excitonic properties in twisted h-GaTe bilayers different from other van der Waals heterostructures. Our results show that the hybridized interlayer and intralayer excitons of twisted h-GaTe bilayers are equipped with long lifetime and strong optical signal properties simultaneously. The exciton energies can vary by more than 200 meV between different local sites across the Moiré lattice, leading to high contrast optical Moiré patterns in both R- and H-type twisted structures. Moreover, we find that different high-symmetric stacking styles can dramatically modify the oscillator strength and radiative lifetime of the bright excitons. Therefore, in R-stacking, long lifetime excitons $\mathrm{X}_\mathrm{A}$ are trapped at two high-symmetry points with opposite electric dipoles within the Moiré supercell. Nevertheless, in the H-stacking case, only one high-symmetry point within the Moiré supercell finds the long lifetime exciton, demonstrating a larger triangular superlattice in contrast to the honeycomb structure from R-stacking. Our results provide new insights into Moiré physics including twistronics and excitonics in the vast family of van der Waals materials and demonstrate that twisted h-GaTe bilayers are promising platforms to study strongly correlated behaviors in exciton–exciton interactions. Acknowledgements. This work was supported by the National Key R&D Program of China (Grant No. 2017YFA0403200), the National Natural Science Foundation of China (Grant No. U1830206), and the Science and Technology Innovation Program of Hunan Province (Grant No. 2021RC4026). 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