Observation of 
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-Valley Moiré Bands and Emergent Hexagonal Lattice in Twisted Transition Metal Dichalcogenides

Pei, Ding; Wang, Binbin; Zhou, Zishu; He, Zhihai; An, Liheng; He, Shanmei; Chen, Cheng; Li, Yiwei; Wei, Liyang; Liang, Aiji; Ávila, J.; Dudin, Pavel; Kandyba, Viktor; Giampietri, Alessio; Cattelan, Mattia; Barinov, Alexei; Liu, Zhongkai; Liu, Jianpeng; Weng, Hongming; Wang, Ning; Xue, Jiamin; Chen, Yulin

doi:10.1103/physrevx.12.021065

Cited by 28 publications

(28 citation statements)

References 45 publications

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“…Further, in semiconducting transition metal dichalcogenide (TMD) moiré systems, the Coulomb interaction strengths between particles in the moiré lattice can be continuously tuned via the moiré period [14,15]. Additionally, different real-space lattice geometries can be found in the low energy valence moiré bands, dependent on the valley degree of freedom: moiré orbitals on a triangular lattice are generally found for Kvalley moiré bands localized on a single atomic layer [14][15][16][17][18][19][20][21] while honeycomb lattices are found for Γ-valley moiré bands spread across each layer [22][23][24][25][26][27][28]. Notably, the energetic ordering of Γ-versus K-derived valence moiré bands is sensitively dependent on material combination, twist angle, and atomic relaxation effects [29].…”

Section: Introductionmentioning

confidence: 99%

The interplay of field-tunable strongly correlated states in a multi-orbital moiré system

Campbell¹,

Vitale²,

Brotons‐Gisbert³

et al. 2023

Preprint

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The interplay of charge, spin, lattice, and orbital degrees of freedom leads to a wide range of emergent phenomena in strongly correlated systems. In heterobilayer transition metal dichalcogenide moiré systems, recent observations of Mott insulators and generalized Wigner crystals are well described by triangular lattice single-orbital Hubbard models based on K-valley derived moiré bands. Richer phase diagrams, mapped onto multi-orbital Hubbard models, are possible with hexagonal lattices in Γ-valley derived moiré bands and additional layer degrees of freedom. Here we report the tunable interaction between strongly correlated hole states hosted by Γ-and K-derived moiré bands in a monolayer MoSe2 / natural WSe2 bilayer device. To precisely probe the nature of the correlated states, we optically characterise the behaviour of exciton-polarons and distinguish the layer and valley degrees of freedom. We find that the honeycomb Γ-band gives rise to a chargetransfer insulator described by a two-orbital Hubbard model with inequivalent ΓA and ΓB orbitals. With an out-of-plane electric field, we re-order the ΓB-and K-derived bands energetically, driving an abrupt redistribution of carriers to the layer-polarized K orbital where new correlated states are observed. Finally, by fine-tuning the band-alignment, we obtain degeneracy of the ΓB and K orbitals at the Fermi level. In this critical condition, stable Wigner crystals with carriers distributed across the two orbitals are observed until the Fermi-level reaches one hole per lattice site, whereupon the system collapses into a filled ΓB orbital. Our results establish a platform to investigate the interplay of charge, spin, lattice, and layer geometry in multi-orbital Hubbard model Hamiltonians.

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Section: Introductionmentioning

confidence: 99%

The interplay of field-tunable strongly correlated states in a multi-orbital moiré system

Campbell¹,

Vitale²,

Brotons‐Gisbert³

et al. 2023

Preprint

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“…In addition, recent ab-initio and continuum model calculations have shown that twisted Γ-valley homobilayers, such as MoS 2 , MoSe 2 , and WS 2 , produce two valence moiré bands with Dirac cone mimicking a honeycomb lattice, while the next set of lower energy four moiré bands simulates the two-orbital asymmetric p x -p y honeycomb lattice model [12][13][14][15]. Moreover, surprisingly in recent ARPES experiments Γ-valley moiré bands have been observed in the twisted WSe 2 [16,17], rendering it also a candidate material to realize the two-orbital honeycomb lattice model. These findings opens up an exciting avenue to simulate multi-orbital Hubbard-like models in TMD moiré materials.…”

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confidence: 96%

Kanamori-Moiré-Hubbard model for transition metal dichalcogenide homobilayers

Kaushal¹,

Dagotto²

2023

Preprint

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Ab-initio and continuum model studies predicted that the Γ valley transition metal dichalcogenide (TMD) homobilayers could simulate the conventional multi-orbital Hubbard model on the moiré Honeycomb lattice. Here, we perform the Wannierization starting from the continuum model and show that a more general Kanamori-Moiré-Hubbard model emerges, beyond the extensively studied standard multi-orbital Hubbard model, which can be used to investigate the many-body physics in the Γ valley TMD homobilayers. Using the unrestricted Hartree-Fock and Lanczos techniques, we study these half-filled multi-orbital moiré bands. By constructing the phase diagrams we predict the presence of an antiferromagnetic state and in addition we found unexepected and dominant states, such as a S = 1 ferromagnetic insulator and a charge density wave state. Our theoretical predictions made using this model can be tested in future experiments on the Γ valley TMD homobilayers.

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“…Recent transport measurements have revealed correlated insulating and zero-resistance states in the p-doped region of twisted bilayer and double-bilayer WSe 2 , − indicating a significant twist-induced modification in the valence band structure. Especially, the emergence of flat mini-bands at the edges of both Γ and K valleys has been predicted. − Although the twist-induced modifications have been estimated through theoretical modeling, the accuracy is limited by structural complexity and certain arbitrary parameters due to the lack of experimental data, such as the degree of lattice relaxation. − Pioneering angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM) studies have confirmed the existence of Γ-valley moiré bands and associated honeycomb and kagome-shaped charge distributions in TB WSe 2 . − However, the absence of evident K-valley flat bands, which are considered the main contributors to the zero-resistance state in twisted bilayer WSe 2 , seemingly contradicts existing transport results. , Theoretically, several causes have been proposed for the absence of K-valley flat bands in TB WSe 2 , such as insufficient lattice relaxation and weak interlayer coupling . Experimentally, indications of band flattening may be gleaned through a comparative analysis of K-valleys in twisted and nontwisted samples, which are currently limited in availability.…”

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confidence: 99%

“…The device used in this work was fabricated using a standard tear-and-stack method . The monolayer and few-layer WSe 2 flakes were mechanically exfoliated from a bulk crystal onto a SiO 2 wafer.…”

mentioning

confidence: 99%

“…The unfolded bandstructures of twisted bilayer WSe 2 are calculated by adopting the tight-binding method. The details of the tight-binding method of the twisted bilayer WSe 2 can be found in our previous work . The structure relaxation of twisted bilayer WSe 2 is performed by first-principles calculation, in which the Vienna ab initio simulation package with the projector-augmented wave potential method − is used.…”

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confidence: 99%

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Twist-Induced Modification in the Electronic Structure of Bilayer WSe₂

Pei

Zhou

et al. 2023

Nano Lett.

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The recent discovery of strongly correlated phases in twisted transitionmetal dichalcogenides (TMDs) highlights the significant impact of twist-induced modifications on electronic structures. In this study, we employed angle-resolved photoemission spectroscopy with submicrometer spatial resolution (μ-ARPES) to investigate these modifications by comparing valence band structures of twisted (5.3°) and nontwisted (AB-stacked) bilayer regions within the same WSe 2 device. Relative to the nontwisted region, the twisted area exhibits pronounced moirébands and ∼90 meV renormalization at the Γ-valley, substantial momentum separation between different layers, and an absence of flat bands at the K-valley. We further simulated the effects of lattice relaxation, which can flatten the Γ-valley edge but not the K-valley edge. Our results provide a direct visualization of twist-induced modifications in the electronic structures of twisted TMDs and elucidate their valley-dependent responses to lattice relaxation.

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Observation of Γ -Valley Moiré Bands and Emergent Hexagonal Lattice in Twisted Transition Metal Dichalcogenides

Cited by 28 publications

References 45 publications

The interplay of field-tunable strongly correlated states in a multi-orbital moiré system

The interplay of field-tunable strongly correlated states in a multi-orbital moiré system

Kanamori-Moiré-Hubbard model for transition metal dichalcogenide homobilayers

Twist-Induced Modification in the Electronic Structure of Bilayer WSe₂

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Observation of Γ -Valley Moiré Bands and Emergent Hexagonal Lattice in Twisted Transition Metal Dichalcogenides

Cited by 28 publications

References 45 publications

The interplay of field-tunable strongly correlated states in a multi-orbital moiré system

The interplay of field-tunable strongly correlated states in a multi-orbital moiré system

Kanamori-Moiré-Hubbard model for transition metal dichalcogenide homobilayers

Twist-Induced Modification in the Electronic Structure of Bilayer WSe2

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Twist-Induced Modification in the Electronic Structure of Bilayer WSe₂