Moiré dispersion of edge states in spin chains on superconductors

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 moiré pattern emerging from the electronic interactions in the superconductor and the discreteness of the spin-chain lattice. By modifying the spin lattice, the moiré dispersion of edge states can be controlled. In particular, we can engineer nondispersive 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.
Financial support from the Spanish State Research Agency grants (Projects No. PID2021-127917NB-I00, No. RTI2018097895-B-C44, and Excelencia EUR2020-112116) funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”, and Eusko Jaurlaritza (Project No. PIBA 2020_1_0017) is gratefully acknowledged.