Quasiperiodic tilings in a magnetic field

We study the electronic properties of a two-dimensional quasiperiodic tiling, the isometric generalized Rauzy tiling, embedded in a magnetic field. Its energy spectrum is computed in a tight-binding approach by means of the recursion method. Then, we study the quantum dynamics of wave packets and discuss the influence of the magnetic field on the diffusion and spectral exponents. Finally, we consider a quasiperiodic superconducting wire network with the same geometry and we determine the critical temperature as a function of the magnetic field.