Phase diagram of a model for topological superconducting wires

We calculate the phase diagram of a model for topological superconducting wires with local s-wave pairing, spin-orbit coupling \(\vec{\lambda}\) and magnetic field \(\vec{B}\) with arbitrary orientations. This model is a generalized lattice version of the one proposed by Lutchyn \(\textit{et al.}\) [Phys. Rev. Lett. \(\textbf{105}\) 077001 (2010)] and Oreg \(\textit{et al.}\) [Phys. Rev. Lett. \(\textbf{105}\) 177002 (2010)], who considered \(\vec{\lambda}\) perpendicular to \(\vec{B}\). The model has a topological gapped phase with Majorana zero modes localized at the ends of the wires. We determine analytically the boundary of this phase. When the directions of the spin-orbit coupling and magnetic field are not perpendicular, in addition to the topological phase and the gapped non topological phase, a gapless superconducting phase appears.