Topological superconductors from one-dimensional periodically modulated Majorana chains

Area of Science:

• Condensed Matter Physics
• Topological Superconductivity
• Quantum Materials

Background:

• Topological models of fermions in 1D lattices offer insights into exotic quantum states.
• Topological superconductors exhibit unique properties like Majorana zero modes.
• Understanding and controlling topological phases is crucial for quantum technologies.

Purpose of the Study:

• To develop a systematic method for constructing topological superconductors in the BDI symmetry class.
• To realize topological superconductors with tunable winding numbers using Majorana fermion superlattices.
• To investigate the nature of chiral symmetries and associated winding numbers in multi-chain systems.

Main Methods:

• Construction of topological superconductors via analogy to 1D fermionic models.
• Creation of Majorana fermion superlattices to interpolate Majorana chains.
• Identification and analysis of chiral symmetries and winding numbers in multi-chain systems.
• Investigation of Majorana zero modes and their collapse into fractional charged states.

Main Results:

• A systematic method for constructing BDI topological superconductors is presented.
• Topological superconductors with arbitrary winding numbers are realized using Majorana superlattices.
• Two distinct winding numbers are identified, related to zero-energy modes and Majorana zero state differences.
• Spatially intertwined Majorana zero modes lead to fractional charged zero states.
• Systems with an odd number of chains exhibit coexistence of fractional and Majorana zero states.
• An intuitive explanation for the Z2 topological invariant in D class superconductors is provided.

Conclusions:

• The developed method offers a pathway to engineer novel topological superconductors.
• The findings contribute to a deeper understanding of topological phases and Majorana fermions.
• The study highlights potential for realizing exotic quantum states with tunable topological properties.