Magnetic manipulation of topological states in p-wave superconductors

Substantial experimental investigation has provided evidence for spin-triplet pairing in diverse classes of materials and in a variety of artificial heterostructures. A fundamental challenge in actual experiments is how to manipulate the topological behavior of $p$-wave superconductors (PSCs) that could open perspectives for applications. Such a control knob is naturally provided by the spin-triplet character of the PSC order parameter, described by the spin d-vector. Therefore, in this work we investigate the magnetic field response of one-dimensional (1d) PSCs and demonstrate that the structure of the Cooper pair spin-configuration is crucial to set topological phases with an enhanced number of Majorana fermions per edge, N, ranging from N=0 to 4. The topological phase diagram, consisting of phases with Majorana modes at the edge, becomes significantly modified when one tunes the strength of the applied field and allows for long range hopping amplitudes in the 1d PSC. We find transitions between phases with different number of Majorana fermions per edge that can be both induced by a variation of the hopping strength and a spin rotation of the d-vector. Hence, the interplay of the applied magnetic field and the internal spin degree of freedom of the PSC opens a new promising route for engineering topological phases with large number of Majorana modes.