Emergence of massless Dirac fermions in graphene's Hofstadter butterfly   at switches of the quantum Hall phase connectivity
  The fractal spectrum of magnetic minibands (Hofstadter butterfly), induced by the moir\'e 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. 
M. Diez, J. P. Dahlhaus, M. Wimmer, and C. W. J. Beenakker
cond-mat.mes-hall