Majorana fermions in vortex lattices.

Area of Science:

• Condensed Matter Physics
• Topological Quantum Matter

Background:

• Majorana fermions are exotic particles with potential applications in quantum computing.
• Superconducting vortices host Majorana zero modes, crucial for topological quantum computation.

Purpose of the Study:

• To investigate Majorana fermion tunneling in 2D chiral p-wave superconductor vortex arrays.
• To determine the impact of superconducting phase profiles on tunneling amplitudes.
• To explore the formation of energy bands in Majorana vortex lattices.

Main Methods:

• Theoretical analysis of Majorana fermion tunneling amplitudes.
• Development of tight-binding models for triangular and square vortex lattices.
• Investigation of the relationship between phase profiles and tunneling.

Main Results:

• Tunneling amplitude is proportional to the sine of half the phase difference between vortices.
• Superlattices emerge, featuring macroscopically degenerate, localizable flat bands at zero energy.
• A finite fraction of Majorana fermions retain zero energy, contrary to prior assumptions.

Conclusions:

• Phase-dependent tunneling in vortex arrays creates robust flat Majorana bands.
• Reduced decoherence in these systems enhances prospects for topological quantum computation.
• This work provides a pathway for scalable Majorana-based quantum computing.