Unconventional Topological Transitions in a Self-Organized Magnetic Ladder

It is commonly assumed that topological phase transitions in topological superconductors are accompanied by a closing of the topological gap or a change of the symmetry of the system. We demonstrate that an unconventional topological phase transition with neither gap closing nor a change of symmetry is possible. We consider a nanoscopic length ladder of atoms on a superconducting substrate, comprising self-organized magnetic moments coupled to itinerant electrons. For a range of conditions, the ground state of such a system prefers helical magnetic textures, a self-sustaining topologically nontrivial phase. Abrupt changes in the magnetic order as a function of induced superconducting pairing or chemical potential can cause topological phase transitions without closing the topological gap. Furthermore, the ground state prefers either parallel or antiparallel configurations along the rungs, and the antiparallel configuration causes an emergent time reversal asymmetry protecting Kramers pairs of Majorana zero modes, but in a BDI topological superconductor. We determine the topological invariant and inspect the boundary Majorana zero modes.