Related references
Note: Only part of the references are listed.
Article
Physics, Multidisciplinary
Zhen Ma et al.
Summary: We report a new family of twisted few layer graphite, which has distinct moire flat band structures that can be highly tuned. The moire band structure strongly depends on the layer number of the graphite, and near the magic angle, it exhibits two nearly flat bands coexisting with dispersive bands. This property enhances the possible superconductivity and also indicates that it is a novel topological flat band system.
FRONTIERS OF PHYSICS
(2023)
Article
Chemistry, Multidisciplinary
ShengNan Zhang et al.
Summary: We propose chiral decomposition rules for twisted N + M multilayer graphene configurations, which include arbitrary stacking order and mutual twist. In the chiral limit at the magic angle, the low-energy bands of these systems consist of chiral pseudospin doublets energetically entangled with two flat bands per valley induced by the moire superlattice potential. Numerical calculations based on realistic parametrization support the analytic construction. We also demonstrate that vertical displacement fields can open energy gaps between the pseudospin doublets and the two flat bands, allowing the flat bands to carry nonzero valley Chern numbers. These findings provide guidelines for the rational design of topological and correlated states in generic twisted graphene multilayers.
Article
Physics, Multidisciplinary
Jie Gu et al.
Summary: Twisted double-and mono-bilayer graphene are graphene-based moire materials hosting strongly correlated fermions in a gate-tunable conduction band with topologically non-trivial properties. The strong electron-electron interactions lead to a non-coplanar magnetic state and a set of competing ferromagnetic, topological charge density waves. The formation of charge density wave order, connected to a skyrmion lattice phase, is consistent with recent experiments.
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
Leonardo A. Navarro-Labastida et al.
Summary: The zero flat band modes in twisted graphene bilayers can converge into coherent Landau states with a dispersion σ2 = 1/3α for high-order magic angles, where α is a coupling parameter incorporating the twist angle and energetic scales. The square of the Hamiltonian is found to be approximately equivalent to a two-dimensional quantum harmonic oscillator. The interlayer currents in graphene can be identified with the angular momentum term, while the confinement potential acts as an effective quadratic potential. A quantization rule for high-order magic angles, αm+1 - αm = 3/2, is obtained through analysis of the zero-mode equation, boundary conditions, and scaling argument, and equipartition and quantization of kinetic, confinement, and angular momentum contributions are found, consistent with numerical calculations.
Article
Physics, Multidisciplinary
Anwei Zhang
Summary: This study investigates the relation between Berry curvature and quantum metric in the Dirac model of even-dimensional Chern insulator. The results suggest that the Chern number can be encoded in quantum metric as well as the surface area of the Brillouin zone on the hypersphere. The study also finds a corresponding relationship between the quantum metric and the metric on such a hypersphere. Additionally, a protocol for measuring the quantum metric in degenerate systems is provided.
Article
Physics, Multidisciplinary
Carmen Rubio-Verdu et al.
Summary: A study on twisted double bilayer graphene reveals the presence of three-fold rotational symmetry breaking, indicative of an interaction-driven electronic nematic phase that emerges from the normal metal state and is related to the scale of the moire lattice.
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
Shihao Zhang et al.
Summary: In this study, we theoretically investigate correlated insulator states and quantum anomalous Hall states in twisted multilayer graphene systems. We show that these systems can exhibit spin-polarized and valley-polarized insulator states under different interactions, and these states can be manipulated by external forces.
PHYSICAL REVIEW LETTERS
(2022)
Article
Multidisciplinary Sciences
Xiaomeng Liu et al.
Summary: The interaction between electrons in graphene under high magnetic fields leads to the formation of various quantum Hall ferromagnetic (QHFM) phases with broken spin or valley symmetry. Using scanning tunneling spectroscopy (STS), we were able to visualize atomic-scale electronic wave functions and observe valley ordering in QHFM phases, as well as spectral features of fractional quantum Hall phases in graphene. The results provide insights into the electronic properties of materials and their topological excitations.
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
Ling-Hui Tong et al.
Summary: Recent studies have shown that twisted monolayer-bilayer graphene (TMBG) has a higher tunability and can host moire flat bands. Through scanning tunneling microscopy and spectroscopy, a direct comparison between TMBG and twisted bilayer graphene (TBG) is conducted, confirming the existence of flat electronic bands in TMBG. The bandwidth of the flat-band peak in TMBG is slightly narrower than that in TBG. Additionally, the flat-band states in TMBG exhibit a unique layer-resolved localization-delocalization coexisting feature.
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
Physics, Multidisciplinary
Guoyu Luo et al.
Summary: In this study, we theoretically investigate the band structures and topological properties of AB-AB and AB-BA stacked twisted double bilayer graphene under heterostrain effect. We find that the heterostrain has different impacts on the two arrangements due to their different band gaps, and these gaps can be modified by a vertical electric field.
FRONTIERS OF PHYSICS
(2022)
Article
Physics, Multidisciplinary
Daniel Varjas et al.
Summary: Band geometry plays a significant role in topological lattice models, and the Berry curvature usually fluctuates in reciprocal space. However, lattice models with three or more degrees of freedom per unit cell can support exactly constant Berry curvature. Nevertheless, maintaining constant Berry curvature does not always enhance the properties of fractional Chern insulator states.
Article
Multidisciplinary Sciences
Le Liu et al.
Summary: This study observes the emergence of new correlated insulators from spin-polarized states to valley-polarized states in twisted double bilayer graphene. The results demonstrate a potential method to achieve isospin control and obtain new phases of matter in twisted multilayer systems.
NATURE COMMUNICATIONS
(2022)
Article
Multidisciplinary Sciences
Si-yu Li et al.
Summary: Researchers observed an electron crystal phase and studied the coupling between strong electron correlation and nontrivial band topology in twisted monolayer-bilayer graphene using scanning tunnelling microscopy.
NATURE COMMUNICATIONS
(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
Materials Science, Multidisciplinary
Leonardo A. Navarro-Labastida et al.
Summary: The chiral Hamiltonian for twisted graphene bilayers is analyzed in terms of its squared Hamiltonian, and the components of the Hamiltonian are examined in relation to the angle of rotation and wave-function localization properties. It is found that the non-Abelian operator represents interlayer currents between layers of triangular sublattices. The first magic-angle is determined by a balance between the negative energy contribution from interlayer currents and the positive contributions from kinetic and confinement energies.
Article
Materials Science, Multidisciplinary
David Bauer et al.
Summary: This paper emphasizes the importance of studying FQH phases where particles partially occupy energy bands that are not Landau levels. The authors construct lattice models for single-particle bands that are distinct from Landau levels even in the continuum limit. They explore the quantification of the difference between these bands and Landau levels through band geometry and electromagnetic response, and also analyze the localization-delocalization transition and the presence of bosonic and fermionic Laughlin states in these models.
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
Minhao He et al.
Summary: The study reveals that spontaneous symmetry breaking plays a crucial role in the correlated insulating and metallic states in twisted double bilayer graphene, which can be tuned by both the twist angle and an external electric field. The metallic states exhibit abrupt drops in resistivity as temperature decreases, suggesting that spontaneous symmetry breaking is the origin of the abrupt resistivity drops, while nonlinear transport seems to be due to Joule heating. These findings imply that similar mechanisms may be relevant across a broader class of semiconducting flat band van der Waals heterostructures.
Article
Multidisciplinary Sciences
Zhen Ma et al.
Summary: Twisted trilayer graphene is a simple realistic system with flat bands and nontrivial topology, making it an ideal platform for studying strongly correlated physics. The band structures of twisted TLG are influenced by the twist angle and perpendicular electric field, resulting in unique correlated states compared to other graphene structures.
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
Physics, Multidisciplinary
Yafei Ren et al.
Summary: Graphene bilayers exhibit zero-energy flatbands at specific magic twist angles, satisfying a Dirac equation with a non-Abelian SU(2) gauge potential. A semiclassical WKB approximation scheme is developed to analyze these zero-energy solutions, finding values of a dimensionless Planck's constant that correspond closely to numerically determined twist angles.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Multidisciplinary
Zhao Liu et al.
Summary: Twisted double bilayer graphene is predicted to be a versatile platform for realizing fractional Chern insulators at high temperatures, without the need for an external magnetic field, by tuning the gate potential and twist angle.
PHYSICAL REVIEW LETTERS
(2021)
Article
Multidisciplinary Sciences
Fabian R. Geisenhof et al.
Summary: In this study, a state with a conductance of 2e(2)h(-1) in bilayer graphene was discovered, exhibiting magnetic hysteresis and QAH behavior driven by orbital magnetism that can be tuned via electric and magnetic fields. The observed octet of QAH phases in bilayer graphene displays peculiar ferrimagnetic and ferrielectric order characterized by quantized anomalous charge, spin, valley and spin-valley Hall behavior.
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
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
Yuan Cao et al.
Summary: In magic-angle twisted bilayer graphene, intertwined phases with broken rotational symmetry have been identified, showing strong thermodynamic anisotropy and appearing above the underdoped region of the superconducting dome. A reduction in critical temperature is observed when it intersects with the superconducting dome, with the superconducting state exhibiting anisotropic response to in-plane magnetic fields, suggesting nematic ordering plays a significant role in the low-temperature phases of magic-angle TBG.
Article
Multidisciplinary Sciences
Xiaoxue Liu et al.
Summary: This study introduces a new device geometry to continuously tune the strength of electron-electron Coulomb interaction within twisted bilayer graphene, revealing opposite effects of charge screening on insulating and superconducting states.
Article
Multidisciplinary Sciences
Canxun Zhang et al.
Nature Communications
(2021)
Article
Materials Science, Multidisciplinary
Rhine Samajdar et al.
Summary: Graphene-based moiré systems have shown a variety of correlated phenomena, with evidence of electronic nematic order in twisted bilayer graphene. Analysis reveals that contributions to the nematic order parameter primarily come from states at the moiré scale, indicating the crucial role of moiré degrees of freedom. Additionally, the orientation of the nematic director in twisted double-bilayer graphene can be tuned by an externally applied electric field, providing a route to electrostatic control of electronic nematicity in moiré systems.
Article
Multidisciplinary Sciences
Minhao He et al.
Summary: The research uncovers a rich correlated phase diagram in twisted monolayer-bilayer graphene and identifies a new insulating state that can be explained by intervalley coherence with broken time reversal symmetry through electrical transport measurements.
NATURE COMMUNICATIONS
(2021)
Article
Materials Science, Multidisciplinary
Bruno Mera et al.
Summary: We describe a systematic method to construct models of Chern insulators with Berry curvature and the quantum volume form coinciding and being flat, which can host fractional Chern insulators. The construction of geometrically flat Kahler bands with Chern number equal to minus the total number of bands is shown, but it is not possible to construct geometrically perfectly flat Kahler bands with a finite number of bands. The effect of truncating hoppings at a finite length is also explored, showing some deviation from perfect Kahler bands but no significant impact on the flatness of geometrical properties.
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
Bartholomew Andrews et al.
Summary: The Hofstadter model is a popular choice for investigating the fractional quantum Hall effect on lattices, with recent experiments detecting richer physical properties in fractional Chern insulators with higher Chern numbers. Through simulations and experiments, the existence of fractional states is confirmed, along with discussions on metal-to-insulator phase transitions and the subtleties in stability distinction. The relative suitability of fractional Chern insulators in higher Chern number bands for proposed modern applications is also commented on.
Article
Materials Science, Multidisciplinary
Bruno Mera et al.
Summary: In this study of Chern insulators, the relationship between quantum metric, Berry curvature, Riemannian metric, and symplectic form is explored, showing that the minimal volume of parameter space is related to the first Chern number. The conditions for achieving minimal volume in both Brillouin zone and twist-angle space are also determined, with implications for the stability of fractional Chern insulators. Additionally, it is found that for two-band systems, the volume of the Brillouin zone is minimal under certain conditions related to Berry curvature and topological constraints.
Article
Materials Science, Multidisciplinary
Tomoki Ozawa et al.
Summary: This study investigates the relationship between topology and quantum metric in two-dimensional Chern insulators, proposing the concept of quantum volume as a measure for inferring the Chern number. Through inequalities and concrete models, it is concluded that quantum volume can provide a good estimate of the system's topology, especially for fermions filling Landau levels.
Article
Materials Science, Multidisciplinary
Gerardo G. Naumis et al.
Summary: The proposed Hamiltonian renormalization method maps zero-mode flat bands into ground states, with modes near zero energy having an antibonding nature in a triangular lattice. At magic angles, the intralayer frustration is exactly zero, suggesting that flat bands at magic angles are akin to floppy-mode bands in flexible crystals or glasses.
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
Simon Becker et al.
Summary: The study explores the unique properties of twisted bilayer graphene, revealing the presence of almost flat bands at certain magic angles and exponential squeezing of bands as the angle approaches zero. The dynamics of magic angles involve nonphysical complex eigenvalues, and the equidistant scaling of inverse magic angles is specific to the choice of tunneling potentials in the continuum model, not protected by symmetries. The protection of zero-energy states in the continuum model depends on the preservation of particle-hole symmetry, while the existence of flat bands and exponential squeezing are special properties of the chiral model.
Article
Materials Science, Multidisciplinary
Fedor K. Popov et al.
Summary: This study investigates the zero-energy states of the chirally symmetric continuum model of twisted bilayer graphene, revealing a hidden flat band of unphysical states with a pole instead of a zero. It is shown that the wave function of any state from the flat band has a zero or pole, with the flat band interpreted as a Landau level in an external magnetic field, leading to the identification of additional flat bands in the magnetic field.
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Materials Science, Multidisciplinary
Yi-Xiang Wang et al.
Summary: In this paper, the valley Chern number phase diagram of twisted double bilayer graphene (TDBG) was calculated, with the effects of spin-splitting and valley-splitting included phenomenologically. It was found that under certain conditions, an orbital Chern insulator emerges in TDBG, associated with a large orbital magnetization (OM), and the OM remains negative when the Fermi energy changes from the bottom to the top of the half-filling gap.
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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.
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