title: Emergence of massless Dirac fermions in graphene's Hofstadter butterfly at switches of the quantum Hall phase connectivity.
abstract: The fractal spectrum of magnetic minibands (Hofstadter butterfly), induced by the moiré superlattice of graphene on a 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 Φ = (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 σ = 2qe(2)/πh and Klein tunneling associated with massless Dirac fermions at these connectivity switches.
authors.affiliation: Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, Netherlands.
authors.forename: M
authors.initials: M
authors.lastname: Diez
authors.affiliation: Department of Physics, University of California, Berkeley, California 95720, USA.
authors.forename: J P
authors.initials: JP
authors.lastname: Dahlhaus
authors.affiliation: Kavli Institute of Nanoscience, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, Netherlands.
authors.forename: M
authors.initials: M
authors.lastname: Wimmer
authors.affiliation: Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, Netherlands.
authors.forename: C W J
authors.initials: CW
authors.lastname: Beenakker