Periodic Landau gauge and Quantum Hall effect in twisted bilayer graphene

Abstract

Energy versus magnetic field (Hofstadter butterfly diagram) in twisted bilayer graphene is studied theoretically. If we take the usual Landau gauge, we cannot take a finite periodicity even when the magnetic flux through a supercell is a rational number. We show that the \textit{periodic} Landau gauge, which has the periodicity in one direction, makes it possible to obtain the Hofstadter butterfly diagram. Since a supercell can be large, magnetic flux through a supercell normalized by the flux quantum can be a fractional number with a small denominator, even when a magnetic field is not extremely strong. As a result, quantized Hall conductance can be a solution of nontrivial Diophantine equation.

9 pages, 10 figures revised

References in corpus (8)

• Electric Field Effect in Atomically Thin Carbon Films
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• Cloning of Dirac fermions in graphene superlattices
• A new magnetic field dependence of Landau levels on a graphene like structure
• Quantum Hall effect and the topological number in graphene
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• Dirac edges of fractal magnetic minibands in graphene with hexagonal moire superlattices
• Floquet Hofstadter Butterfly on the Kagome and Triangular Lattices
• Landau Levels as a Probe for Band Topology in Graphene Moiré Superlattices
• Quantum oscillations of magnetization in the tight-binding electrons on honeycomb lattice
• Topologically Universal Spectral Hierarchies of Quasiperiodic Systems
• Convenient Peierls phase choice for periodic atomistic systems under magnetic field
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• Atomistic theory of moiré Hofstadter's butterfly in magic-angle graphene
• Floquet engineering the Hofstadter butterfly in the square lattice and its effective Hamiltonian
• Twist Angle, Strain, Corrugation and Moire Unit cell in Twisted Bilayer Graphene
• Relativistic particles in super-periodic potentials: exploring graphene and fractal systems
• Merged Four Dirac Points at the Critical Interlayer Distance in Commensurately Twisted Bilayer Graphene: the Origin of the Zero Velocity
• Quantum Monte Carlo study of magnetism and chiral d+id-wave superconductivity in twisted bilayer graphene
• Magic-angle twisted bilayer graphene under orthogonal and in-plane magnetic fields