Zero energy modes of artificial spin chains from first-principles calculations

The conditions under which Majorana zero modes (MZM) appear and what are their physical properties in realistic materials have been of high interest over the past few years triggered by their possible applications as fault-tolerant quantum bits. The MZMs are topological states corresponding to triplet pairing at zero energy emerging in an inner gap inside the superconducting gap. However, experimentally it is very challenging to uniquely identify MZMs based solely on their spectral properties. Fully relativistic first-principles calculations based on the solution of the Bogoliubov-de Gennes equations are able to reproduce the measured spectral quantities and provide additional information on the nature of the in-gap states reported in corresponding experiments. In this work we present calculations in the superconducting state of the in-gap density of states, the singlet and triplet order parameters and various related quantities for Fe and Mn chains on pure Ta(110) and Au monolayer covered Nb(110) surface. The chains of magnetic ad-atoms are also assumed to be in various artificial spin-spiral states. In a wide range of the spin-spiral wavelength, we find an inner gap with states at zero energy and a large triplet pairing order parameter. Our results are then compared to experiments where possible and discuss the formation of MZMs in a material-specific way