The Joint Condensed Matter Seminar (JCMS) series is organised by KTH Royal Insitute of Technology, Nordita, and Stockholm University.
On Monday, November 4th, 2024 from 11 am to 12 am we will host a seminar by Patric Holmvall from Uppsala University.
Josephson effect in a Fibonacci quasicrystal
Quasiperiodicity has recently been proposed to enhance superconductivity and its proximity effect. At the same time, there has been significant experimental progress in the fabrication of quasiperiodic structures, also in reduced dimensions. Motivated by these developments, we use microscopic tight-binding theory to investigate the DC Josephson effect through a ballistic Fibonacci chain attached to two superconducting leads. The Fibonacci chain is one of the most studied examples of quasicrystals, hosting a rich multifractal spectrum, containing gaps with different winding subgap states. We study how the Andreev bound states (ABS), current-phase relation, and the critical current depend on the quasiperiodic degrees of freedom, from short to long junctions. While the current-phase relation shows a traditional 2π sinusoidal or sawtooth profile, we find that the ABS obtain quasiperiodic oscillations and that the Andreev reflection is qualitatively altered, leading to quasiperiodic oscillations in the critical current as a function of junction length. Surprisingly, despite earlier proposals of quasiperiodicity enhancing superconductivity, we do not in general find an enhanced critical current. However, we find significant enhancement for reduced interface transparency due to the modified Andreev reflection. Furthermore, by varying the chemical potential, e.g. by an applied gate voltage, we find a fractal oscillation between superconductor-normal metal-superconductor (SNS) and superconductor-insulator-superconductor (SIS) behavior. Finally, we show that the winding of the subgap states leads to an equivalent winding in the critical current, such that the winding numbers can be determined.
[1] A. Sandberg, O. A. Awoga, A. M. Black-Schaffer, P. Holmvall, “Josephson effect in a Fibonacci quasicrystal”, Phys. Rev. B 110, 104513 (2024).