Majorana fermion fingerprints in spin-polarised scanning tunnelling microscopy

We calculate the spatially resolved tunnelling conductance of topological superconductors (TSCs) based on ferromagnetic chains, measured by means of spin-polarised scanning tunnelling microscopy (SPSTM). Our analysis reveals novel signatures of MFs arising from the interplay of their strongly anisotropic spin-polarisation and the magnetisation content of the tip. We focus on the deep Yu-Shiba-Rusinov (YSR) limit where only YSR bound states localised in the vicinity of the adatoms govern the low-energy as also the topological properties of the system. Under these conditions, we investigate the occurrence of zero/finite bias peaks (ZBPs/FBPs) for a single or two coupled TSC chains forming a Josephson junction. Each TSC can host up to two Majorana fermions (MFs) per edge if chiral symmetry is preserved. Here we retrieve the conductance for all the accessible configurations of the MF number of each chain. Our results illustrate innovative spin-polarisation-sensitive experimental routes for arresting the MFs by either restoring or splitting the ZBP in a predictable fashion via: (i) weakly breaking chiral symmetry, e.g. by the SPSTM tip itself or by an external Zeeman field and (ii) tuning the superconducting phase difference of the TSCs, which is encoded in the 4π-Josephson coupling of neighbouring MFs.