Topological charge density waves at half-integer filling of a moiré superlattice

Polshyn, Hryhoriy; Zhang, Yuxuan; Kumar, Manish; Soejima, Tomohiro; Ledwith, Patrick J.; Watanabe, Kenji; Taniguchi, Takashi; Vishwanath, Ashvin; Zaletel, Michael P.; Young, Andrea

doi:10.1038/s41567-021-01418-6

Cited by 44 publications

(29 citation statements)

References 42 publications

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“…The TSbroken FCI, as well as the observed TS-broken Chern insulators, imply an intriguing hybridization of conventional CDW and topological phase. Such combination of CDW and topological features is also numerically discovered in  = 0, ±1, 2 bands of several toy tight-binding models [84,139,189] and experimentally observed in other moiré materials [165,186]. The hybrid states in || = 2 bands may originate from ferromagnetism of internal degree of freedoms and their entanglement with real-space translation in high Chern number bands [186,189].…”

Section: Experiments In Bernal-stacked Bilayer Graphenesupporting

confidence: 64%

“…Values of and trivial correlated insulator = 0 and integer ≠ 0 charge density wave = 0 and fractional integer quantum Hall states in LLs integer ≠ 0 and = 0 TS-preserving Chern insulators integer ≠ 0 and integer ≠ 0 TS-broken Chern insulators (also observed in Refs. [165,186]) integer ≠ 0 and fractional fractional quantum states in LLs fractional and = 0 TS-preserving fractional Chern insulators fractional and fractional , and have the same denominator TS-broken fractional Chern insulators fractional and fractional , denominator of is a multiple of that of exotic fractional Chern insulators fractional and fractional , and have the coprime denominators Ample attention has been directed towards understanding these high- FCIs. Intuitively, they may have a relation with the conventional FQH states in || copies of the LLL, which also carry Chern number  as a whole.…”

Section: Incompressible Statesmentioning

confidence: 99%

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Recent Developments in Fractional Chern Insulators

Liu¹,

Bergholtz²

2022

Preprint

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Fractional Chern insulators (FCIs) are lattice generalizations of the conventional fractional quantum Hall effect (FQHE) in two-dimensional (2D) electron gases. They typically arise in a 2D lattice without time-reversal symmetry when a nearly flat Bloch band with nonzero Chern number is partially occupied by strongly interacting particles. Band topology and interactions endow FCIs exotic topological orders which are characterized by the precisely quantized Hall conductance, robust ground-state degeneracy on high-genus manifolds, and fractionalized quasiparticles. Since in principle FCIs can exist at zero magnetic field and be protected by a large energy gap, they provide a potentially experimentally more accessible avenue for observing and harnessing FQHE phenomena. Moreover, the interplay between FCIs and lattice-specific effects that do not exist in the conventional continuum FQHE poses new theoretical challenges. In this chapter, we provide a general introduction of the theoretical model and numerical simulation of FCIs, then pay special attention on the recent development of this field in moiré materials while also commenting on potential alternative implementations in cold atom systems. With a plethora of exciting theoretical and experimental progress, topological flat bands in moiré materials such as magic-angle twisted bilayer graphene on hexagonal boron nitride have indeed turned out to be a remarkably versatile platform for FCIs featuring an intriguing interplay between topology, geometry, and interactions.

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Section: Experiments In Bernal-stacked Bilayer Graphenesupporting

confidence: 64%

Section: Incompressible Statesmentioning

confidence: 99%

Recent Developments in Fractional Chern Insulators

Liu¹,

Bergholtz²

2022

Preprint

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“…Topological states have also been proposed in these materials based on valley contrast physics, that is, moiré bands possess opposite Chern numbers in the K and K' valleys of the Brillouin zone 1,22,[25][26][27][28][29][30] . In particular, the QAH effect has been observed in graphene-based moiré systems [8][9][10][11][12][13] , and is consistent with a fully valley-polarized ground state as a result of the interaction-driven valley symmetry…”

mentioning

confidence: 56%

Valley-coherent quantum anomalous Hall state in AB-stacked MoTe2/WSe2 bilayers

Mak

Tao

Shen

et al. 2022

Preprint

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Moiré materials provide fertile ground for the correlated and topological quantum phenomena. Among them, the quantum anomalous Hall (QAH) effect, in which the Hall resistance is quantized even under zero magnetic field, is a direct manifestation of the intrinsic topological properties of a material and an appealing attribute for low-power electronics applications. The QAH effect has been observed in both graphene and transition metal dichalcogenide (TMD) moiré materials. It is thought to arise from the interaction-driven valley polarization of the narrow moiré bands. Here, we show surprisingly that the newly discovered QAH state in AB-stacked MoTe2/WSe2 moiré bilayers is not valley-polarized but valley-coherent. The layer- and helicity-resolved optical spectroscopy measurement reveals that the QAH ground state possesses spontaneous spin (valley) polarization aligned (anti-aligned) in two TMD layers. In addition, saturation of the out-of-plane spin polarization in both layers occurs only under high magnetic fields, supporting a canted spin texture. Our results call for a new mechanism for the QAH effect and highlight the potential of TMD moiré materials with strong electronic correlations and spin-orbit interactions for exotic topological states.

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“…6a), which exceeds the value for Wigner crystallization in 2DEGs 49 . The zero Chern number indicates a trivial band topology different from the topological charge density wave and fractional Chern insulator residing in the first moiré band of other moiré graphene systems [50][51][52] . Notably, the Chern number is non-zero in twisted double bilayer graphene of the stacking of AB-AB at the same fillings and D field, indicating that the stacking order plays a crucial role in forming the Wigner crystal.…”

Section: Criterion For the Wigner Crystal Statementioning

confidence: 98%

Tunable quantum criticalities in an isospin extended Hubbard model simulator

Cheng

Chen

et al. 2022

Nature

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Studying strong electron correlations has been an essential driving force for pushing the frontiers of condensed matter physics. In particular, in the vicinity of correlation-driven quantum phase transitions (QPTs), quantum critical fluctuations of multiple degrees of freedom facilitate exotic many-body states and quantum critical behaviours beyond Landau’s framework1. Recently, moiré heterostructures of van der Waals materials have been demonstrated as highly tunable quantum platforms for exploring fascinating, strongly correlated quantum physics2–22. Here we report the observation of tunable quantum criticalities in an experimental simulator of the extended Hubbard model with spin–valley isospins arising in chiral-stacked twisted double bilayer graphene (cTDBG). Scaling analysis shows a quantum two-stage criticality manifesting two distinct quantum critical points as the generalized Wigner crystal transits to a Fermi liquid by varying the displacement field, suggesting the emergence of a critical intermediate phase. The quantum two-stage criticality evolves into a quantum pseudo criticality as a high parallel magnetic field is applied. In such a pseudo criticality, we find that the quantum critical scaling is only valid above a critical temperature, indicating a weak first-order QPT therein. Our results demonstrate a highly tunable solid-state simulator with intricate interplay of multiple degrees of freedom for exploring exotic quantum critical states and behaviours.

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Topological charge density waves at half-integer filling of a moiré superlattice

Cited by 44 publications

References 42 publications

Recent Developments in Fractional Chern Insulators

Recent Developments in Fractional Chern Insulators

Valley-coherent quantum anomalous Hall state in AB-stacked MoTe2/WSe2 bilayers

Tunable quantum criticalities in an isospin extended Hubbard model simulator

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