Odd-frequency superconducting pairing due to multiple Majorana edge modes in driven topological superconductors

Eslam Ahmed; Shun Tamura; Yukio Tanaka; Jorge Cayao

AI summary · arXiv: 2404.09517v2 · cond-mat.supr-con

Odd-frequency superconducting pairing due to multiple Majorana edge modes in driven topological superconductors

Eslam Ahmed, Shun Tamura, Yukio Tanaka, Jorge Cayao

Original paper Submitted to arXiv on 15 Apr. 2024 19 pages, 8 figures License: NONEXCLUSIVE-DISTRIB 1.0

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The essentials

Researchers explore Majorana zero modes and odd-frequency pairing in $p$-wave spin-polarized superconductors under a time-dependent drive
Dynamic formation of Majorana modes is linked to tuning of drive frequency and chemical potential
Presence of Majorana modes enhances odd-frequency spin-polarized $s$-wave pairing
Pairing trends differ based on the type of Majorana mode present (zero or $\pi$)
Divergent behavior in pair correlations persists across multiple Majorana modes and remains robust against scalar disorder
Establishment of spectral bulk-boundary correspondence linking boundary odd-$\omega$ pairing with bulk topological invariants in driven chiral systems

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Original abstract

, , , , In their recent work, Eslam Ahmed, Shun Tamura, Yukio Tanaka, and Jorge Cayao delve into the intricate realm of Majorana zero modes and odd-frequency pairing in $p$-wave spin-polarized superconductors under a time-dependent drive. Building upon existing theoretical frameworks that have primarily focused on the static regime, the researchers explore the dynamic formation of Majorana modes and their implications for odd-frequency pairing. The study reveals that the driven system exhibits multiple Majorana modes emerging at both zero and $\pi$, with their formation intricately linked to the tuning of drive frequency and chemical potential. This observation aligns with previous research findings and underscores the controllability of Majorana mode generation in such systems. Further investigation uncovers a profound impact on pair correlations within the system, particularly in terms of odd-frequency spin-polarized $s$-wave pairing. The researchers observe significant enhancements in these pair correlations in the presence of Majorana modes, shedding light on the interplay between quasiparticle behavior and external driving forces. Notably, the team identifies distinct trends in odd-frequency pairing based on the type of Majorana mode present. While pairing is proportional to $\sim1/\omega$ when Majorana zero modes are dominant, it shifts to $\sim 1/(\omega-\pi\hbar/T)$ in the presence of Majorana $\pi$ modes, where $T$ represents the periodicity of the drive. This nuanced understanding highlights the complex dynamics at play in these driven topological superconductors. Moreover, despite the emergence of multiple Majorana modes leading to larger amounts of odd-frequency pairing, a consistent divergent profile as a function of frequency persists. The researchers also demonstrate that this divergent behavior remains robust against scalar disorder, underscoring the resilience of odd-frequency pair correlations in such systems. One key contribution of this work is establishing a spectral bulk-boundary correspondence that links boundary odd-$\omega$ pairing with bulk topological invariants in driven chiral systems. This correspondence is shown to be safeguarded by chiral symmetry and resistant to disorder-induced perturbations, offering valuable insights into the underlying mechanisms governing emergent pair correlations in driven topological superconductors. Overall, this comprehensive study not only advances our understanding of Majorana modes and odd-frequency pairing dynamics but also lays a solid foundation for further exploration into emergent phenomena within driven topological superconducting systems.

Introduction

The study of Majorana zero modes and odd-frequency pairing in topological superconductors has garnered significant attention in recent years. These exotic quasiparticles, first proposed by Ettore Majorana in 1937, have been the subject of intense research due to their potential applications in quantum computing and fault-tolerant information storage. In this context, a team of researchers led by Eslam Ahmed from the University of Tokyo set out to explore the dynamic formation of Majorana modes and their impact on odd-frequency pairing in spin-polarized $p$-wave superconductors under a time-dependent drive.

Theoretical Framework

The team's work builds upon existing theoretical models that have primarily focused on static systems. By incorporating external driving forces into the equation, they aim to shed light on how these factors influence the emergence and behavior of Majorana modes and odd-frequency pair correlations. The researchers employ a tight-binding model with Rashba spin-orbit coupling to simulate a chiral $p$-wave superconductor driven by an oscillating magnetic field along the $z$ direction.

Formation of Multiple Majorana Modes

One key finding from this study is that multiple Majorana modes can emerge at both zero energy ($\omega=0$) and $\pi$ energy ($\omega=\pi\hbar/T$, where $T$ is the periodicity of the drive). This observation aligns with previous research findings and highlights the controllability of Majorana mode generation through external driving forces.

Impact on Odd-Frequency Pairing

The presence of these multiple Majorana modes has a profound effect on odd-frequency pairing within the system. The researchers observe significant enhancements in these pair correlations when compared to static systems without any external driving forces. Interestingly, they also identify distinct trends based on the type of Majorana mode present. When Majorana zero modes dominate, pairing is proportional to $\sim1/\omega$, while it shifts to $\sim 1/(\omega-\pi\hbar/T)$ in the presence of Majorana $\pi$ modes.

Robustness Against Disorder

To further explore the resilience of odd-frequency pair correlations, the team introduces scalar disorder into their model. Despite this perturbation, they find that the divergent behavior as a function of frequency remains consistent, emphasizing the robustness of these emergent phenomena in driven topological superconductors.

Spectral Bulk-Boundary Correspondence

One key contribution of this work is establishing a spectral bulk-boundary correspondence between boundary odd-$\omega$ pairing and bulk topological invariants in driven chiral systems. This correspondence is shown to be safeguarded by chiral symmetry and resistant to disorder-induced perturbations, offering valuable insights into the underlying mechanisms governing emergent pair correlations in driven topological superconductors.

Conclusion

In conclusion, Eslam Ahmed and his team's study sheds light on the dynamic formation of Majorana modes and their impact on odd-frequency pairing in spin-polarized $p$-wave superconductors under a time-dependent drive. Their findings not only advance our understanding of these exotic quasiparticles but also lay a solid foundation for further exploration into emergent phenomena within driven topological superconducting systems. The researchers' comprehensive approach provides valuable insights into how external driving forces can be used to control and manipulate these intriguing behaviors, paving the way for potential applications in quantum computing and information storage.

Created on 04 Nov. 2024

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Odd-frequency superconducting pairing due to multiple Majorana edge modes in driven topological superconductors

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Introduction

Theoretical Framework

Formation of Multiple Majorana Modes

Impact on Odd-Frequency Pairing

Robustness Against Disorder

Spectral Bulk-Boundary Correspondence

Conclusion

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