Fractional Chern insulator states in twisted bilayer graphene: An analytical approach

Ledwith, Patrick J.; Tarnopolsky, Grigory; Khalaf, Eslam; Vishwanath, Ashvin

doi:10.1103/physrevresearch.2.023237

Cited by 186 publications

(111 citation statements)

References 54 publications

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“…Moreover, interlayer bias is known to generate internal valley currents in twisted graphene bilayers [5,6,21,22], creating topological networks at low angles [5,6,21] and generating valley fluxes in flat band regimes [22]. This interplay of correlations and topology in twisted graphene multilayers makes these materials a powerful platform to explore exotic states of matter [23][24][25][26] in a realistically feasible manner.…”

Section: Introductionmentioning

confidence: 99%

Electrical band flattening, valley flux, and superconductivity in twisted trilayer graphene

López-Bezanilla

Lado

2020

Phys. Rev. Research

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Twisted graphene multilayers have been demonstrated to yield a versatile playground to engineer controllable electronic states. Here, by combining first-principles calculations and low-energy models, we demonstrate that twisted graphene trilayers provide a tunable system where Van Hove singularities can be controlled electrically. In particular, it is shown that besides the band flattening, bulk valley currents appear, which can be quenched by local chemical dopants. We finally show that in the presence of electronic interactions, a nonuniform superfluid density emerges whose nonuniformity gives rise to spectroscopic signatures in dispersive higher-energy bands. Our results put forward twisted trilayers as a tunable van der Waals heterostructure displaying electrically controllable flat bands and bulk valley currents.

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Section: Introductionmentioning

confidence: 99%

Electrical band flattening, valley flux, and superconductivity in twisted trilayer graphene

López-Bezanilla

Lado

2020

Phys. Rev. Research

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“…Notably, experimental evidence has already been presented for latticegeneralized FQH states in graphene twisted on a substrate of hexagonal boron nitride [7]. Since then there have also been several works on the analytical [8] and numerical [9] theory of FQH states in moiré superstructures, as well as interest in moiré systems in a perpendicular magnetic field [10] and the construction of effective tight-binding models to expedite many-body numerics [11]. In particular, there have been many proposals for effective lattice models for such systems of "two-orbital Hubbard" type [12,13].…”

Section: Introductionmentioning

confidence: 99%

Fractional quantum Hall states for moiré superstructures in the Hofstadter regime

Andrews

Soluyanov

2020

Phys. Rev. B

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We study the transition of =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 =1/3 and 2/5 states corresponding to the honeycomb Hofstadter model survive up to 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.

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“…In particular, we will show that the most compact excitonic Laughlin state, which is presumably also the most stable one, has zero valley polarization in spite of spontaneously breaking the time reversal symmetry with a charge Hall conductivity of σ xy = ±e 2 /h. These excitonic Laughlin states are sharply distinct from the more conventional analogs of Laughlin states studied in fractionally filled chern bands of moiré materials [56][57][58].…”

Section: Introductionmentioning

confidence: 73%

Excitonic Laughlin states in ideal topological insulator flat bands and their possible presence in moiré superlattice materials

Stefanidis

Sodemann

2020

Phys. Rev. B

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We investigate few-and many-body states in half-filled ideal topological insulator flat bands realized by two degenerate Landau levels which experience opposite magnetic fields. This serves as a toy model of flat bands in moiré materials in which valleys have Chern numbers C = ±1. We argue that although the spontaneously polarized Ising Chern magnet is a natural ground state for repulsive Coulomb interactions, it can be in reasonable energetic competition with correlated Laughlin states of excitons when short-distance corrections to interactions are included. This is because charge neutral excitons in these bands behave effectively as charged particles in ordinary Landau levels. In particular, the Ising Chern magnet is no longer the ground state once the strength of a short-range intravalley repulsion is about 30% larger than the intervalley repulsion. Remarkably, these excitonic Laughlin states feature valley number fractionalization but no charge fractionalization and a quantized charge Hall conductivity identical to the Ising magnet, σ xy = ±e 2 /h, and thus cannot be distinguished from it by ordinary charge transport measurements. The Laughlin state with the highest density of excitons that can be constructed in these bands is an analog of ν = 1/4 bosonic Laughlin state and has no valley polarization even though it spontaneously breaks time reversal symmetry.

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Fractional Chern insulator states in twisted bilayer graphene: An analytical approach

Cited by 186 publications

References 54 publications

Electrical band flattening, valley flux, and superconductivity in twisted trilayer graphene

Electrical band flattening, valley flux, and superconductivity in twisted trilayer graphene

Fractional quantum Hall states for moiré superstructures in the Hofstadter regime

Excitonic Laughlin states in ideal topological insulator flat bands and their possible presence in moiré superlattice materials

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