We study the transition of $ν=1/3$ and $2/5$ fractional quantum Hall states of the honeycomb Hofstadter model as we tune to a two-orbital moiré superlattice Hamiltonian, motivated by the flat bands of twisted bilayer graphene in a perpendicular magnetic field. In doing so, we address the extent to which these states survive in moiré systems and analyze the nature of the transition. Through the use of a Peierls substitution, we determine the Landau-level splitting for the moiré Hamiltonian, and study the structure of the Chern bands for a range of magnetic flux per plaquette. We identify topological flat bands in the spectrum at low energies, with numerically tractable lattice geometries that can support the fractional quantum Hall effect. As we tune the model, we find that the orbital-polarized $ν=1/3$ and $2/5$ states corresponding to the honeycomb Hofstadter model survive up to $\approx 30\%$ of typical moiré superlattice parameters, beyond which they transition into an insulating phase. We present evidence for this through density matrix renormalization group calculations on an infinite cylinder, by verifying the charge pumping, spectral flow, entanglement scaling, and conformal field theory edge counting. We conclude that fractional quantum Hall states from the Hofstadter model can persist up to hopping amplitudes of the same order as those typical for moiré superlattice Hamiltonians, which implies generally that fractional states for moiré superstructures can be discerned simply by analyzing the dominant terms in their effective Hamiltonians.
Moiré superlattices in two-dimensional (2D) van der Waals (vdW) heterostructures provide 20 an efficient way to engineer electron band properties. The recent discovery of exotic quantum phases and their interplay in twisted bilayer graphene (tBLG) has built this moiré system one of the most renowned condensed matter platforms (1-10). So far the studies of tBLG has been mostly focused on the lowest two flat moiré bands at the first magic angle θm1 ~ 1.1°, leaving high-order moiré bands and magic angles largely unexplored. Here we report 25 an observation of multiple well-isolated flat moiré ban…
We theoretically explore 2d moiré heterostructures in lattice-commensurate magnetic fields as platforms for quantum simulation of a paradigmatic model of non-Fermi liquid physics: a Fermi-surface coupled to a fluctuating gauge field. In these moiré-Hofstadter (MH) systems, long-wavelength acoustic phonons exhibit singular interactions with electrons analogous to those of electrons with 2d gauge fields. This leads to a breakdown of Fermi-liquid theory at low temperatures. We show that a combination of large moiré-unit cell size, tunable Fermi-surface topology, and enhanced coupling to interlaye…
In magic angle twisted bilayer graphene (MATBG), the moiré superlattice potential gives rise to narrow electronic bands1 which support a multitude of many-body quantum phases. Further richness arises in the presence of a perpendicular magnetic field, where the interplay between moiré and magnetic length scales leads to fractal Hofstadter subbands. In this strongly correlated Hofstadter platform, multiple experiments have identified gapped topological and correlated states, but little is known about the phase transitions between them in the intervening compressible regimes. Here, using a scanni…
Fractal Hofstadter bands have become widely accessible with the advent of moiré superlattices, opening the door to studies of the effect of interactions in these systems. In this work we employ a renormalization group (RG) analysis to demonstrate that the combination of repulsive interactions with the presence of a tunable manifold of Van Hove singularities provides a new mechanism for driving unconventional superconductivity in Hofstadter bands. Specifically, the number of Van Hove singularities at the Fermi energy can be controlled by varying the flux per unit cell and the electronic filling…
Room-temperature multistage metastability in a moiré superstructure
Tsung-Dao Lee Institute, School of Physics and Astronomy, Shanghai Jiao Tong University（上海交大李政道理论与计算科学中心，物理与天文学院）；Massachusetts Institute of Technology（麻省理工学院）；Stanford University（斯坦福大学）；Peking University（北京大学）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Tianjin University of Technology（天津理工大学）
Topological Chiral Superconductivity in the Triangular-Lattice Hofstadter-Hubbard Model
The Hamburg Centre for Ultrafast Imaging and Institute for Quantum Physics, University of Hamburg（汉堡超快成像中心与量子物理研究所，汉堡大学）；Department of Physics and Astronomy, California State University Northridge（加州州立大学北岭分校物理与天文系）；Kavli Institute for Theoretical Physics, University of California, Santa Barbara（加州大学圣塔芭芭拉分校卡弗里理论物理研究所）；French American Center for Theoretical Science, CNRS, KITP, Santa Barbara（法国美国理论科学中心，法国国家科学研究中心，KITP，圣塔芭芭拉）；Canadian Institute for Advanced Research（加拿大高级研究院）
Emergent Gauge Flux and Spin Ordering in Magnetized Triangular Spin Liquids: Applications to Hofstadter-Hubbard Model
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料中心）；Beijing Key Laboratory of Quantum Devices, Peking University（北京大学北京量子器件重点实验室）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）
Chiral Spin Liquid and Quantum Phase Transition in the Triangular Lattice Hofstadter-Hubbard Model
University of California, Berkeley（加州大学伯克利分校）；Center for Computational Quantum Physics, Flatiron Institute（Flatiron Institute计算量子物理中心）；Harvard University（哈佛大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Columbia University（哥伦比亚大学）
The interplay of topological characteristics in real space and reciprocal space can lead to the emergence of unconventional topological phases. In this Letter, we implement a novel mechanism for generating higher-Chern flat bands on the basis of twisted bilayer graphene (TBG) coupled to topological magnetic structures in the form of the skyrmion lattice. In particular, we discover a scenario for generating $|C|=2$ dispersionless electronic bands when the skyrmion periodicity and the moiré periodicity are matched. Following the Wilczek argument, the statistics of the charge-carrying excitations…
Spin-charge separation in the triangular-lattice Hofstadter-Hubbard model
School of Intelligence Science and Technology, Peking University（北京大学智能科学学院）；Department of Physics and Astronomy, University of Pittsburgh（匹兹堡大学物理与天文系）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）
The discovery of flat bands with non-trivial band topology in magic angle twisted bi-layer graphene (MATBG) has provided a unique platform to study strongly correlated phe-nomena including superconductivity, correlated insulators, Chern insulators and magnetism. A fundamental feature of the MATBG, so far unexplored, is its high magnetic field Hof-stadter spectrum. Here we report on a detailed magneto-transport study of a MATBG de-vice in external magnetic fields of up to B = 31 T, corresponding to one magnetic flux quan-tum per moiré unit cell Φ0. At Φ0, we observe a re-entrant correlated insu…
At partial filling of a flat band, strong electronic interactions may favor gapped states harboring emergent topology with quantized Hall conductivity. Emergent topological states have been found in partially filled Landau levels and Hofstadter bands; in both cases, a large magnetic field is required to engineer the underlying flat band. The recent observation of quantum anomalous Hall effects (QAH) in narrow band moiré systems has led to the theoretical prediction that such phases may be realized even at zero magnetic field. Here we report the experimental observation of insulators with Chern…
Abstract We theoretically study the realization of quantum anomalous Hall insulator (QAHI) of composite fermions (CFs) in the twisted bilayer graphene (TBG) system. We show that the moiré pattern in TBG is not only able to provide a commensurate moiré superlattice, but also a tunable effective periodic potential necessary for the realization, without the need of imposing an additional superstructure as in the conventional GaAs system. These make the TBG an ideal platform for realizing the QAHI of CFs. We establish the phase diagram with respect to tunable experimental parameters based on the D…
Fractional Quantum Geometry in Topological Mott Regime
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）；Beijing Key Laboratory of Quantum Devices（北京量子器件重点实验室）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）
