Interplay between topology and interactions in superconducting chains.

Area of Science:

• Condensed Matter Physics
• Quantum Materials
• Topological Matter

Background:

• Non-trivial topological systems are often studied using simplified non-interacting models.
• Real systems contain electronic correlations and disorder, which may alter topological properties.
• Exact solutions for correlated topological systems are rare, limiting understanding.

Purpose of the Study:

• To extend the solvable Kitaev p-wave superconducting chain model to include electronic correlations.
• To investigate the interplay between correlations, disorder, and non-trivial topological behavior.
• To provide a solvable framework for studying Majorana modes in correlated systems.

Main Methods:

• Investigated a superconducting Kitaev chain model interacting via a Falicov-Kimball Hamiltonian.
• Introduced a background of localized electrons to model correlations and disorder.
• Mapped the interacting model to a non-interacting one for exact solvability.

Main Results:

• Developed an exactly solvable model for a correlated superconducting Kitaev chain.
• Demonstrated the feasibility of studying the interplay between correlations and topology.
• Observed new effects arising from the random occupation of the chain by local moments (disorder).

Conclusions:

• The extended Kitaev chain model provides a valuable tool for exploring correlated topological phases.
• Electronic correlations and disorder significantly impact topological properties and emergent quasiparticles.
• The model offers fundamental insights into the behavior of Majorana modes in realistic quantum materials.