Interactions in Quasicrystals

TL;DR

This paper explores how electron interactions in one-dimensional quasicrystals lead to unique transport properties, distinct from those in periodic or disordered systems, advancing understanding of quasicrystalline electronic behavior.

Contribution

It provides a controlled model demonstrating the impact of interactions on transport in quasicrystals, a less understood area compared to periodic structures.

Findings

Interactions cause anomalous transport in quasicrystals.

Transport properties are intermediate between periodic and disordered systems.

The model offers insights into electron behavior in non-periodic structures.

Abstract

Although the effects of interactions in solid state systems still remains a widely open subject, some limiting cases such as the three dimensional Fermi liquid or the one-dimensional Luttinger liquid are by now well understood when one is dealing with interacting electrons in {\it periodic} crystalline structures. This problem is much more fascinating when periodicity is lacking as it is the case in {\it quasicrystalline} structures. Here, we discuss the influence of the interactions in quasicrystals and show, on a controlled one-dimensional model, that they lead to anomalous transport properties, intermediate between those of an interacting electron gas in a periodic and in a disordered potential.