Emergence of massless Dirac fermions in graphene's Hofstadter butterfly at switches of the quantum Hall phase connectivity
arXiv:1401.4401 · doi:10.1103/PhysRevLett.112.196602
Abstract
The fractal spectrum of magnetic minibands (Hofstadter butterfly), induced by the moiré super- lattice of graphene on an hexagonal crystal substrate, is known to exhibit gapped Dirac cones. We show that the gap can be closed by slightly misaligning the substrate, producing a hierarchy of conical singularities (Dirac points) in the band structure at rational values Phi = (p/q)(h/e) of the magnetic flux per supercell. Each Dirac point signals a switch of the topological quantum number in the connected component of the quantum Hall phase diagram. Model calculations reveal the scale invariant conductivity sigma = 2qe^2 / pi h and Klein tunneling associated with massless Dirac fermions at these connectivity switches.
4 pages, 6 figures + appendix (3 pages, 1 figure)
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- Electronic optics in graphene in the semiclassical approximation
- Electrostatic Superlattices on Scaled Graphene Lattices
- Moiré effects in graphene--hBN heterostructures
- Zero-energy modes and valley asymmetry in the Hofstadter spectrum of bilayer graphene van der Waals heterostructures with hBN
- Geometric interference in a high-mobility graphene annulus p-n junction device
- Excitation Gap of Fractal Quantum Hall States in Graphene