Anomalous Hall Crystals in Rhombohedral Multilayer Graphene. I. Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Magnetic Field

Physical Review Letters, Journal Year: 2024, Volume and Issue: 133(20)

Published: Nov. 12, 2024

Recent experiments on rhombohedral pentalayer graphene with a substrate-induced moiré potential have identified both Chern insulators and fractional quantum Hall states at zero magnetic field. Surprisingly, these are observed in strong displacement fields where the effects of lattice weak, seem to be readily accessed without fine-tuning. To address experimental puzzles, we study model interacting electrons this geometry. Within self-consistent Hartree-Fock (SCHF) calculations, find an isolated band small bandwidth good Exact diagonalization density-matrix renormalization group calculations confirm hosts Remarkably, is stable wide range angles, four through six layers, varying hopping parameters, and-most strikingly-survives SCHF when vanishes. In limit, state spontaneously breaks time-reversal translation symmetry simultaneously, giving topological crystalline that term "anomalous crystal." We argue general mechanism create bands multilayer graphene, opening door studying interplay between electronic topology, fractionalization, spontaneous breaking.

Language: Английский

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Fractional Quantum Anomalous Hall Effect in Rhombohedral Multilayer Graphene in the Moiréless Limit

Physical Review Letters, Journal Year: 2024, Volume and Issue: 133(20)

Published: Nov. 12, 2024

The standard theoretical framework for fractional quantum anomalous Hall (FQAH) effect assumes an isolated flat Chern band in the single particle level. In this Letter, we challenge paradigm FQAH recently observed pentalayer rhombohedrally stacked graphene aligned with hexagonal boron nitride. We show that external moiré superlattice potential is simply a perturbation model continuous translation symmetry. Through Hartree-Fock calculations, find interaction opens sizable remote-band gap, resulting narrow C=1 at filling ν=1. From exact diagonalization identify phases various fillings. However, states also exist calculations without any potential. suggest (QAH) insulator ν=1 should be viewed as interaction-driven topological Wigner crystal QAH effect, which subsequently pinned by small robust period around 10 nm 4-layer, 5-layer, 6-layer, and 7-layer systems. Our work suggests new direction to explore interplay between topology spontaneous formation vanishing limit. propose system generate control both honeycomb triangular potentials through Coulomb from another layer, can stabilize or suppress depending on density of layer.

Language: Английский

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Tunable moiré materials for probing Berry physics and topology

Nature Reviews Materials, Journal Year: 2024, Volume and Issue: 9(7), P. 481 - 498

Published: April 26, 2024

Language: Английский

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Moiré band structure engineering using a twisted boron nitride substrate

Nature Communications, Journal Year: 2025, Volume and Issue: 16(1)

Published: Jan. 2, 2025

Applying long wavelength periodic potentials on quantum materials has recently been demonstrated to be a promising pathway for engineering novel phases of matter. Here, we utilize twisted bilayer boron nitride (BN) as moiré substrate band structure engineering. Small-angle-twisted BN is endowed with periodically arranged up and down polar domains, which imprints electrostatic potential target two-dimensional (2D) material placed top. As proof concept, use Bernal graphene the material. The resulting modulation appears superlattice resistance peaks, tunable by varying twist angle, Hofstadter butterfly physics under magnetic field. Additionally, demonstrate tunability altering dielectric thickness underneath BN. Finally, find that near-60°-twisted also leads features in graphene, may come from in-plane piezoelectric effect or out-of-plane corrugation effect. Tunable serve versatile platforms engineer electronic, optical, mechanical properties 2D van der Waals heterostructures.

Language: Английский

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Efficient Prediction of Superlattice and Anomalous Miniband Topology from Quantum Geometry

Physical Review X, Journal Year: 2025, Volume and Issue: 15(1)

Published: Jan. 13, 2025

Two-dimensional materials subject to long-wavelength modulations have emerged as novel platforms study topological and correlated quantum phases. In this article, we develop a versatile computationally inexpensive method predict the properties of subjected superlattice potential by combining degenerate perturbation theory with symmetry indicators. absence electronic interactions, our analysis provides systematic rule find Chern number superlattice-induced miniband starting from harmonics applied few material-specific coefficients. Our also applies anomalous (interaction-generated) bands, for which derive an efficient algorithm determine all numbers compatible self-consistent solution Hartree-Fock equations. approach gives microscopic understanding Hall insulators recently observed in rhombohedral graphene multilayers. Published American Physical Society 2025

Language: Английский

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Moiré-driven topological electronic crystals in twisted graphene

Nature, Journal Year: 2025, Volume and Issue: unknown

Published: Jan. 22, 2025

Language: Английский

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Higher Vortexability: Zero-Field Realization of Higher Landau Levels

Physical Review Letters, Journal Year: 2025, Volume and Issue: 134(10)

Published: March 10, 2025

The rise of moiré materials has led to experimental realizations integer and fractional Chern insulators in small or vanishing magnetic fields. At the same time, a set minimal conditions sufficient guarantee an Abelian state flat band were identified, namely, "ideal" "vortexable" quantum geometry. Such vortexable bands share essential features with lowest Landau level (LL), while excluding need for more fine-tuned aspects such as Berry curvature. A natural important generalization is ask if can be extended capture geometry higher levels, particularly first LL (1LL), where non-Abelian states at ν=1/2,2/5 are known competitive. possibility realizing these zero field, perhaps even exotic ones, could become reality we identify structure 1LL bands. In this work, introduce precise definition geometry, along figure merit that measures how closely given approaches 1LL. Periodically strained Bernal graphene shown realize field. locked icon Physics Subject Headings (PhySH)Chern insulatorsFractional Hall effectGeometric & topological phasesLandau levelsQuantum anomalous effectBilayer grapheneTwisted bilayer

Language: Английский

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Parent Berry Curvature and the Ideal Anomalous Hall Crystal

Physical Review X, Journal Year: 2024, Volume and Issue: 14(4)

Published: Nov. 12, 2024

We study a model of electrons moving in parent band uniform Berry curvature. At sufficiently high curvature, we show that strong repulsive interactions generically lead to the formation an anomalous Hall crystal: topological state with spontaneously broken continuous translation symmetry. Our results are established via mapping problem Wigner crystallization regular 2D electron gas. Interestingly, find periodic electrostatic potential induces competing opposite Chern number. theory offers unified perspective for understanding several aspects recently observed integer and fractional quantum effects rhombohedral multilayer graphene provides recipe engineering new states. Published by American Physical Society 2024

Language: Английский

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Extended quantum anomalous Hall states in graphene/hBN moiré superlattices

Nature, Journal Year: 2025, Volume and Issue: unknown

Published: Jan. 22, 2025

Language: Английский

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Chern Insulators at Integer and Fractional Filling in Moiré Pentalayer Graphene

Physical Review X, Journal Year: 2025, Volume and Issue: 15(1)

Published: Feb. 27, 2025

The advent of moiré platforms for engineered quantum matter has led to discoveries integer and fractional anomalous Hall effects, with predictions correlation-driven topological states based on electron crystallization. Here, we report an array trivial insulators formed in a lattice rhomobohedral pentalayer graphene (R5G). At doping one per unit cell (ν=1), see correlated insulator Chern number that can be tuned between C=0 +1 by electric displacement field. This is accompanied series additional C=+1 originating from fillings the lattice—ν=1/4, 1/3, 2/3—associated formation moiré-driven electronic crystals. ν=2/3 system exhibits effect at zero magnetic field, but further develops hints incipient C=2/3 modest Our results establish R5G as fertile platform studying competition potential intertwining insulators. Published American Physical Society 2025

Language: Английский

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