Regensburg 2013 – scientific programme

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MM: Fachverband Metall- und Materialphysik

MM 8: Topical Session: Quasicrystals & Complex Metallic Alloys II

MM 8.1: Talk

Monday, March 11, 2013, 11:45–12:00, H25

Electronic Wave Functions of Quasiperiodic Systems in Momentum Space — •Stefanie Thiem, Sebastian Rolof, and Michael Schreiber — Institut für Physik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany

In quasicrystalline tilings often multifractal electronic wave functions can be found, which are neither extended over the whole system nor exponentially localized. In order to obtain a better insight into their localization properties, we study the wave functions of quasiperiodic tilings in momentum space. The models are based on one-dimensional quasiperiodic chains, in which the atoms are coupled by weak and strong bonds aligned according to the Fibonacci sequences. The associated hypercubic tilings and labyrinth tilings in d dimensions are then constructed from the direct product of d such chains.

The results show that each wave function is described by a hierarchy of wave vectors and is always dominated by a single wave vector which is directly related to the energy eigenvalue of the wave function. Combining the information of all wave functions of the system, we observe a hierarchy of branches with different intensities. Each branch is a copy of the main branch containing the dominant wave vectors for each wave function. Using perturbation theory and a renormalization group approach we determine the shape of the branches for the limit cases of weak and strong coupling.