Fractional Spin and Josephson Effect in Time-Reversal-Invariant Topological Superconductors

Area of Science:

• Condensed Matter Physics
• Quantum Information Science
• Materials Science

Background:

• Time-reversal-invariant topological superconducting (TRITOPS) wires are predicted to host exotic quasiparticles with fractional spin (ℏ/4) at their ends.
• Josephson junctions are crucial for understanding quantum transport phenomena and developing superconducting electronic devices.
• The interplay between topological superconductivity and quantum dot systems offers a platform for exploring novel quantum states and phenomena.

Purpose of the Study:

• To investigate the influence of fractional spin at the ends of TRITOPS wires on the Josephson current in a TRITOPS-quantum dot-TRITOPS Josephson junction.
• To explore the tunability of the TRITOPS wire model between topological and nontopological phases and its effect on quantum transport.
• To elucidate the mechanism behind the 0-to-π transition in such hybrid systems.

Main Methods:

• Utilized continuous-time Monte Carlo simulations to compute the equilibrium Josephson current in the full TRITOPS-quantum dot-TRITOPS model.
• Employed an effective low-energy theory to interpret the simulation results and understand the underlying physics.
• Modeled the TRITOPS wire in a manner that allows tuning between topological and nontopological phases.

Main Results:

• Demonstrated that the fractional spin at the ends of TRITOPS wires significantly affects the Josephson current.
• Observed that in the topological phase, the 0-to-π transition is suppressed or 'quenched'.
• Identified the formation of a spin singlet, arising from the coupling between the quantum dot spin and the fractional spins of the adjacent topological superconductors, as the mechanism for quenching the transition.

Conclusions:

• The fractional spin of TRITOPS wires plays a critical role in determining the transport properties of Josephson junctions.
• The quantum dot acts as a mediator, enabling the formation of a spin singlet with the fractional spins, thereby altering the junction's superconducting phase behavior.
• These findings provide insights into controlling and manipulating quantum states in topological superconducting heterostructures.