High-order fractal states in graphene superlattices
arXiv:1804.09476 · doi:10.1073/pnas.1804572115
Abstract
Graphene superlattices were shown to exhibit high-temperature quantum oscillations due to periodic emergence of delocalized Bloch states in high magnetic fields such that unit fractions of the flux quantum pierce a superlattice unit cell. Under these conditions, semiclassical electron trajectories become straight again, similar to the case of zero magnetic field. Here we report magnetotransport measurements that reveal second, third and fourth order magnetic Bloch states at high electron densities and temperatures above 100 K. The recurrence of these states creates a fractal pattern intimately related to the origin of Hofstadter butterflies. The hierarchy of the fractal states is determined by the width of magnetic minibands, in qualitative agreement with our band structure calculations.
References in corpus (21)
- Hofstadter's butterfly in moire superlattices: A fractal quantum Hall effect
- Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure
- Micrometer-scale ballistic transport in encapsulated graphene at room temperature
- Cloning of Dirac fermions in graphene superlattices
- STM Spectroscopy of ultra-flat graphene on hexagonal boron nitride
- Quantum Transport in Semiconductor Nanostructures
- Emergence of Superlattice Dirac Points in Graphene on Hexagonal Boron Nitride
- Commensurate-incommensurate transition for graphene on hexagonal boron nitride
- Electronic Properties of Graphene Encapsulated with Different Two-Dimensional Atomic Crystals
- Photo-induced Doping in Graphene/Boron Nitride Heterostructures
- Generic Miniband Structure of Graphene on a Hexagonal Substrate
- Observation of fractional Chern insulators in a van der Waals heterostructure
- Electronic properties of graphene hexagonal boron nitride moiré superlattice
- Quantum oscillations of the critical current and high-field superconducting proximity in ballistic graphene
- Second generation Dirac cones and inversion symmetry breaking induced gaps in graphene/hexagonal boron nitride
- Fractional fractal quantum Hall effect in graphene superlattices
- Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices
- High-temperature quantum oscillations caused by recurring Bloch states in graphene superlattices
- Dirac edges of fractal magnetic minibands in graphene with hexagonal moire superlattices
- Emergence of massless Dirac fermions in graphene's Hofstadter butterfly at switches of the quantum Hall phase connectivity
- Zero-energy modes and valley asymmetry in the Hofstadter spectrum of bilayer graphene van der Waals heterostructures with hBN
Cited by in corpus (28)
- Interlayer hybridization and moiré superlattice minibands for electrons and excitons in heterobilayers of transition-metal dichalcogenides
- Composite super-moiré lattices in double aligned graphene heterostructures
- Giant oscillations in a triangular network of one-dimensional states in marginally twisted graphene
- Strain Modulated Superlattices in Graphene
- Superlattices based on van der Waals 2D materials
- Brown-Zak and Weiss oscillations in a gate-tunable graphene superlattice: A unified picture of miniband conductivity
- Minibands in twisted bilayer graphene probed by magnetic focusing
- Long-range ballistic transport of Brown-Zak fermions in graphene superlattices
- Mixing of surface and bulk electronic states at a graphite-hexagonal boron nitride interface
- Band structure engineering using a moiré polar substrate
- Transport measurements on van der Waals heterostructures under pressure
- Electrical conductivity in the Hubbard model: orbital effects of magnetic field
- Universal magnetic oscillations of DC conductivity in the incoherent regime of correlated systems
- Heteromoiré Engineering on Magnetic Bloch Transport in Twisted Graphene Superlattices
- Dimensional reduction from magnetic field in moiré superlattices
- Moiré-Induced Transport in CVD-Based Small-Angle Twisted Bilayer Graphene
- Interplay of valley, layer and band topology towards interacting quantum phases in moiré bilayer graphene
- Magnetic Bloch States at Integer Flux Quanta Induced by Super-moiré Potential in Graphene Aligned with Twisted Boron Nitride
- Wannier Diagram and Brown-Zak Fermions of Graphene on Hexagonal Boron-Nitride
- Emergent flat band lattices in spatially periodic magnetic fields
- Controlling Umklapp scattering in bilayer graphene moir'e superlattice
- Towards numerically exact computation of conductivity in the thermodynamic limit of interacting lattice models
- Kagomé quantum oscillations in graphene superlattices
- Field-induced insulating states in a graphene superlattice
- Boosting proximity spin orbit coupling in graphene/WSe heterostructures via hydrostatic pressure
- Confinement of wave-function in Fractal geometry, a detection using DFT
- Hofstadter Butterfly in Graphene
- Coexisting Massive and Massless Dirac Fermions in Moire'-Reconstructed Bilayer Graphene