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End Superconductivity and Three Distinct Critical Temperatures in Fibonacci Quasicrystal Approximants: A Numerical Study


Core Concepts
Fibonacci quasicrystals exhibit unique superconducting properties, including end superconductivity with three distinct critical temperatures (left end, right end, and bulk), arising from the interplay of topological bound states and critical states.
Abstract
  • Bibliographic Information: Zhu, Q., Zha, G., Shanenko, A. A., & Chen, Y. (2024). End superconductivity and three critical temperatures in Fibonacci quasicrystals. arXiv preprint arXiv:2410.02900v1.
  • Research Objective: This study investigates the phenomenon of end superconductivity in Fibonacci quasicrystals, specifically focusing on the interplay between topological bound states and critical states in determining the critical temperatures.
  • Methodology: The researchers numerically solved the self-consistent Bogoliubov-de Gennes (BdG) equations for a Fibonacci chain under superconducting proximity, considering finite approximants (Sn) of the chain. They analyzed the spatial distribution of the pair potential, single-species quasiparticle contributions, and the dependence of critical temperatures on chain length (n) and hopping amplitudes (tA).
  • Key Findings: The study reveals three distinct critical temperatures in Fibonacci quasicrystals: TcL (left end), TcR (right end), and Tcb (bulk). The interplay between topological bound states and critical states leads to asymmetric end superconductivity, with TcL and TcR potentially exceeding Tcb. The study also finds that TcL and Tcb are independent of the Fibonacci sequence number (n), while TcR shows significant dependence on the parity of n.
  • Main Conclusions: The research demonstrates the existence of end superconductivity in Fibonacci quasicrystals, highlighting the role of topological bound states and critical states in this phenomenon. The findings suggest that Fibonacci quasicrystals could offer alternative pathways for discovering materials with higher superconducting critical temperatures.
  • Significance: This study contributes to the understanding of superconductivity in quasicrystalline systems, which are characterized by unique electronic properties due to their aperiodic structure. The discovery of multiple critical temperatures and the potential for enhanced superconductivity at the ends of Fibonacci chains opens up new avenues for research and potential applications in superconducting devices.
  • Limitations and Future Research: The study focuses on a one-dimensional Fibonacci chain as a simplified model. Further research could explore higher-dimensional quasicrystals and the effects of factors like disorder and magnetic fields on end superconductivity. Investigating the experimental realization and potential applications of these findings in superconducting devices is also crucial.
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Stats
The maximal enhancement of TcR occurs for even n, reaching up to 50% relative to Tcb. TcL can increase by up to 23%. The bulk critical temperature reaches its minimum Tcb = 0.186 at tA = 1.2.
Quotes

Deeper Inquiries

How would the findings of this study be affected by considering higher-dimensional Fibonacci quasicrystals?

Extending the study of end superconductivity from one-dimensional Fibonacci chains to higher-dimensional Fibonacci quasicrystals introduces exciting complexities and potential modifications to the observed phenomena. Here's a breakdown of the potential impacts: Increased Complexity of Quasiparticle Interference: In higher dimensions, the interference patterns of topological bound quasiparticles and critical quasiparticles would become significantly more intricate. This could lead to a richer variety of end and edge superconducting states, potentially with variations not only in critical temperatures but also in the spatial distribution of the superconducting order parameter. Influence of Surface Geometry: The geometry of the quasicrystal's surface would play a crucial role in shaping the end superconductivity. Different facets or edges of the quasicrystal could exhibit varying degrees of superconducting enhancement due to the anisotropy inherent in quasicrystalline structures. Challenges in Numerical Modeling: Solving the Bogoliubov-de Gennes equations for higher-dimensional quasicrystals poses significant computational challenges due to the lack of translational symmetry. Advanced numerical techniques and approximations would be necessary to tackle these systems effectively. Potential for Novel Topological Superconducting States: Higher-dimensional Fibonacci quasicrystals, especially in conjunction with spin-orbit coupling or external magnetic fields, could host exotic topological superconducting states. These states might exhibit unique properties, such as Majorana zero modes, which are of great interest for fault-tolerant quantum computing. In essence, while the fundamental principles of end superconductivity observed in one-dimensional Fibonacci chains might still hold in higher dimensions, the interplay of quasiparticle interference, surface geometry, and the potential for novel topological states could lead to a diverse range of superconducting behaviors in these fascinating materials.

Could the presence of disorder in the Fibonacci chain suppress or enhance the observed end superconductivity?

The impact of disorder on end superconductivity in Fibonacci chains is a multifaceted issue, with the potential for both suppression and enhancement depending on the nature and strength of the disorder: Potential Suppression Mechanisms: Localization of Quasiparticles: Disorder can lead to Anderson localization, where quasiparticle states become spatially confined. If the localization length becomes comparable to or smaller than the characteristic length scale of end superconductivity, it can disrupt the constructive interference required for the enhancement, thereby suppressing the effect. Pair-Breaking Effects: Certain types of disorder, particularly magnetic impurities, can break Cooper pairs and directly suppress superconductivity throughout the system, including at the ends. Potential Enhancement Mechanisms: Enhanced Density of States: Disorder can create localized states within the energy gap of the superconductor, effectively increasing the density of states at low energies. This can enhance the pairing interaction and potentially lead to higher critical temperatures, including at the ends. Modification of Quasiparticle Interference: Disorder can alter the interference patterns of quasiparticles, potentially leading to constructive interference in regions where it was previously absent. This could enhance end superconductivity in specific disorder configurations. Key Factors Determining the Outcome: Type of Disorder: The specific nature of disorder (e.g., site disorder, bond disorder, magnetic impurities) will significantly influence its impact on end superconductivity. Strength of Disorder: Weak disorder might have a negligible effect or even enhance end superconductivity, while strong disorder is more likely to suppress it. Spatial Distribution of Disorder: The arrangement of impurities or defects within the Fibonacci chain can lead to varying effects on end superconductivity. In summary, the presence of disorder in a Fibonacci chain can either suppress or enhance end superconductivity depending on a delicate interplay of factors. A comprehensive understanding of these factors is crucial for predicting the behavior of realistic quasicrystalline superconductors.

What are the potential implications of these findings for the development of novel superconducting devices, particularly those operating at higher temperatures?

The discovery of end superconductivity in Fibonacci quasicrystals, particularly the observation of distinct and potentially higher critical temperatures at the ends, opens up intriguing possibilities for novel superconducting devices, especially those targeting higher operating temperatures: Engineering High-Temperature Superconducting Junctions: The enhanced critical temperatures at the ends of Fibonacci chains could be exploited to create Josephson junctions with higher operating temperatures. These junctions are fundamental building blocks for various superconducting devices, including SQUIDs (Superconducting Quantum Interference Devices) and qubits. Tailoring Superconducting Properties through Geometry: The sensitivity of end superconductivity to the chain length and hopping parameters suggests the possibility of tailoring the superconducting properties of Fibonacci quasicrystals by carefully engineering their geometry and composition. This could lead to materials with enhanced superconducting properties for specific applications. Exploring Novel Device Architectures: The unique properties of end superconductivity in Fibonacci quasicrystals might inspire novel device architectures that exploit the spatial inhomogeneity of the superconducting order parameter. For instance, devices could be designed to take advantage of the enhanced superconductivity at the edges or interfaces of quasicrystalline structures. Potential for Topological Quantum Computing: While the specific Fibonacci chain model studied in the paper doesn't exhibit topological superconductivity, the interplay of topology and superconductivity in quasicrystals remains an active area of research. If realized, topological superconducting states in these materials could pave the way for more robust and fault-tolerant qubits for quantum computing. Challenges and Future Directions: Material Synthesis and Characterization: Synthesizing high-quality Fibonacci quasicrystals with precise control over their structure and purity remains a significant challenge. Scalability and Integration: Integrating Fibonacci quasicrystal-based devices into existing technologies and scaling up their production pose considerable hurdles. Theoretical Understanding of Higher-Dimensional Systems: Further theoretical investigations are needed to fully understand the behavior of end superconductivity in higher-dimensional Fibonacci quasicrystals, which are more relevant for practical applications. Despite these challenges, the findings of this study provide a compelling motivation to further explore the potential of Fibonacci quasicrystals for developing novel superconducting devices, particularly those operating at higher temperatures, which could revolutionize various fields, including electronics, computing, and sensing.
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