Moir\'e dispersion of edge states in spin chains on superconductors

Abstract

Our calculations of ferromagnetic spin chains on s-wave superconductors show that the energy oscillations of edge states with the chain's length are due to a moir\'e pattern emerging from Friedel-like oscillations and the discreteness of the spin-chain lattice. By modifying the spin lattice, the moir\'e dispersion of edge states can be controlled. In particular, we can engineer non-dispersive edge states that remain at fixed energy regardless of the size distribution of the spin chains. This is an important step in the study of edge states of spin chains that can be fabricated with a certain size dispersion.