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Quantum wires subject to the combined action of spin-orbit and Zeemancoupling in the presence of \emph{s}-wave pairing potentials (superconductingproximity effect in semiconductors or superfluidity in cold atoms) are one ofthe most promising systems for the developing of topological phases hostingMajorana fermions. The breaking of time-reversal symmetry is essential for theappearance of unpaired Majorana fermions. By implementing a\emph{time-dependent} spin rotation, we show that the standard magnetostaticmodel maps into a \emph{non-magnetic} one where the breaking of time-reversalsymmetry is guaranteed by a periodical change of the spin-orbit coupling axisas a function of time. This suggests the possibility of developing thetopological superconducting state of matter driven by external forces in theabsence of magnetic fields and magnetic elements. From a practical viewpoint,the scheme avoids the disadvantages of conjugating magnetism andsuperconductivity, even though the need of a high-frequency driving ofspin-orbit coupling may represent a technological challenge. We describe thebasic properties of this Floquet system by showing that finite samples hostunpaired Majorana fermions at their edges despite the fact that the bulkFloquet quasienergies are gapless and that the Hamiltonian at each instant oftime preserves time-reversal symmetry. Remarkably, we identify the mean energyof the Floquet states as a topological indicator. We additionally show that thelocalized Floquet Majorana fermions are robust under local perturbations. Ourresults are supported by complementary numerical Floquet simulations.

Unpaired Floquet Majorana fermions without magnetic fields