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Quasiperiodicity has recently been proposed to enhance superconductivity and its proximity effect. Simultaneously, there has been significant experimental progress in the fabrication of quasiperiodic structures, including 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 develop 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 compared to crystalline junctions, we do not, in general, find that it enhances the critical current. However, we find significant current enhancement for reduced interface transparency because of 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. Published by the American Physical Society 2024
Quasiperiodicity has recently been proposed to enhance superconductivity and its proximity effect. Simultaneously, there has been significant experimental progress in the fabrication of quasiperiodic structures, including 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 develop 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 compared to crystalline junctions, we do not, in general, find that it enhances the critical current. However, we find significant current enhancement for reduced interface transparency because of 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. Published by the American Physical Society 2024
We investigate the properties of a Fibonacci quasicrystal (QC) arrangement of a one-dimensional topological superconductor, such as a magnetic atom chain deposited on a superconducting surface. We uncover a general mutually exclusive competition between the QC properties and the topological superconducting phase with Majorana bound states (MBS): there are no MBS inside the QC gaps and the MBS never behave as QC subgap states and, likewise, no critical or winding QC subgap states exist inside the topological superconducting gaps. Surprisingly, despite this competition, we find that the QC is still highly beneficial for realizing topological superconductivity with MBS. It both leads to additional large nontrivial regions with MBS in parameter space, that are topologically trivial in crystalline systems, and increases the topological gap protecting the MBS. We also find that shorter approximants of the Fibonacci QC display the largest benefits. As a consequence, our results promote QCs, and especially their short approximants, as an appealing platform for improved experimental possibilities to realize MBS as well as generally highlight the fundamental interplay between different topologies. Published by the American Physical Society 2024
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