Long-range ballistic transport of Brown-Zak fermions in graphene superlattices

Abstract

In quantizing magnetic fields, graphene superlattices exhibit a complex fractal spectrum often referred to as the Hofstadter butterfly. It can be viewed as a collection of Landau levels that arise from quantization of Brown-Zak minibands recurring at rational ($p/q$) fractions of the magnetic flux quantum per superlattice unit cell. Here we show that, in graphene-on-boron-nitride superlattices, Brown-Zak fermions can exhibit mobilities above 10${}^6$ cm${}^2$V${}^{-1}$s${}^{-1}$ and the mean free path exceeding several micrometers. The exceptional quality of our devices allows us to show that Brown-Zak minibands are $4q$ times degenerate and all the degeneracies (spin, valley and mini-valley) can be lifted by exchange interactions below 1K. We also found negative bend resistance at $1/q$ fractions for electrical probes placed as far as several micrometers apart. The latter observation highlights the fact that Brown-Zak fermions are Bloch quasiparticles propagating in high fields along straight trajectories, just like electrons in zero field.

16 pages, 13 figures

References in corpus (12)

• 2D materials and van der Waals heterostructures
• Boron nitride substrates for high-quality graphene electronics
• Micrometer-scale ballistic transport in encapsulated graphene at room temperature
• Emergence of Superlattice Dirac Points in Graphene on Hexagonal Boron Nitride
• Interaction phenomena in graphene seen through quantum capacitance
• Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices
• High-temperature quantum oscillations caused by recurring Bloch states in graphene superlattices
• New generation of moiré superlattices in doubly aligned hBN/graphene/hBN heterostructures
• Composite super-moiré lattices in double aligned graphene heterostructures
• A semi-Dirac point in the Hofstadter spectrum
• Self-similar occurrence of massless Dirac particles in graphene under magnetic field
• Fractional Hofstadter States in Graphene on Hexagonal Boron Nitride

Cited by in corpus (18)

• Out-of-equilibrium criticalities in graphene superlattices
• Brown-Zak and Weiss oscillations in a gate-tunable graphene superlattice: A unified picture of miniband conductivity
• Controlled alignment of supermoiré lattice in double-aligned graphene heterostructures
• Electrical conductivity in the Hubbard model: orbital effects of magnetic field
• Spectroscopy of the Fractal Hofstadter Energy Spectrum
• Higher-order Bragg gaps in the electronic band structure of bilayer graphene renormalized by recursive supermoiré potential
• de Haas-van Alphen spectroscopy and fractional quantization of magnetic-breakdown orbits in moiré graphene
• Universal magnetic oscillations of DC conductivity in the incoherent regime of correlated systems
• Effect of boron nitride defects and charge inhomogeneity on 1/f noise in encapsulated graphene
• Probing miniband structure and Hofstadter butterfly in gated graphene superlattices via magnetotransport
• Band gap formation in commensurate twisted bilayer graphene/hBN moiré lattices
• 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
• Milli-Tesla Quantization enabled by Tuneable Coulomb Screening in Large-Angle Twisted Graphene
• Wannier Diagram and Brown-Zak Fermions of Graphene on Hexagonal Boron-Nitride
• Negative longitudinal resistance of monolayer graphene in the quantum Hall regime
• Orthonormal wave functions for periodic fermionic states under an applied magnetic field
• Magnetic Bloch bands and Weiss oscillations in Dirac mass superlattices