## Bremen-Cardiff Physics Seminar

### Topological effects in the interacting Fibonacci chain

**Speaker: Gautam Rai (USC Los Angeles working with Prof. S. Haas)**

**Date: Tuesday 11 May 2021**

**Time: 15:00 in UK**

**Venue: Zoom**

The term quasicrystals refers to a special class of materials that have no translational symmetry and yet have long-range order—the X-ray diffraction pattern of these materials consists of discrete δ-peaks. In crystals, this type of long-range order is easily understood to stem from the fact that a finite arrangement repeats itself indefinitely. In quasicrystals, a weaker condition is met—local configurations of any given size are almost alike at every scale. This quasicrystalline symmetry is often accompanied by a non-trivial topology. The discovery of a superconducting quasicrystal in 2018 begs the question, how do correlated electrons behave in quasicrystals and what is the interplay between topology and interactions? We found that we could make considerable progress towards an answer to this question by considering the simplest possible model of a superconducting quasicrystal—the one-dimensional Fibonacci hopping model with pairing introduced via the Bogoliubov-de Gennes self-consistent field method. In the first part of my talk, I will introduce the non-trivial topology of the Fibonacci chain and present our work on a new proposed method for measuring the topological invariants of the Fibonacci chain. In the second part of my talk, I will share our results on proximity-induced superconductivity at a superconductor-quasicrystal interface where the highlight is the appearance of a signature of the quasicrystal’s topological edge states in the induced pair amplitude.