Phase diagram of a model for topological superconducting wires

Abstract

We calculate the phase diagram of a model for topological superconducting wires with local s-wave pairing, spin-orbit coupling λ and magnetic field B - with arbitrary orientations. This model is a generalized lattice version of the one proposed by Lutchyn et al. [Phys. Rev. Lett. 105, 077001 (2010)PRLTAO0031-900710.1103/PhysRevLett.105.077001] and Oreg et al. [Phys. Rev. Lett. 105, 177002 (2010)PRLTAO0031-900710.1103/PhysRevLett.105.177002], who considered λ - perpendicular to 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 nontopological phase, a gapless superconducting phase appears.