Interplay of Majorana and Yu-Shiba-Rusinov States in a Minimal Kitaev Chain Coupled to Superconducting Leads: Impact on Transport Properties and Majorana Signatures

Core Concepts

Coupling a minimal Kitaev chain to superconducting leads leads to the emergence of Yu-Shiba-Rusinov (YSR) states, which can hybridize with Majorana zero modes (MZMs), impacting transport properties and potentially obscuring Majorana signatures, especially in systems with finite spin-polarization.

Abstract

Alvarado, M., Levy Yeyati, A., Aguado, R., & Seoane Souto, R. (2024). Interplay between Majorana and Shiba states in a minimal Kitaev chain coupled to a superconductor. arXiv preprint arXiv:2407.07050v2.

This research paper investigates the transport properties and spectral features of a minimal Kitaev chain, a promising platform for realizing Majorana zero modes (MZMs), when coupled to both normal and superconducting leads. The study aims to understand how the interplay between MZMs and Yu-Shiba-Rusinov (YSR) states, induced by the superconducting lead, affects the system's behavior and the detectability of Majorana signatures.

Key Insights Distilled From

Interplay between Majorana and Shiba states in a minimal Kitaev chain coupled to a superconductor

by Migu... at arxiv.org 11-06-2024

https://arxiv.org/pdf/2407.07050.pdf

Deeper Inquiries

How would the presence of disorder or interactions between electrons in the Kitaev chain affect the interplay between YSR and MZMs?

This is a crucial question, as real-world systems inevitably deviate from idealized models. Here's a breakdown of how disorder and interactions could influence the YSR-MZM interplay:
Disorder:

Localization: Disorder tends to localize electronic states. In the context of the Kitaev chain, even weak disorder can localize Majorana zero modes, hindering their hybridization with the more extended YSR state. This could either suppress or enhance the YSR-MZM interplay depending on the specific disorder configuration.
Gap Closing: Strong disorder can potentially close the topological gap of the Kitaev chain, destroying the Majorana zero modes altogether. In this scenario, the YSR state would dominate the subgap physics.
Emergent Phenomena: Interestingly, disorder can also lead to the emergence of new subgap states within the superconducting gap. These disorder-induced states could interact with both the YSR and Majorana states, leading to more complex and potentially richer physics.
Interactions:

Competing Ground States: Electron-electron interactions can give rise to competing ground states in the Kitaev chain, such as charge density waves or magnetic order. These competing phases can suppress superconductivity and consequently, affect the formation of both YSR and Majorana states.
Fractional Excitations: Strong interactions can potentially fractionalize the Majorana zero modes, leading to exotic quasiparticles with non-Abelian statistics beyond Majorana fermions. The interplay of these fractional excitations with the YSR state is an open question with potential for novel physics.
Shiba Band Formation: In systems with multiple magnetic impurities (like the partially polarized QD in the context), interactions can lead to the formation of Shiba bands. These bands, originating from the hybridization of individual YSR states, could hybridize with the Majorana modes, leading to a complex interplay and potentially new avenues for manipulating Majorana states.
Overall:
The presence of disorder and interactions significantly complicates the YSR-MZM interplay, potentially leading to both detrimental effects and new emergent phenomena. Further theoretical and experimental investigations are needed to fully understand these complex interactions and their implications for Majorana-based quantum technologies.

Could the hybridization between YSR and MZMs be exploited for novel quantum information processing schemes, rather than being viewed solely as a detrimental effect?

While the paper primarily focuses on the destructive aspects of YSR-MZM hybridization, viewing it solely as detrimental might be limiting. Here's how this interplay could be harnessed for potential benefits in quantum information processing:

Tunable Qubit States: The hybridization between YSR and MZMs leads to the formation of new hybridized subgap states. These states, with energies tunable by parameters like the coupling to the superconducting lead or the QD levels, could potentially be used as a basis for encoding and manipulating qubit states.
Braiding Protocols: The hybridization process itself, involving the exchange of energy and information between the YSR and MZMs, could be incorporated into braiding protocols. By carefully controlling the system parameters, one might be able to induce braiding operations between Majorana modes mediated by the YSR state.
Long-Range Entanglement: YSR states are known to mediate long-range interactions between magnetic impurities. In the context of a Kitaev chain, the hybridization with YSR states could potentially facilitate long-range entanglement between spatially separated Majorana zero modes, a crucial ingredient for scalable topological quantum computation.
Probing and Detection: The hybridization between YSR and MZMs leads to distinct signatures in transport measurements, as demonstrated in the paper. This sensitivity could be exploited for developing more efficient and robust detection schemes for Majorana zero modes in experimental setups.
Overall:
Instead of perceiving the YSR-MZM hybridization solely as a challenge, exploring its potential for qubit control, braiding operations, and long-range entanglement generation could unlock new possibilities in topological quantum information processing.

If we consider the analogy of MZMs as emergent particles at the edges of a topological material, what would be the equivalent analogy for the observed interplay between YSR and MZMs in this system, and what new physics might it reveal?

Let's extend the analogy of MZMs as emergent edge particles to understand the YSR-MZM interplay:

MZMs as Edge Modes: Imagine a 1D topological insulator (like the Kitaev chain) as a "string" with MZMs as exotic particles bound to its ends. These particles are robust due to the topological protection offered by the "string."
YSR State as a Defect: Now, introduce a localized "defect" on the string, represented by the QD strongly coupled to the superconducting lead. This defect hosts the YSR state, which can be pictured as another type of emergent particle localized at the defect site.
Hybridization as Interaction: The observed hybridization between YSR and MZMs can be visualized as an interaction between these emergent particles. This interaction is mediated by the "string" itself, allowing the edge MZMs to "feel" the presence of the localized YSR state.
New Physics and Analogies:

Scattering and Interference: The YSR state acts as a scatterer for the MZMs, leading to interference effects in transport, analogous to electron scattering off impurities in condensed matter systems.
Bound State Formation: In the strong coupling regime, the YSR state and one of the MZMs can form a "bound state," effectively trapping the MZM near the defect site. This is similar to the formation of excitons in semiconductors, where an electron and a hole are bound together.
Topological Phase Transitions: The interplay between YSR and MZMs can potentially drive topological phase transitions in the system. For example, by tuning the coupling strength to the superconducting lead, one might be able to transition between a phase with well-defined MZMs and a phase where they are strongly hybridized with the YSR state.
Overall:
This analogy provides a more intuitive understanding of the YSR-MZM interplay in terms of emergent particles interacting on a topological "string." It highlights the potential for observing rich physics, including scattering phenomena, bound state formation, and even topological phase transitions, by manipulating the interaction between these emergent particles. This perspective could guide future research towards exploring and exploiting these phenomena for novel applications in topological quantum technologies.