DIII topological superconductivity with emergent time-reversal symmetry

We find a class of topological superconductors which possess an emergent time-reversal symmetry that is present only after projecting to an effective low-dimensional model. We show that a topological phase in symmetry class DIII can be realized in a noninteracting system coupled to an $s$-wave superconductor only if the physical time-reversal symmetry of the system is broken, and we provide three general criteria that must be satisfied in order to have such a phase. We also provide an explicit model which realizes the class DIII topological superconductor in 1D. We show that, just as in time-reversal invariant topological superconductors, the topological phase is characterized by a Kramers pair of Majorana fermions that are protected by the emergent time-reversal symmetry.

Figure 1

Two nanowires, separated by a distance $d$, are coupled to an infinite superconducting plane. The two nanowires are assumed to have opposite Zeeman splittings.

Figure 2

Phase diagram of our model. A phase boundary at ${\mathrm{\Delta }}_Z^2={\mathrm{\Delta }}_d^2-{\mathrm{\Delta }}_c^2$ separates trivial and DIII topological superconducting phases. The topological phase is characterized by the presence of a Kramers pair of Majorana fermions that is protected by the emergent time-reversal symmetry.