Yu-Shiba-Rusinov (YSR) states Vs Majorana bound states : A Simplified Guide

The distinction between Yu-Shiba-Rusinov (YSR) states and Majorana bound states lies in their physical origins, properties, and roles in quantum systems, particularly in condensed matter physics.

Origin and Nature

YSR States:

• YSR states emerge in superconductors when a magnetic impurity induces a local perturbation. This interaction creates in-gap states due to the competition between superconducting pairing and the impurity's magnetic moment.
• They are localized states that decay rapidly away from the impurity.

Majorana Bound States:

• Majorana states arise at the ends of a topological superconductor. They result from the non-trivial topology of the system and represent exotic quasiparticles that are their own antiparticles.
• Unlike YSR states, Majorana states are non-local and exhibit topological protection.

Experimental Signatures

YSR States:

• Appears as symmetric subgap peaks in tunneling spectroscopy around the Fermi energy. The position of the peaks depends on the impurity interaction strength.
• Typically localized and associated with individual magnetic impurities.

Majorana Bound States:

• Characterized by a zero-bias conductance peak in tunneling spectroscopy, which is robust and does not shift with varying parameters, such as magnetic field or gate voltage.
• Often associated with the ends of one-dimensional topological superconductors (e.g., semiconductor nanowires proximitized by superconductors).

Symmetry and Robustness

YSR States:

• These states are not topologically protected and can be affected by local perturbations or disorder.
• Their energy depends on the strength of the exchange interaction between the impurity and the superconductor.

Majorana Bound States:

• Majorana states are protected by the system's topology and certain symmetries.
• They are robust against local perturbations and are highly sought after for fault-tolerant quantum computation due to their non-Abelian statistics.

Practical Applications

YSR States:

• Primarily a probe to study impurity effects and interactions in superconductors.
• Provides insight into the local density of states and magnetic properties of superconductors.

Majorana Bound States:

• A key candidate for realizing topological qubits in quantum computing.
• Their non-local nature enables encoding of quantum information that is inherently resistant to local decoherence.

In summary, YSR states are impurity-induced localized subgap states in conventional superconductors, while Majorana bound states are exotic quasiparticles tied to the topology of the superconductor and are promising for quantum computation.

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