Zero energy modes in a superconductor with ferromagnetic adatom chains and quantum phase transitions

Area of Science:

• Condensed Matter Physics
• Materials Science
• Quantum Phenomena

Background:

• Majorana zero energy modes (MZEM) are exotic quasiparticles with potential applications in topological quantum computing.
• Their realization is often sought in systems with superconductivity and spin-orbit interaction, such as ferromagnetic chains on s-wave superconductors.

Purpose of the Study:

• To investigate the behavior of MZEM in ferromagnetic chains on an s-wave superconducting surface.
• To analyze the impact of Rashba spin-orbit interaction (SOI) and varying superconducting order treatments (non-self-consistent vs. self-consistent) on MZEM properties.
• To explore the relationship between exchange interaction, chain width, and MZEM delocalization for experimental guidance.

Main Methods:

• Theoretical modeling of a ferromagnetic (FM) chain of adatoms on an s-wave superconducting surface.
• Inclusion of Rashba spin-orbit interaction (SOI).
• Analysis using both non-self-consistent and self-consistent superconducting order parameters.
• Calculation of superconducting gap function and MZEM decay length as a function of system parameters.

Main Results:

• A discontinuous drop in the average superconducting gap function was observed with increasing exchange interaction in the self-consistent solution, coinciding with a topological phase transition.
• The decay length of MZEM was found to be a linear function of exchange coupling strength, chemical potential, and superconducting order.
• Wider ferromagnetic chains exhibited MZEM at smaller exchange couplings, with an increasing slope of decay length versus exchange coupling.

Conclusions:

• The study reveals distinct behaviors of MZEM under different treatments of superconducting order.
• The observed correlation between chain width and MZEM delocalization provides a promising avenue for experimental detection and manipulation.
• The findings contribute to the understanding of topological phase transitions and Majorana physics in hybrid material systems.