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1. Moiré synaptic transistor with room-temperature neuromorphic functionality

   https://doi.org/10.1038/s41586-023-06791-1  

   Yan, Xiaodong; Zheng, Zhiren; Sangwan, Vinod K; Qian, Justin H; Wang, Xueqiao; Liu, Stephanie E; Watanabe, Kenji; Taniguchi, Takashi; Xu, Su-Yang; Jarillo-Herrero, Pablo; et al (December 2023, Nature)

   The convergence of topology and correlations represents a highly coveted realm in the pursuit of novel quantum states of matter [1, 2]. Introducing electron correlations to a quantum spin Hall (QSH) insulator can lead to the emergence of a fractional topological insulator and other exotic time-reversal-symmetric topological order [3– 10], not possible in quantum Hall and Chern insulator systems. However, the QSH insulator with quantized edge conductance remains rare, let alone that with significant correlations. In this work, we report a novel dual QSH insulator within the intrinsic monolayer crystal of TaIrTe4, arising from the interplay of its single-particle topology and density-tuned electron correlations. At charge neutrality, monolayer TaIrTe4 demonstrates the QSH insulator that aligns with single-particle band structure calculations, manifesting enhanced nonlocal transport and quantized helical edge conductance. Interestingly, upon introducing electrons from charge neutrality, TaIrTe4 only shows metallic behavior in a small range of charge densities but quickly goes into a new insulating state, entirely unexpected based on TaIrTe4’s single-particle band structure. This insulating state could arise from a strong electronic instability near the van Hove singularities (VHS), likely leading to a charge density wave (CDW). Remarkably, within this correlated insulating gap, we observe a resurgence of the QSH state, marked by the revival of nonlocal transport and quantized helical edge conduction. Our observation of helical edge conduction in a CDW gap could bridge spin physics and charge orders. The discovery of a dual QSH insulator introduces a new method for creating topological flat minibands via CDW superlattices, which offer a promising platform for exploring time-reversal-symmetric fractional phases and electromagnetism [3–5, 11, 12]. 

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2. Fractional Chern insulators in magic-angle twisted bilayer graphene

   https://doi.org/10.1038/s41586-021-04002-3  

   Xie, Yonglong; Pierce, Andrew T.; Park, Jeong Min; Parker, Daniel E.; Khalaf, Eslam; Ledwith, Patrick; Cao, Yuan; Lee, Seung Hwan; Chen, Shaowen; Forrester, Patrick R.; et al (December 2021, Nature)

   Abstract Fractional Chern insulators (FCIs) are lattice analogues of fractional quantum Hall states that may provide a new avenue towards manipulating non-Abelian excitations. Early theoretical studies 1–7 have predicted their existence in systems with flat Chern bands and highlighted the critical role of a particular quantum geometry. However, FCI states have been observed only in Bernal-stacked bilayer graphene (BLG) aligned with hexagonal boron nitride (hBN) 8 , in which a very large magnetic field is responsible for the existence of the Chern bands, precluding the realization of FCIs at zero field. By contrast, magic-angle twisted BLG 9–12 supports flat Chern bands at zero magnetic field 13–17 , and therefore offers a promising route towards stabilizing zero-field FCIs. Here we report the observation of eight FCI states at low magnetic field in magic-angle twisted BLG enabled by high-resolution local compressibility measurements. The first of these states emerge at 5 T, and their appearance is accompanied by the simultaneous disappearance of nearby topologically trivial charge density wave states. We demonstrate that, unlike the case of the BLG/hBN platform, the principal role of the weak magnetic field is merely to redistribute the Berry curvature of the native Chern bands and thereby realize a quantum geometry favourable for the emergence of FCIs. Our findings strongly suggest that FCIs may be realized at zero magnetic field and pave the way for the exploration and manipulation of anyonic excitations in flat moiré Chern bands. 

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3. Chern Insulators at Integer and Fractional Filling in Moiré Pentalayer Graphene

   https://doi.org/10.1103/PhysRevX.15.011045  

   Waters, Dacen; Okounkova, Anna; Su, Ruiheng; Zhou, Boran; Yao, Jiang; Watanabe, Kenji; Taniguchi, Takashi; Xu, Xiaodong; Zhang, Ya-Hui; Folk, Joshua; et al (February 2025, Physical Review X)

   The advent of moiré platforms for engineered quantum matter has led to discoveries of integer and fractional quantum anomalous Hall effects, with predictions for correlation-driven topological states based on electron crystallization. Here, we report an array of trivial and topological insulators formed in a moiré lattice of rhomobohedral pentalayer graphene (R5G). At a doping of one electron per moiré unit cell ( $\nu =1$), we see a correlated insulator with a Chern number that can be tuned between $C=0$and $+1$by an electric displacement field. This is accompanied by a series of additional Chern insulators with $C=+1$originating from fractional fillings of the moiré lattice— $\nu =1/4$, $1/3$, and $2/3$—associated with the formation of moiré-driven topological electronic crystals. At $\nu =2/3$the system exhibits an integer quantum anomalous Hall effect at zero magnetic field, but further develops hints of an incipient $C=2/3$fractional Chern insulator in a modest field. Our results establish moiré R5G as a fertile platform for studying the competition and potential intertwining of integer and fractional Chern insulators. Published by the American Physical Society2025 

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4. Realization of topological Mott insulator in a twisted bilayer graphene lattice model

   https://doi.org/10.1038/s41467-021-25438-1  

   Chen, Bin-Bin; Liao, Yuan Da; Chen, Ziyu; Vafek, Oskar; Kang, Jian; Li, Wei; Meng, Zi Yang (December 2021, Nature Communications)

   Abstract Magic-angle twisted bilayer graphene has recently become a thriving material platform realizing correlated electron phenomena taking place within its topological flat bands. Several numerical and analytical methods have been applied to understand the correlated phases therein, revealing some similarity with the quantum Hall physics. In this work, we provide a Mott-Hubbard perspective for the TBG system. Employing the large-scale density matrix renormalization group on the lattice model containing the projected Coulomb interactions only, we identify a first-order quantum phase transition between the insulating stripe phase and the quantum anomalous Hall state with the Chern number of ±1. Our results not only shed light on the mechanism of the quantum anomalous Hall state discovered at three-quarters filling, but also provide an example of the topological Mott insulator, i.e., the quantum anomalous Hall state in the strong coupling limit. 

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5. Insulators at fractional fillings in twisted bilayer graphene partially aligned to hexagonal boron nitride

   https://doi.org/10.1063/10.0019422  

   Wong, Dillon; Nuckolls, Kevin P.; Oh, Myungchul; Lee, Ryan L.; Watanabe, Kenji; Taniguchi, Takashi; Yazdani, Ali (June 2023, Low Temperature Physics)

   At partial fillings of its flat electronic bands, magic-angle twisted bilayer graphene (MATBG) hosts a rich variety of competing correlated phases that show sample-to-sample variations. Divergent phase diagrams in MATBG are often attributed to the sublattice polarization energy scale, tuned by the degree of alignment of the hexagonal boron nitride (hBN) substrates typically used in van der Waals devices. Unaligned MATBG exhibits unconventional superconductor and correlated insulator phases, while nearly perfectly aligned MATBG/hBN exhibits zero-field Chern insulating phases and lacks superconductivity. Here we use scanning tunneling microscopy and spectroscopy (STM/STS) to observe gapped phases at partial fillings of the flat bands of MATBG in a new intermediate regime of sublattice polarization, observed when MATBG is only partially aligned (θGr-hBN ≈ 1.65°) to the underlying hBN substrate. Under this condition, MATBG hosts not only phenomena that naturally interpolate between the two sublattice potential limits, but also unexpected gapped phases absent in either of these limits. At charge neutrality, we observe an insulating phase with a small energy gap (Δ < 5 meV) likely related to weak sublattice symmetry breaking from the hBN substrate. In addition, we observe new gapped phases near fractional fillings ν = ±1/3 and ν = ±1/6, which have not been previously observed in MATBG. Importantly, energy-resolved STS unambiguously identifies these fractional filling states to be of single-particle origin, possibly a result of the super-superlattice formed by two moiré superlattices. Our observations emphasize the power of STS in distinguishing single-particle gapped phases from many-body gapped phases in situations that could be easily confused in electrical transport measurements, and demonstrate the use of substrate engineering for modifying the electronic structure of a moiré flat-band material. 

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