  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, 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 anti-parallel configurations along the rungs, and
the anti-parallel configuration causes an emergent time reversal asymmetry
protecting Kramer's pair's of Majorana zero modes, but in a BDI topological
superconductor. We determine the topological invariant and inspect the boundary
Majorana zero modes.
