For systems that can be modeled as a single-particle lattice extended along a privileged direction as, e.g., quantum wires, the so-called eigenvalue method provides full information about the propagating and evanescent modes as a function of energy.
This complex-band structure method can be applied either to lattices consisting of an infinite succession of interconnected layers described by the same local Hamiltonian or to superlattices: Systems in which the spatial periodicity involves more than one layer. Here, for time-dependent systems subject to a periodic driving, we present an adapted version of the superlattice scheme capable of obtaining the Floquet states and the Floquet quasienergy spectrum. Within this scheme the time periodicity is treated as existing along spatial dimension added to the original system. The solutions at a single energy for the enlarged artificial system provide the solutions of the original Floquet problem. The method is suited for arbitrary periodic excitations including strong and anharmonic drivings. We illustrate the capabilities of the methods for both time-independent and time-dependent systems by discussing: (a) topological superconductors in multimode quantum wires with spin-orbit interaction and (b) microwave driven quantum dot in contact with a topological superconductor.
Quantum wires subject to the combined action of spin-orbit and Zeeman coupling in the presence of emph{s}-wave pairing potentials (superconducting proximity effect in semiconductors or superfluidity in cold atoms) are one of the most promising system
s for the developing of topological phases hosting Majorana fermions. The breaking of time-reversal symmetry is essential for the appearance of unpaired Majorana fermions. By implementing a emph{time-dependent} spin rotation, we show that the standard magnetostatic model maps into a emph{non-magnetic} one where the breaking of time-reversal symmetry is guaranteed by a periodical change of the spin-orbit coupling axis as a function of time. This suggests the possibility of developing the topological superconducting state of matter driven by external forces in the absence of magnetic fields and magnetic elements. From a practical viewpoint, the scheme avoids the disadvantages of conjugating magnetism and superconductivity, even though the need of a high-frequency driving of spin-orbit coupling may represent a technological challenge. We describe the basic properties of this Floquet system by showing that finite samples host unpaired Majorana fermions at their edges despite the fact that the bulk Floquet quasienergies are gapless and that the Hamiltonian at each instant of time preserves time-reversal symmetry. Remarkably, we identify the mean energy of the Floquet states as a topological indicator. We additionally show that the localized Floquet Majorana fermions are robust under local perturbations. Our results are supported by complementary numerical Floquet simulations.
We propose a new architecture for implementing electronic interferometry in quantum Hall bars. It exploits scattering among parallel edge channels. In contrast to previous developments, this one employs a simply-connected mesa admitting serial concat
enation of building elements closer to optical analogues. Implementations of Mach-Zehnder and Hambury-Brown-Twiss interferometers are discussed together with new structures yet unexplored in quantum electronics.
