Brown-Zak and Weiss oscillations in a gate-tunable graphene superlattice: A unified picture of miniband conductivity

Abstract

Electrons exposed to a two-dimensional (2D) periodic potential and a uniform, perpendicular magnetic field exhibit a fractal, self-similiar energy spectrum known as the Hofstadter butterfly. Recently, related high-temperature quantum oscillations (Brown-Zak oscillations) were discovered in graphene moiré systems, whose origin lie in the repetitive occurrence of extended minibands/magnetic Bloch states at rational fractions of magnetic flux per unit cell giving rise to an increase in band conductivity. In this work, we report on the experimental observation of band conductivity oscillations in an electrostatically defined and gate-tunable graphene superlattice, which are governed both by the internal structure of the Hofstadter butterfly (Brown-Zak oscillations) and by a commensurability relation between the cyclotron radius of electrons and the superlattice period (Weiss oscillations). We obtain a complete, unified description of band conductivity oscillations in two-dimensional superlattices, yielding a detailed match between theory and experiment.

References in corpus (5)

• The electronic properties of graphene
• Boron nitride substrates for high-quality graphene electronics
• Emergence of Superlattice Dirac Points in Graphene on Hexagonal Boron Nitride
• High-temperature quantum oscillations caused by recurring Bloch states in graphene superlattices
• Few-layer graphene patterned bottom gates for van der Waals heterostructures

Cited by in corpus (20)

• Engineering high quality graphene superlattices via ion milled ultra-thin etching masks
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• Higher-order Bragg gaps in the electronic band structure of bilayer graphene renormalized by recursive supermoiré potential
• Formation of artificial Fermi surfaces with a triangular superlattice on a conventional two dimensional electron gas
• Patterned bilayer graphene as a tunable, strongly correlated system
• Probing miniband structure and Hofstadter butterfly in gated graphene superlattices via magnetotransport
• Dimensional reduction from magnetic field in moiré superlattices
• Magnetic Bloch States at Integer Flux Quanta Induced by Super-moiré Potential in Graphene Aligned with Twisted Boron Nitride
• Interplay of valley, layer and band topology towards interacting quantum phases in moiré bilayer graphene
• Wannier Diagram and Brown-Zak Fermions of Graphene on Hexagonal Boron-Nitride
• Controlling Umklapp scattering in bilayer graphene moir'e superlattice
• Designing Band Structures by Patterned Dielectric Superlattices
• Understanding Disorder in Monolayer Graphene Devices with Gate-Defined Superlattices
• Kagomé quantum oscillations in graphene superlattices
• Quantized Hall conductance in graphene by nonperturbative magnetic-field-containing relativistic tight-binding approximation method
• High mobility transport in isotopically-enriched ${}^{12}$C and ${}^{13}$C exfoliated graphene
• Designing (higher) Hall crystals
• Magnetic Bloch bands and Weiss oscillations in Dirac mass superlattices