Fractional fermions with non-Abelian statistics

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Materials Science

Background:

• Topological phases of matter exhibit unique properties protected by topology.
• Fractionalization and non-Abelian statistics are key features in exotic quantum systems.
• Tight-binding models are crucial for understanding electronic properties in materials.

Purpose of the Study:

• Introduce a new class of low-dimensional topological tight-binding models.
• Investigate the emergence of fractionally charged fermions and non-Abelian braiding statistics.
• Characterize the topological phase transitions and bound states within these models.

Main Methods:

• Analytical study in the continuum limit.
• Numerical simulations in the tight-binding representation.
• Investigation of spinless and spinful fermions in ladder systems with magnetic fields.

Main Results:

• Identification of bound states with fractional charges and non-Abelian braiding statistics.
• Observation of a topological phase transition in the BDI topological class.
• Discovery of two degenerate, robust midgap bound states localized at ladder ends.

Conclusions:

• The novel topological models provide a platform for realizing exotic quantum phenomena.
• Fractional charges and non-Abelian statistics are achievable in these low-dimensional systems.
• The robustness of the bound states suggests potential applications in topological quantum computing.