1208.2742 (Andres A. Reynoso et al.)

Topological phases and Majorana Fermions in quantum wires: from

magnetostatic to non-magnetic Floquet platforms    [PDF]

Andres A. Reynoso, Diego Frustaglia

Quantum wires subject to the combined action of spin-orbit and Zeeman coupling in the presence of s-wave pairing potentials (superconducting proximity effect in semiconductors or superfluidity in cold atoms) are one of the most promising systems for the developing of topological phases hosting Majorana fermions. Other potential platforms can be obtained by applying appropriate transformations to the quantum-wire model. One example is the recent proposal by Kjaergaard et al. [Phys. Rev. B 85, 020503(R) (2012)], where an effective spin-orbit coupling is obtained in electronic systems subject to magnetic textures after applying a local spin-rotation mapping. Here, instead, we employ a \emph{time-dependent} spin rotation that maps the standard magnetostatic model into a \emph{non-magnetic} one where the spin-orbit coupling axis changes as a function of time. This represents a proposal for the development of a topological state of matter driven by external forces. From a practical viewpoint, though the scheme avoids the disadvantages of conjugating magnetism and superconductivity, the need of a high-frequency driving of spin-orbit coupling represents a technological challenge. We describe the basic properties of this Floquet system and show that in finite samples it hosts Floquet Majorana fermions at its edges despite the fact that the bulk Floquet quasienergies are gapless and that the Hamiltonian at each instant of time is a time-reversal symmetric operator. The exact mapping to the static system allows us to show that the localized Floquet Majorana fermions are robust to local perturbations, this result is found to be in agreement with numerical simulations fully performed in the time-dependent system.

View original: http://arxiv.org/abs/1208.2742