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. One of the fundamental challenges in this framework is how to manipulate the topological behavior of p-wave superconductors (PSC). In this work we investigate the magnetic field response of one-dimensional (1d) PSCs and we focus on the relation between the structure of the Cooper pair spin-configuration and the occurrence of topological phases with an enhanced number of Majorana fermions per edge. The topological phase diagram, consisting of phases harboring Majorana modes, becomes significantly modified when one tunes the strength of the applied field, the direction of the d-vector and allows for long range hopping amplitudes in the 1d PSC. We find transitions between phases with different number N of Majorana fermions per edge and we show how they can be both induced by a variation of the hopping strength and a spin rotation of d.