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Article
Physics, Multidisciplinary
Zhen Ma et al.
Summary: We study the electronic structure of double-twisted few-layer graphite and find that it can host two pairs of degenerate Moire flat bands, twice that of the magic angle twisted bilayer graphene. The density of states at the Fermi level is doubled in double-twisted few-layer graphite, indicating potentially stronger correlation effects.
SCIENCE CHINA-PHYSICS MECHANICS & ASTRONOMY
(2023)
Article
Multidisciplinary Sciences
Jiaqi Cai et al.
Summary: This study reports experimental evidence of fractional quantum anomalous Hall (FQAH) states in twisted MoTe2 bilayers. By using magnetic circular dichroism measurements and trion photoluminescence as a sensor, the researchers demonstrate the presence of FQAH states by observing the corresponding dispersion curves and linear shifts. These topological states can be electrically driven into topologically trivial states and provide a platform for exploring fractional excitations.
Article
Multidisciplinary Sciences
Kevin P. Nuckolls et al.
Article
Multidisciplinary Sciences
Aviram Uri et al.
Summary: Researchers have created a highly tunable quasicrystal structure by twisting three layers of graphene and forming two mutually incommensurate moire patterns. This 'moire quasicrystal' allows for control over the electronic system between periodic and quasiperiodic regimes, and exhibits superconductivity and flavour-symmetry-breaking phase transitions.
Article
Physics, Multidisciplinary
Qiang Gao et al.
Summary: This article proposes a setup based on periodically strained graphene that reproduces key aspects of twisted moire heterostructures. The system has almost ideal flat bands with valley-resolved Chern number +/- 1, exhibiting larger interaction-induced gaps and smaller quasiparticle dispersion compared to twisted graphene systems.
PHYSICAL REVIEW LETTERS
(2023)
Article
Multidisciplinary Sciences
Jiachen Yu et al.
Nature Communications
(2023)
Article
Physics, Multidisciplinary
Naoto Nakatsuji et al.
Summary: This study presents comprehensive theoretical studies on the lattice relaxation and electronic structures of general nonsymmetric twisted trilayer graphenes. It reveals that the lattice structure forms patchwork of moire-of-moire domains and exhibits distinct chiral and alternating stacks. The electronic band calculations show the existence of topological boundary states in the chiral case and the coexistence of flat bands and monolayerlike Dirac cones in the alternating trilayer.
Article
Physics, Multidisciplinary
Junkai Dong et al.
Summary: Motivated by higher Chern bands in twisted graphene multilayers, we investigate flat bands with arbitrary Chern number C and ideal quantum geometry. We find exact fractional Chern insulator (FCI) ground states for C > 1 bands with short-range interactions. By decomposing the higher Chern bands into separate bands with Chern number 1, we establish an SU(C) action combining real and momentum space translations and derive analytical constructions of FCI ground states. We confirm our predictions through numerical simulations and discuss implications for experimentally accessible systems such as monolayer graphene twisted relative to a Bernal bilayer.
PHYSICAL REVIEW RESEARCH
(2023)
Article
Physics, Multidisciplinary
Jie Wang et al.
Summary: In this work, a theory for all topological ideal flatbands with non-zero Chern number is presented, disproving the common belief that nonuniform Berry curvature destabilizes fractional Chern insulators. The theory shows that both Abelian and non-Abelian model fractional Chern insulators can be stabilized as exact zero-energy ground states, regardless of the nonuniformity of the Berry curvature.
PHYSICAL REVIEW RESEARCH
(2023)
Article
Materials Science, Multidisciplinary
Yuncheng Mao et al.
Summary: Stacking three monolayers of graphene with a twist creates two moire patterns, resulting in a moire-of-moire structure at larger distances. A low-energy theory is developed to describe the spectrum beyond the moire length scale, which includes one Dirac cone at the FM point and two weakly gapped points at KM and K'M in each valley of the underlying graphene. The model exhibits spatially varying velocities and small gaps in the moire-of-moire unit cell, and the resulting spectrum is protected by time-reversal and twofold-rotation symmetries.
Article
Materials Science, Multidisciplinary
Patrick J. Ledwith et al.
Summary: Fractional Chern insulators, a type of crystalline system with Chern bands, exhibit the physics of fractional quantum Hall effect. This study introduces the concept of vortexability from a real-space perspective to stabilize fractional Chern insulators. Vortexable Chern bands allow the introduction of vortices into any band wavefunction while remaining within the same band, enabling the realization of FCI states. These vortexable bands are more general than the lowest Landau level (LLL), and a recipe for constructing them in graphene-based systems is provided. Various examples are presented to demonstrate the effectiveness of this approach.
Article
Physics, Multidisciplinary
H. Polshyn et al.
Summary: Strong Coulomb interactions between electrons can lead to the emergence of topological gapped states in partially filled flat bands. Recent observations in twisted monolayer-bilayer graphene have shown insulators with Chern number C=1 at zero-magnetic-field limit, suggesting potential for further exploration of zero-magnetic-field phases with fractional statistics.
Article
Physics, Multidisciplinary
Jiachen Yu et al.
Summary: This study examines the phase diagram of isospin polarization in magic-angle twisted bilayer graphene and discovers multiple many-body quantum phases and topological states in narrow energy bands, providing insights into the transitions between these states and their interplay with interactions and symmetry breaking.
Article
Physics, Multidisciplinary
Jie Wang et al.
Summary: This paper proposes models of twisted multilayer graphene that have exactly flat Bloch bands with arbitrary Chern numbers and ideal band geometries. The ideal band geometries and high Chern numbers of the flatbands imply the possibility of hosting exotic fractional Chern insulators, which have unique properties under short-range interactions.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Multidisciplinary
Glenn Wagner et al.
Summary: We investigate the phase diagram of twisted bilayer graphene (TBG) in the normal state, considering doping and strain dependence. Our comprehensive calculations reveal the competition and coexistence of three intertwined orders: a fully symmetric phase, flavor-symmetry-breaking states, and an incommensurate Kekule spiral (IKS) order. The IKS order is found to be ubiquitous for noninteger doping as well, consistent with experimental observations of electronic compressibility and Fermi surface structure. This study suggests a unified picture of the phase diagram in terms of IKS order.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Multidisciplinary
Patrick J. Ledwith et al.
Summary: This study considers a family of twisted graphene multilayers and shows that they exhibit similar features to twisted bilayer graphene, including specific "magic angle" positions and ideal quantum geometry. Furthermore, it is found that ideal quantum geometry is closely related to the construction of fractional quantum Hall model wave functions.
PHYSICAL REVIEW LETTERS
(2022)
Article
Multidisciplinary Sciences
Simon Turkel et al.
Summary: The magic-angle twisted trilayer graphene has shown a potential for engineering strongly correlated flat bands. Using low-temperature scanning tunneling microscopy, researchers have observed a strong reconstruction of the moire lattice in real trilayer samples, leading to the formation of localized twist-angle faults. These localized regions exhibit different electronic structures compared to the background regions, resulting in a doping-dependent, spatially granular electronic landscape.
Review
Nanoscience & Nanotechnology
Kin Fai Mak et al.
Summary: This article elaborates on the recent developments and future opportunities and challenges in fundamental research on semiconductor moire materials, with a particular focus on transition metal dichalcogenides.
NATURE NANOTECHNOLOGY
(2022)
Article
Physics, Multidisciplinary
Sameer Grover et al.
Summary: Using a scanning superconducting quantum interference device on a tip, a spatial patchwork of different Chern insulator states in twisted bilayer graphene is imaged. The nanoscale equilibrium orbital magnetism induced by the Berry curvature is detected, along with its two constituent components.
Article
Physics, Multidisciplinary
Jung Pyo Hong et al.
Summary: Experimental works have shown that magic angle twisted bilayer graphene exhibits spontaneous symmetry-breaking transitions, and scientists have identified competitive symmetry-breaking states by analyzing sublattice polarization and Kekule distortions in scanning tunneling microscopy.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Multidisciplinary
Dumitru Calugaru et al.
Summary: This article analytically computes the scanning tunneling microscopy (STM) signatures of integer-filled correlated ground states of the magic angle twisted bilayer graphene (TBG) narrow bands and assesses the possibility of Kekule distortion (KD). The results show that coupling the two opposite graphene valleys does not always result in KD.
PHYSICAL REVIEW LETTERS
(2022)
Article
Materials Science, Multidisciplinary
Miao Liang et al.
Summary: In this paper, we theoretically investigate the moire band structures of double twisted few layer graphene (DTFLG) with different arrangements of monolayer graphene (MLG) and bilayer graphene (BLG). We classify DTFLG into four categories based on the relative rotation direction of the twist angles and the middle van der Waals layer, and find that they exhibit unique band structures, including perfect flat bands at the magic angle and isolated narrow bands. The influence of electric field and topological features of the moire bands are also explored. Our findings suggest that DTFLG, especially (X + 1 + Z)-ATFLG and (X + 2 + Z)-CTFLG, are promising platforms to study moire flat band induced correlation and topological effects.
Article
Physics, Multidisciplinary
Shaowen Chen et al.
Summary: Twisted monolayer-bilayer graphene (tMBG) systems exhibit various correlated metallic and insulating states, as well as topological magnetic states. The phase diagram of tMBG can be switched under different perpendicular electric fields, providing a tunable platform for investigating correlated and topological states.
Article
Physics, Multidisciplinary
Patrick J. Ledwith et al.
Summary: This paper provides a comprehensive review of a recently developed strong coupling theory of magic-angle graphene, showcasing its ability to capture both insulating and superconducting states and discussing potential realizations of various states such as fractional Chern states and flavor ordered insulators. The importance of charged topological textures in inducing superconductivity, along with the role of effective super-exchange coupling in pairing and setting the effective mass of Cooper pairs, is emphasized. Furthermore, the potential for predicting new superconducting platforms, including the alternating twist trilayer platform, is explored and contrasted with strong coupling theories for other superconductors.
Article
Multidisciplinary Sciences
Yonglong Xie et al.
Summary: Fractional Chern insulators (FCIs) are lattice analogues of fractional quantum Hall states and have been recently observed in magic-angle twisted BLG at low magnetic field. The appearance of these states at 5 T is accompanied by the disappearance of nearby topologically trivial charge density wave states.
Article
Physics, Multidisciplinary
Xi Zhang et al.
Summary: This study demonstrates a higher-order moire of moire superlattice in twisted trilayer graphene, showing correlated insulating states near the half filling of the moire superlattice at an extremely low carrier density, where zero-resistance transport behavior is also observed. The full-occupancy states are semimetallic and gapless, distinct from the twisted bilayer systems.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Multidisciplinary
Petr Stepanov et al.
Summary: Research has shown that the odd integer filling factors in h-BN nonaligned devices correspond to symmetry broken Chern insulators with a Chern number of C = +1 and a relatively high Curie temperature. Under a perpendicular magnetic field, the Chern insulator at v = +1 transitions from C = +1 to C = 3, characterized by a quantized Hall plateau. Additionally, the device exhibits strong superconducting phases with critical temperatures up to Tc ≈ 3.5 K.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Multidisciplinary
Jie Wang et al.
Summary: Flatbands are present in various condensed matter systems and exhibit intrinsic geometric properties. This study investigates the relationship between flatbands with specific geometric properties and Landau levels, as well as the impact of geometric fluctuations on interactions.
PHYSICAL REVIEW LETTERS
(2021)
Article
Multidisciplinary Sciences
Jeong Min Park et al.
Summary: Moire superlattices have become a platform for studying correlated physics and superconductivity with unprecedented tunability. This study on magic-angle twisted trilayer graphene reveals a better tunability of electronic structure and superconducting properties than magic-angle twisted bilayer graphene, with implications for the understanding of strongly coupled superconductivity. The results suggest that the system can be electrically tuned close to the crossover to a two-dimensional Bose-Einstein condensate, indicating the potential for revolutionizing applications of superconductivity.
Article
Physics, Multidisciplinary
Shuigang Xu et al.
Summary: The study of electronic transport properties of twisted monolayer-bilayer graphene reveals highly tunable van Hove singularities that can cause strong correlation effects under optimum conditions by changing the twist angle or applying an electric field. This demonstrates the potential for correlated insulating states in a structure of monolayer and bilayer graphene with a small twist between them.
Article
Multidisciplinary Sciences
Zeyu Hao et al.
Summary: By constructing a van der Waals heterostructure with three stacked graphene layers at alternating twist angles, researchers observed tunable superconductivity at a specific twist angle. The superconducting regions are associated with flavor polarization of moire bands and are bounded by a van Hove singularity at high displacement fields, indicating unconventional moire superconductivity.
Editorial Material
Nanoscience & Nanotechnology
Eva Y. Andrei et al.
Summary: Moire systems formed by 2D atomic layers have versatile electrical and optical properties, hosting exotic phenomena like superconductivity, correlated insulator states, and orbital magnetism. In this Viewpoint, researchers studying various aspects of moire materials discuss the most exciting directions in this rapidly expanding field.
NATURE REVIEWS MATERIALS
(2021)
Article
Materials Science, Multidisciplinary
B. Andrei Bernevig et al.
Summary: We derive the explicit Hamiltonian of twisted bilayer graphene with Coulomb interaction, demonstrating positive semidefinite Hamiltonians when projected into flat bands. It is proved that the interacting TBG Hamiltonian exhibits an exact U(4) symmetry in the flat band limit. The existence of chiral limits with enlarged symmetry suggests a possible undiscovered duality of the model.
Article
Materials Science, Multidisciplinary
Yarden Sheffer et al.
Summary: In the chiral model of magic-angle twisted bilayer graphene, the flat bands remain exactly flat in the presence of a perpendicular magnetic field, with an exact mapping to the lowest Landau level wave functions under an effective magnetic field. A topological phase transition occurs when the external field reaches a specific value, allowing for analysis of fractional Chern insulators states. Unconventional dependence of the energy gap on the magnetic field is also observed.
Article
Materials Science, Multidisciplinary
Yves H. Kwan et al.
Summary: In this study, it was found that magic-angle twisted bilayer graphene exhibits a robust quantized anomalous Hall effect at a specific filling factor, which is attributed to the formation of a particular ground state with valley- and spin-polarization. Furthermore, three different types of domain wall were identified and studied in terms of their properties and energies using theoretical arguments and Hartree-Fock calculations adapted for inhomogeneous moire systems. These results have implications for transport and scanning probe experiments.
Article
Materials Science, Multidisciplinary
Oskar Vafek et al.
Summary: The study revisits the localized Wannier state description of twisted bilayer graphene, focusing on the chiral limit. It provides a simple method for constructing two-dimensional exponentially localized yet valley-polarized Wannier states while maintaining all unobstructed symmetries. The analysis includes unitary particle-hole symmetry, C2T symmetry, and chiral particle-hole symmetry.
Article
Physics, Multidisciplinary
Jie Wang et al.
Summary: This paper presents a mathematical and numerical analysis of flat-band wave functions in the chiral model of twisted bilayer graphene at magic twist angles. It demonstrates exact intravalley inversion symmetry and discusses the increased circulating current at higher magic angles. The study also explores physical implications for scanning tunneling spectroscopy, orbital magnetization, and interaction effects.
PHYSICAL REVIEW RESEARCH
(2021)
Article
Materials Science, Multidisciplinary
Patrick Wilhelm et al.
Summary: An extensive study was conducted on interaction-driven insulators in spin- and valley-polarized moire flat bands of twisted bilayer graphene, revealing fractional Chern insulator phases and competing charge-density-wave phases. Analysis at different parameters highlighted the competition between these phases, with kinetic energy and Coulomb interaction strength playing crucial roles. The ground-state selection was intuitively understood to be driven by the interplay between single-particle and interaction-induced hole dispersion with the Berry curvature of the Chern bands. The resulting phase diagram showed remarkable agreement with experimental findings, extending the relevance of the results beyond graphene-based materials.
Article
Materials Science, Multidisciplinary
Jingtian Shi et al.
Summary: The quantum anomalous Hall (QAH) effect is sometimes observed in twisted bilayer graphene (tBG) when nearly aligned with an encapsulating hexagonal boron nitride (hBN) layer. The presence or absence of the QAH effect in individual devices is related to the commensurability between graphene/graphene and graphene/hBN moire patterns. The QAH effect is likely to occur when the moire patterns form a supermoire pattern near a commensurate point and have a percolating topologically nontrivial QAH phase.
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Physics, Multidisciplinary
Ming Xie et al.
PHYSICAL REVIEW LETTERS
(2020)
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