Long-Range Kitaev Chain Edge States: Exponential vs. Algebraic Decay

The analytical study by Jager, Dell'Anna, and Morigi reveals how edge states in the long-range Kitaev chain decay spatially, with behavior dictated by the anisotropy of tunneling and pairing terms. When parameters are isotropic—equal decay exponents and coefficients—the decay is purely exponential, localized sharply at the edges. In anisotropic cases, where exponents or coefficients differ, the decay starts exponentially but transitions to an algebraic tail at larger distances, governed by the smallest exponent. This dual behavior underscores the model's flexibility in describing topological superconductors, with implications for robust quantum devices. Numerical validations confirm the analytical predictions, highlighting the model's accuracy across various parameter sets. The findings provide a foundational understanding of edge state localization, essential for advancing quantum material design.