Linking topological features of the Hofstadter model to optical diffraction figures

  title={Linking topological features of the Hofstadter model to optical diffraction figures},
  author={F. Di Colandrea and Alessio D’Errico and Maria Maffei and Hannah M. Price and Maciej Lewenstein and Lorenzo Marrucci and Filippo Cardano and Alexandre Dauphin and Pietro Massignan},
  journal={New Journal of Physics},
In two, three and even four spatial dimensions, the transverse responses experienced by a charged particle on a lattice in a uniform magnetic field are fully controlled by topological invariants called Chern numbers, which characterize the energy bands of the underlying Hofstadter Hamiltonian. These remarkable features, solely arising from the magnetic translational symmetry, are captured by Diophantine equations which relate the fraction of occupied states, the magnetic flux and the Chern… 

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