Séminaire du LPTMS: Jean-Noël Fuchs


11:00 - 12:00

LPTMS, salle 201, 2ème étage, Bât 100, Campus d'Orsay
15 Rue Georges Clemenceau, Orsay, 91405

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Magnetic field properties of itinerant electrons in a quasicrystal

Jean-Noël Fuch (LPS, Univeristé Paris-Sud & LPTMC, Université Paris 6)

Quasicrystals are solids with long range order but without periodicity. Here we study the properties of electrons moving in a 2D quasicrystal in the presence of a perpendicular magnetic field. The motion of electrons on a two-dimensional isometric Rauzy tiling is described by a tight-binding model. A magnetic field perpendicular to the plane is applied, which couples to the orbital motion of electrons via a Peierls phase in the hopping amplitudes and to the spin via a Zeeman coupling. For several approximants to the quasicrystal, the energy spectrum in a magnetic field is computed numerically with open or periodic boundary conditions. The resulting Hofstadter butterfly is studied in detail (Landau levels, labeling of gaps, etc). The grand potential is then obtained at a given temperature and chemical potential and its derivatives allow us to study the orbital magnetic susceptibility as well as the spin susceptibility of the Rauzy tiling. The spin susceptibility is a temperature-smoothed version of the zero-field density of states. The orbital susceptibility has a complicated structure – it changes sign several times – as a function of the chemical potential except near the band edges where it is approximatively described by an effective mass tensor.

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