Josephson effect in a Fibonacci quasicrystal
arxiv(2024)
Abstract
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 topological gaps with different winding numbers. 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 enhanced 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, and
thus the topological invariant, can be determined.
MoreTranslated text
AI Read Science
Must-Reading Tree
Example
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined