Summary
The study analyzes the joint dynamics of the phase bias and the propagating Majorana fermions of the edge modes in Josephson junctions containing 2D time-reversal invariant topological superconductors (TRITOPS). The research considers TRITOPS-TRITOPS junctions and junctions between topological and non-topological superconductors (TRITOPS-S).
Highlights
- The study examines the effect of phase fluctuations in the junction and the impact of solitonic solutions of ϕ generated by fluxons trapped in the junction.
- The research shows that these solitons generate a spatial-dependent mass with a sign change akin to the Jackiw-Rebbi model.
- The localized bound states hybridize in soliton-antisoliton configurations, generating an effective attraction or repulsion in the dynamics of the soliton-antisoliton collision.
- The study analyzes the impact of the electron bound states on the collision of solitons.
- The research considers the stability of the mean-field description in the TRITOPS-S junction.
- The study discusses the equation of motion for the phase and the corresponding solitonic solutions in the different junctions.
- The research examines the type of electronic bound states generated by these solitonic profiles in the phase.
Key Insights
- The study reveals that the phase fluctuations in the TRITOPS-S junction can destroy the stability of the state with broken time-reversal symmetry, and the phase stiffness must overcome a critical value for the mean-field description to be stable.
- The research demonstrates that the solitonic solutions of ϕ in the TRITOPS-TRITOPS junction generate a spatial-dependent mass with a sign change, leading to the formation of zero-energy fermionic states localized at the fluxon.
- The study shows that the localized bound states in the soliton-antisoliton configurations can hybridize, resulting in an effective attraction or repulsion in the dynamics of the soliton-antisoliton collision.
- The research highlights the importance of considering the impact of the electron bound states on the collision of solitons, as they can play a crucial role in the tunneling processes connecting the edge modes through the junction.
- The study reveals that the TRITOPS-TRITOPS junction can exhibit a double sine-Gordon equation, leading to a more complex phase diagram compared to the TRITOPS-S junction.
- The research demonstrates that the solitonic profiles in the phase can introduce important changes in the mass term of the effective Hamiltonian, leading to the formation of zero-energy bound states.
- The study highlights the potential applications of these localized zero modes, as they can be manipulated and moved in these systems by the motions of the fluxons at the junction.
Mindmap
Citation
Ruiz, G. F. R., Reich, A., Shnirman, A., Schmalian, J., & Arrachea, L. (2024). Binding zero modes with fluxons in Josephson junctions of time-reversal invariant topological superconductors (Version 2). arXiv. https://doi.org/10.48550/ARXIV.2403.14277