Majorana fermions in chiral topological ferromagnetic nanowires

Motivated by a recent experiment in which zero-bias peaks have been observed in scanning tunneling microscopy (STM) experiments performed on chains of magnetic atoms on a superconductor, we show, by generalizing earlier work, that a multichannel ferromagnetic wire deposited on a spin-orbit coupled superconducting substrate can realize a nontrivial chiral topological superconducting state with Majorana bound states localized at the wire ends. The nontrivial topological state occurs for generic parameters requiring no fine tuning, at least for very large exchange spin splitting in the wire. We theoretically obtain the signatures which appear in the presence of an arbitrary number of Majorana modes in multiwire systems incorporating the role of finite temperature, finite potential barrier at the STM tip, and finite wire length. These signatures are presented in terms of spatial profiles of STM differential conductance, which clearly reveal zero-energy Majorana end modes and the prediction of a multiple Majorana based fractional Josephson effect. A substantial part of this work is devoted to a detailed critical comparison between our theory and the recent STM experiment claiming the observation of Majorana fermions in ferromagnetic atomic chains on a superconductor. The conclusion of this detailed comparison is that although the experimental observations are not manifestly inconsistent with our theoretical findings, the very small topological superconducting gap and the very high temperature of the experiment make it impossible to decisively verify the existence of a localized Majorana zero mode, as the spectral weight of the Majorana mode is necessarily spread over a very broad energy regime exceeding the size of the gap. Such an extremely broad (and extremely weak) conductance peak could easily arise from any subgap states existing in the rather complex system studied experimentally and may or may not have anything to do with a putative Majorana zero mode as discussed in the first half of our paper. Thus, although the experimental findings are indeed consistent with a highly broadened and weakened Majorana zero-bias peak, much lower experimental temperatures (and/or much larger experimental topological superconducting gaps) are necessary for any definitive conclusion.