From Andreev bound states to Majorana fermions in topological wires on superconducting substrates : a story of mutation

We study the proximity effect in a topological nanowire tunnel coupled to an s-wave superconducting substrate. We use a general Green's function approach that allows us to study the evolution of the Andreev bound states in the wire into Majorana fermions. We show that the strength of the tunnel coupling induces a topological transition in which the Majorana fermionic states can be destroyed when the coupling is very strong. Moreover, we provide a phenomenologial study of the effects of disorder in the superconductor on the formation of Majorana fermions. We note a non-trivial effect of a quasiparticle broadening term which can take the wire from a topological into a non-topological phase in certain ranges of parameters. Our results have also direct consequences for a nanowire coupled to an inhomogenous superconductor

Majorana Fermions in Honeycomb Lattices

We study the formation of Majorana fermions in honeycomb-lattice structures in the presence of a Zeeman field, Rashba spin-orbit coupling, and in the proximity of an s-wave superconductor. We show that an exact mapping exists between an anisotropic hexagonal-lattice nanoribbon at k = 0 and a one-dimensional chain, for which the existence of Majorana fermions has been extensively discussed. Consequently we can predict the conditions for the emergence of Majorana fermions at the edges of such ribbon, and relate the existence of Majoranas to a band inversion in the bulk band structure. Moreover we find that similar situations arise in isotropic lattices and we give some examples which show the formation of Majorana fermions in these structures.Comment: 7 pages, 9 figure

Effects of finite superconducting coherence lengths and of phase gradients in topological SN and SNS junctions and rings

We study the effect of a finite proximity superconducting (SC) coherence length in SN and SNS junctions consisting of a semiconducting topological insulating wire whose ends are connected to either one or two s-wave superconductors. We find that such systems behave exactly as SN and SNS junctions made from a single wire for which some regions are sitting on top of superconductors, the size of the topological SC region being determined by the SC coherence length. We also analyze the effect of a non-perfect transmission at the NS interface on the spatial extension of the Majorana fermions. Moreover, we study the effects of continuous phase gradients in both an open and closed (ring) SNS junction. We find that such phase gradients play an important role in the spatial localization of the Majorana fermions

Frequency-Domain Measurement of the Spin Imbalance Lifetime in Superconductors

We have measured the lifetime of spin imbalances in the quasiparticle population of a superconductor ($\tau_s$) in the frequency domain. A time-dependent spin imbalance is created by injecting spin-polarised electrons at finite excitation frequencies into a thin-film mesoscopic superconductor (Al) in an in-plane magnetic field (in the Pauli limit). The time-averaged value of the spin imbalance signal as a function of excitation frequency, $f_{RF}$ shows a cut-off at $f_{RF} \approx 1/(2\pi\tau_s)$. The spin imbalance lifetime is relatively constant in the accessible ranges of temperatures, with perhaps a slight increase with increasing magnetic field. Taking into account sample thickness effects, $\tau_s$ is consistent with previous measurements and of the order of the electron-electron scattering time $\tau_{ee}$. Our data are qualitatively well-described by a theoretical model taking into account all quasiparticle tunnelling processes from a normal metal into a superconductor.Comment: Includes Supplementary Informatio

Response of the warm absorber cloud to a variable nuclear flux in active galactic nuclei

Recent modeling of the warm absorber in active galactic nuclei has proved the usefulness of constant total (gas plus radiation) pressure models, which are highly stratified in temperature and density. We explore the consistency of those models when the typical variation of the flux from the central source is taken into account. We perform a variability study of the warm absorber response, based on timescales and our photoionization code TITAN. We show that the ionization and recombination timescales are much shorter than the dynamical timescale. Clouds very close to the central black hole will maintain their equilibrium since the characteristic variability timescales of the nuclear source are longer than cloud timescales. For more distant clouds, the density structure has no time to vary, in response to the variations of the temperature or ionization structure, and such clouds will show the departure from the constant pressure equilibrium. We explore the impact of this departure on the observed properties of the transmitted spectrum and soft X-ray variability: (i) non uniform velocities, of the order of sound speed, appear due to pressure gradients, up to typical values of 100 km/s. These velocities lead to the broadening of lines. This broadening is usually observed and very difficult to explain otherwise. (ii) Energy-dependent fractional variability amplitude in soft X-ray range has a broader hump around ~ 1-2 keV, and (iv) the plot of the equivalent hydrogen column density vs. ionization parameter is steeper than for equilibrium clouds. The results have the character of a preliminary study and should be supplemented in the future with full time-dependent radiation transfer and dynamical computations.Comment: 9 pages, 7 figures, accepted for publication by Astronomy & Astrophysic

Superconductor spintronics: Modeling spin and charge accumulation in out-of-equilibrium NS junctions subjected to Zeeman magnetic fields

We study the spin and charge accumulation in junctions between a superconductor and a ferromagnet or a normal metal in the presence of a Zeeman magnetic field, when the junction is taken out of equilibrium by applying a voltage bias. We write down the most general form for the spin and charge current in such junctions, taking into account all spin-resolved possible tunneling processes. We make use of these forms to calculate the spin accumulation in NS junctions subjected to a DC bias, and to an AC bias, sinusoidal or rectangular. We observe that in the limit of negligeable changes on the superconducting gap, the NS dynamical conductance is insensitive to spin imbalance. Therefore to probe the spin accumulation in the superconductor, one needs to separate the injection and detection point, i. e. the electrical spin detection must be non-local. We address also the effect of the spin accumulation induced in the normal leads by driving a spin current and its effects on the detection of the spin accumulation in the superconductor. Finally, we investigate the out-of-equilibrium spin susceptibility of the SC, and we show that it deviates drastically from it's equilibrium value

Mid-infrared sub-wavelength grating mirror design: tolerance and influence of technological constraints

High polarization selective Si/SiO2 mid-infrared sub-wavelength grating mirrors with large bandwidth adapted to VCSEL integration are compared. These mirrors have been automatically designed for operation at \lambda = 2.3 $\mu$m by an optimization algorithm which maximizes a specially defined quality factor. Several technological constraints in relation with the grating manufacturing process have been imposed within the optimization algorithm and their impact on the optical properties of the mirror have been evaluated. Furthermore, through the tolerance computation of the different dimensions of the structure, the robustness with respect to fabrication errors has been tested. Finally, it appears that the increase of the optical performances of the mirror imposes a less tolerant design with severer technological constraints resulting in a more stringent control of the manufacturing process.Comment: The final publication is available at http://iopscience.iop.org/2040-8986/13/12/125502

The puzzle of the soft X-ray excess in AGN: absorption or reflection?

The 2-10 keV continuum of AGN is generally well represented by a single power law. However, at smaller energies the continuum displays an excess with respect to the extrapolation of this power law, called the ''soft X-ray excess''. Until now this soft X-ray excess was attributed, either to reflection of the hard X-ray source by the accretion disk, or to the presence of an additional comptonizing medium, giving a steep spectrum. An alternative solution proposed by Gierlinski and Done (2004) is that a single power law well represents both the soft and the hard X-ray emission and the impression of the soft X-ray excess is due to absorption of a primary power law by a relativistic wind. We examine the advantages and drawbacks of reflection versus absorption models, and we conclude that the observed spectra can be well modeled, either by absorption (for a strong excess), or by reflection (for a weak excess). However the physical conditions required by the absorption models do not seem very realistic: we would prefer an ''hybrid model''.Comment: 4 pages, 3 figures, abstracts SF2A-2005, published by EDP-Sciences Conference Serie