Majorana fermion (MF) excitations in solid state system have non-Abelian statistics which is essential for topological quantum computation. Previous proposals to realize MF, however, generally requires fine-tuning of parameters. Here we explore a pla
tform which avoids the fine-tuning problem, namely a ferromagnetic chain deposited on the surface of a spin-orbit coupled $s$-wave superconductor. We show that it generically supports zero-energy topological MF excitations near the two ends of the chain with minimal fine-tuning. Depending on the strength of the ferromagnetic moment in the chain, the number of MFs at each end, $n$, can be either one or two, and should be revealed by a robust zero-bias peak (ZBP) of height $2ne^2/h$ in scanning tunneling microscopy (STM) measurements which would show strong (weak) signals at the ends (middle) of the chain. The role of an approximate chiral symmetry which gives an integer topological invariant to the system is discussed.
Charge and spin transport in a junction involving two triplet superconductors and a ferromagnetic barrier are studied. We use Bogoliubov-de Gennes wavefunctions to construct the Greens function, from which we obtain the Josephson currents in terms of
the Andreev reflection coefficients. We focus on the consequences of a finite barrier width for the occurrence of 0-pi transitions and for the spin currents, and examine the appropriateness of the common delta-function approximation for the tunneling region.
