Abstract

Quasicrystals are expected, by virtue of their complex structural order and lack of translational invariance, to possess unusual electronic properties. Studies of simple models in one, two and three dimensions indicate that typical wave-functions of an electron in a quasiperiodic environment are intermediate between extended and localized, and characterized by multifractal exponents. Such states are called critical states in analogy with the states at the critical point of a metal-insulator transition. Quantum diffusion in a quasicrystal is expected to be anomalous, with small or vanishing diffusivity. Experiments indicate that quasicrystals are indeed very poor conductors. After an introduction to quasicrystals, I will discuss the state of our current understanding of these solids, and some of the theoretical problems. A scheme for an experimental realization of a quantum simulator for a two dimensional quasicrystal using an optical potential (1) will be presented, as a step towards providing answers to open questions.

(1) N.Mace, A.Jagannathan and M.Duneau, Crystals, 6(10) 124 (2016)