We investigate the topological properties and the accessible Majorana fermion (MF) phases arising in a hybrid device consisting of a chain of magnetic adatoms placed on the surface of a conventional superconductor with Rashba spin-orbit coupling (SOC). By identifying the favored classical magnetic ground state of the adatom chain, we extract the corresponding phase diagram which exhibits an interplay of ferromagnetic (FM), antiferromagnetic (AFM) and spiral orders. We determine the parameter regime for which the FM or AFM phases dominate over the spiral and additionally become stable against thermal and quantum fluctuations. For the topological analysis we focus on the FM and AFM cases and employ a low-energy effective model relying on Shiba bound states. We find that for both magnetic patterns the hybrid system behaves as a topological superconductor which can harbor one or even two MFs per edge, due to chiral symmetry. As we show, the two magnetic orderings lead to qualitatively and quantitatively distinct topological features that are reflected in the spatial profile of the MF wavefunctions. Finally, we propose directions on how to experimentally access the diverse MF phases by varying the adatom spacing, the SOC strength, or the magnetic moment of the adatoms in consideration.Materials with Rashba spin-orbit coupling (SOC) have recently attracted renewed attention due to their pivotal role for realizing artificial topological superconductors (TSCs) which harbor Majorana fermions (MFs) [1][2][3][4][5]. Early proposals involved materials with SOC, such as topological insulators [6], noncentrosymmetric SCs [7], and Rashba semiconductors [8][9][10][11], which stimulated significant experimental progress. Remarkably, a number of promising but yet not fully conclusive MF-signatures have been already reported in semiconductor-based heterostructures [12][13][14][15]. The unsettled witnessing of MFs [16][17][18] constitutes a strong motivation for engineering and testing alternative hybrid devices. For instance, platforms based on magnetic adatoms which can be manipulated and probed via spin-polarized and spatially-resolved scanning tunneling microscopy (STM) techniques, appear capable of unambiguously revealing the presence of MFs.This new perspective opened the door for new MF devices based on magnetic adatoms on the surface of conventional superconductors. One finds implementations with magnetic adatoms where the ordering is random [19], spiral [20-29], antiferromagnetic (AFM) with SOC induced by the combination of Zeeman fields and supercurrents [30], and ferromagnetic (FM) on top of a superconducting surface with Rashba SOC [31,32]. According to very recent experimental findings [33], MFs seem to indeed emerge in magnetic adatom hybrid devices, where the ordering of the chain appears to be FM. This type of ordering can lead to MFs only if Rashba SOC is present, arising from the broken inversion associated with the Pb superconducting substrate. In fact, this is a plausible scenario for Pb which owes already a non-...

We determine the nature of the magnetic order on the surface of a topological insulator (TI) which develops due to hexagonal warping and the resulting Fermi surface (FS) nesting in the presence of a repulsive Hubbard interaction. For this purpose we investigate the spin susceptibility and derive a Landau theory to compare the different accessible phases. For a nearly hexagonal FS and sufficiently strong interaction the magnetic ground state is formed by a skyrmion lattice, i.e., by a superposition of three helical spin density waves which preserves C3 symmetry. The magnetic ground state is topologically nontrivial with a nonzero skyrmion charge, which can be stabilized and controlled by an applied magnetic field. By bringing the TI in proximity to a conventional superconductor one can engineer a C3-symmetric topological superconductor. We explore the modification of the phase diagram as well as the mutual influence between the skyrmion structure and a multipolar distribution of supercurrents, which can provide information about the underlying skyrmion charge.

We calculate the spatially resolved tunneling conductance of topological superconductors (TSCs) based on ferromagnetic chains, measured by means of spin-polarised scanning tunneling 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 YuShiba-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 occurence 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-polarisationsensitive 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.

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