Imaging two-dimensional generalized Wigner crystals

Li, Hongyuan; Li, Shaowei; Regan, Emma C.; Wang, Danqing; Zhao, Wenyu; Kahn, Salman; Yumigeta, Kentaro; Blei, Mark; Taniguchi, Takashi; Watanabe, Kenji; Tongay, Sefaattin; Zettl, Alex; Crommie, Michael F.; Wang, Feng

doi:10.1038/s41586-021-03874-9

Cited by 198 publications

(135 citation statements)

References 39 publications

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“…Moiré-trapped valley excitons and Wigner crystal states in TMDC bilayer twisted structures have also been reported. [513,514] The fabrication of 2D heterostructures, which is usually more complex than single homogeneous 2D materials, is critical for fully exploiting their properties, and artificial layer-bylayer stacking is a key approach. Early work mainly focused on conventional wet or dry transfer methods, [504][505][506] but it was found that the polymer residuals on top of the 2D crystals could deteriorate the device performance and hinder further stacking for the multilayers.…”

Section: D Heterostructuresmentioning

confidence: 99%

Fabrication Technologies for the On‐Chip Integration of 2D Materials

Jia

Zhang

et al. 2022

Small Methods

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The carrier mobilities of all the listed materials are experimental results except for those of SnSe, MoO 3 , MoSSe, WSSe, and graphdiyne that are theoretical calculated values; b) The n, k values for all the listed materials are at 1550 nm except for BP at 800 nm and h-BN at 1200 nm; c) The NLO parameters of PdSe 2 , PtSe 2 , BP, h-BN, MoO 3 , and CsPbBr 3 are at 800 nm. Those of MoS 2 and Bi 2 Te 3 are at 1060 nm. Those of other materials are at 1550 nm. In addition to third-order optical nonlinearity, strong second-order optical nonlinearity has been observed for graphene, GO, MoS 2 , WSe 2 , PdSe 2 , and h-BN, with typical χ (2) values varying from 10 -12 -10 -7 m V -1 . [33,[116][117][118][119][120] ; d) The values of n 2 and β are dependent on the film thickness, here we only provide typical values obtained from experimental measurements.

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Section: D Heterostructuresmentioning

confidence: 99%

Fabrication Technologies for the On‐Chip Integration of 2D Materials

Jia

Zhang

et al. 2022

Small Methods

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“…However, the physical situation at N = 1 lies beyond the strict regime of control within our approach and is possibly described by an entirely different fixed-point. Moreover, the specific form of translational symmetry breaking at large−N in our theory is different from the √ 3× √ 3 charge ordering observed experimentally [19]. It would be interesting to use a combination of more sophisticated numerical and analytical techniques to directly study the strongly coupled theory in the N = 1 limit in the future.…”

Section: Discussionmentioning

confidence: 79%

“…If g < 0, λ > |g| the ground state for s < 0 corresponds to having only one of the vortex flavors condensed, leading to an insulator with a single chargon on every third site [16]; see Figure 1. This is the Wigner crystalline phase that one would expect from purely classical considerations due to the further neighbor Coulomb repulsion on the triangular lattice, and is quite likely the phase observed in certain moiré TMD bilayers at strong interactions [19]. On the other hand, for g > 0 it will be energetically favorable to condense all of the vortex flavors, leading to other charge-ordered insulators [16] (see Figure 5(a)).…”

Section: B Dual Vortex Theorymentioning

confidence: 81%

Theory of a Continuous Bandwidth-tuned Wigner-Mott Transition

Musser,

Senthil,

Chowdhury

2021

Preprint

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We develop a theory for a continuous bandwidth-tuned transition at fixed fractional electron filling from a metal with a generic Fermi surface to a 'Wigner-Mott' insulator that spontaneously breaks crystalline space-group symmetries. Across the quantum critical point, (i) the entire electronic Fermi surface disappears abruptly upon approaching from the metallic side, and (ii) the insulating charge gap and various order-parameters associated with the spontaneously broken space-group symmetries vanish continuously upon approaching from the insulating side. Additionally, the insulating side hosts a Fermi surface of neutral spinons. We present a framework for describing such continuous metal-insulator transitions (MIT) and analyze the example of a bandwidth-tuned transition at a filling, ν = 1/6, for spinful electrons on the triangular lattice. By extending the theory to a certain large-N limit, we provide a concrete example of such a continuous MIT and discuss numerous experimental signatures near the critical point. We place our results in the context of recent experiments in moiré transition metal dichalcogenide materials.

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“…1(a)) and localized Wannier orbitals form a uniquely simple platform to explore phases driven by strong interactions [2,3]. Indeed, upon sweeping the density of electrons per Moiré unit cell, incompressible charge ordered states have been observed at various fractional fillings [3][4][5]. These charge orders can be viewed as a generalized Wigner crystalline state that reduces the symmetry of the underlying Moiré lattice, as they are driven by the long-range Coulomb interaction.…”

mentioning

confidence: 99%

Melting of generalized Wigner crystals in transition metal dichalcogenide heterobilayer Moiré systems

Matty¹,

Kim²

2021

Preprint

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Moiré superlattice systems such as transition metal dichalcogenide heterobilayers have garnered significant recent interest due to their promising utility as tunable solid state simulators. Recent experiments on a WSe2/WS2 heterobilayer detected incompressible charge ordered states that one can view as generalized Wigner crystals. The tunability of the hetero-TMD Moiré system presents an opportunity to study the rich set of possible phases upon melting these charge-ordered states.Here we use Monte Carlo simulations to study these intermediate phases in between incompressible charge-ordered states in the strong coupling limit. We find two distinct stripe solid states to be each preceded by distinct types of nematic states. In particular, we discover microscopic mechanisms that stabilize each of the nematic states, whose order parameter transforms as the two-dimensional E representation of the Moiré lattice point group. Our results provide a testable experimental prediction of where both types of nematic occur, and elucidate the microscopic mechanism driving their formation.

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Imaging two-dimensional generalized Wigner crystals

Cited by 198 publications

References 39 publications

Fabrication Technologies for the On‐Chip Integration of 2D Materials

Fabrication Technologies for the On‐Chip Integration of 2D Materials

Theory of a Continuous Bandwidth-tuned Wigner-Mott Transition

Melting of generalized Wigner crystals in transition metal dichalcogenide heterobilayer Moiré systems

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