One-dimensional spin-orbit coupled Dirac system with extendeds-wave superconductivity: Majorana modes and Josephson...

Area of Science:

• Condensed Matter Physics
• Topological Materials
• Superconductivity

Background:

• Investigates electron spin-momentum locking in topological insulators.
• Studies one-dimensional systems with spin-orbit coupling and s-wave superconductivity.

Purpose of the Study:

• To explore the emergence of Majorana zero energy modes in spin-orbit coupled superconducting systems.
• To analyze topological phase transitions in hybrid Schrödinger-Dirac systems.
• To investigate Andreev bound states and the AC Josephson effect in superconductor junctions.

Main Methods:

• Utilized both lattice and continuum models for theoretical analysis.
• Employed numerical and analytical calculations, including winding number.
• Studied systems with extended s-wave pairing, Dirac-like terms, and superconductor junctions with phase differences.

Main Results:

• Identified single Majorana zero energy modes at the ends of finite lattice systems with extended s-wave pairing.
• Observed zero energy end modes in the continuum model.
• Found a topological transition in a hybrid Schrödinger-Dirac system.
• Discovered a single Andreev bound state localized at the junction of two s-wave superconductors.
• Observed novel Shapiro plateaus in the AC Josephson effect when the Josephson frequency is a rational fraction of the applied AC frequency.

Conclusions:

• Spin-orbit coupling in superconducting systems can host exotic phenomena like Majorana modes.
• The system exhibits topological phase transitions tunable by the relative strength of Schrödinger and Dirac terms.
• Superconductor junctions display unique Andreev bound states and modified AC Josephson effects, with potential for experimental realization.