Non-Abelian Braiding in Spin Superconductors Utilizing the Aharonov-Casher Effect

Area of Science:

• Condensed matter physics
• Topological quantum phenomena
• Quantum computing

Background:

• Spin superconductors (SSC) represent an exciton condensate with charge-neutral, spin-triplet exciton superfluidity.
• Topological superconductors host Majorana zero modes (MZMs) exhibiting non-Abelian braiding statistics.
• Understanding novel topological states is crucial for advancing quantum information science.

Purpose of the Study:

• To theoretically propose and investigate a novel topological bound state in spin superconductors (SSCs).
• To explore the potential for non-Abelian braiding statistics in SSCs, analogous to MZMs.
• To identify experimentally distinct features of these SSC-bound states compared to MZMs.

Main Methods:

• Theoretical analysis of the interplay between spin superconductor properties and band topology.
• Investigation of topological bound states arising from exciton condensate phenomena.
• Application of the Aharonov-Casher effect to understand non-Abelian geometric phases.

Main Results:

• A novel topological bound state is predicted to exist in SSCs, obeying non-Abelian braiding statistics.
• The non-Abelian geometric phase originates from the Aharonov-Casher effect of a "half-charge", not the Aharonov-Bohm effect.
• These SSC-bound states are associated with electric flux gradients and possess an electric charge, distinguishing them from MZMs.

Conclusions:

• Spin superconductors offer a new platform for realizing and studying non-Abelian braiding physics.
• The proposed topological bound states in SSCs provide an experimentally accessible alternative to MZMs for quantum information applications.
• This work opens new avenues for exploring topological phenomena beyond conventional charge superconductors.