Mott transition and electron correlation effects in an octagonal quasicrystal

Abstract

Flat-band systems, where electronic kinetic energy is quenched, provide fertile ground for studying strong correlation effects. In such systems, interactions dom inate the physics, giving rise to rich phases. While most existing studies have focused on periodic or translationally invariant systems, quasicrystals present a unique, intermediate class of materials that combine long-range order with ape riodicity. Specifically Ammann–Beenker, an octagonal aperiodic tiling, support strictly localized states due to interference effects and offer a rich platform for exploring interaction-driven physics. In this thesis, we investigate the effects of electron–electron interactions on the electronic properties of the periodic approximant of the Ammann–Beenker tiling, obtained with cut and project method, using the slave-rotor mean-field theory. We focus particularly on the metal–Mott insulator transition and the behavior of strictly localized states under correlation effects. Our analysis reveals a first order Mott transition at half-filling, with the spatial distribution of quasiparticle weights and Lagrange multipliers reflecting the underlying local geometry of the tiling. Furthermore, we demonstrate that interactions induce energy splitting between different types of localized states and can partially delocalize them via hybridization with extended states. To establish confidence in the method, we benchmark the slave-rotor approach on simple models, starting from a two-site Hubbard system and extending to a one-dimensional chain before applying it to the Ammann–Beenker tiling. By solving the resulting self-consistent equations numerically, we map out the phase diagram and explore the evolution of localized states under increasing interaction strength. These findings contribute to the broader understanding of correlated phases in aperiodic systems and highlight the role of local connectivity in shaping their electronic behavior.