Using Josephson junctions to determine the pairing state of superconductors without crystal inversion symmetry

Theoretical studies of a planar tunnel junction between two superconductors with antisymmetric spin-orbit coupling are presented. The half-space Green's function for such a superconductor is determined. This is then used to derive expressions for the dissipative current and the Josephson current of the junction. Numerical results are presented in the case of the Rashba spin-orbit coupling, relevant to the much studied compound CePt$_3$Si. Current-voltage diagrams, differential conductance and the critical Josephson current are presented for different crystallographic orientations and different weights of singlet and triplet components of the pairing state. The main conclusion is that Josephson junctions with different crystallographic orientations may provide a direct connection between unconventional pairing in superconductors of this kind and the absence of inversion symmetry in the crystal.Comment: 16 pages, 10 figure

Andreev reflection from non-centrosymmetric superconductors and Majorana bound state generation in half-metallic ferromagnets

We study Andreev reflection at an interface between a half metal and a superconductor with spin-orbit interaction. While the absence of minority carriers in the half metal makes singlet Andreev reflection impossible, the spin-orbit interaction gives rise to triplet Andreev reflection, i.e., the reflection of a majority electron into a majority hole or vice versa. As an application of our calculation, we consider a thin half metal film or wire laterally attached to a superconducting contact. If the half metal is disorder free, an excitation gap is opened that is proportional to the spin-orbit interaction strength in the superconductor. For electrons with energy below this gap a lateral half-metal--superconductor contact becomes a perfect triplet Andreev reflector. We show that the system supports localized Majorana end states in this limit.Comment: 14 pages, 3 figure

Supersymmetric Electroweak Cosmic Strings

We study the connection between $N=2$ supersymmetry and a topological bound in a two-Higgs-doublet system with an $SU(2)\times U(1)_Y\times U(1)_{Y^{\prime}}$ gauge group. We derive the Bogomol'nyi equations from supersymmetry considerations showing that they hold provided certain conditions on the coupling constants, which are a consequence of the huge symmetry of the theory, are satisfied. Their solutions, which can be interpreted as electroweak cosmic strings breaking one half of the supersymmetries of the theory, are studied. Certain interesting limiting cases of our model which have recently been considered in the literature are finally analyzed.Comment: 20 pages, RevTe

Phases of dual superconductivity and confinement in softly broken N=2 supersymmetric Yang-Mills theories

We study the electric flux tubes that undertake color confinement in N=2 supersymmetric Yang-Mills theories softly broken down to N=1 by perturbing with the first two Casimir operators. The relevant Abelian Higgs model is not the standard one due to the presence of an off-diagonal coupling among different magnetic U(1) factors. We perform a preliminary study of this model at a qualitative level. BPS vortices are explicitely obtained for particular values of the soft breaking parameters. Generically however, even in the ultrastrong scaling limit, vortices are not critical but live in a "hybrid" type II phase. Also, ratios among string tensions are seen to follow no simple pattern. We examine the situation at the half Higgsed vacua and find evidence for solutions with the behaviour of superconducting strings. In some cases they are solutions to BPS equations.Comment: 15 pages, 1 figure, revtex; v2: typos corrected, final versio

New non compact Calabi-Yau metrics in D=6

A method for constructing explicit Calabi-Yau metrics in six dimensions in terms of an initial hyperkahler structure is presented. The equations to solve are non linear in general, but become linear when the objects describing the metric depend on only one complex coordinate of the hyperkahler 4-dimensional space and its complex conjugated. This situation in particular gives a dual description of D6-branes wrapping a complex 1-cycle inside the hyperkahler space, which was studied by Fayyazuddin. The present work generalize the construction given by him. But the explicit solutions we present correspond to the non linear problem. This is a non linear equation with respect to two variables which, with the help of some specific anzatz, is reduced to a non linear equation with a single variable solvable in terms of elliptic functions. In these terms we construct an infinite family of non compact Calabi-Yau metrics.Comment: A numerical error has been corrected together with the corresponding analysis of the metri

Quantum transport in noncentrosymmetric superconductors and thermodynamics of ferromagnetic superconductors

We consider a general Hamiltonian describing coexistence of itinerant ferromagnetism, spin-orbit coupling and mixed spin-singlet/triplet superconducting pairing in the context of mean-field theory. The Hamiltonian is diagonalized and exact eigenvalues are obtained, thus allowing us to write down the coupled gap equations for the different order parameters. Our results may then be applied to any model describing coexistence of any combination of these three phenomena. As a specific application of our results, we consider tunneling between a normal metal and a noncentrosymmetric superconductor with mixed singlet and triplet gaps. The conductance spectrum reveals information about these gaps in addition to how the influence of spin-orbit coupling is manifested. We also consider the coexistence of itinerant ferromagnetism and triplet superconductivity as a model for recently discovered ferromagnetic superconductors. The coupled gap equations are solved self-consistently, and we study the conditions necessary to obtain the coexistent regime of ferromagnetism and superconductivity. Analytical expressions are presented for the order parameters, and we provide an analysis of the free energy to identify the preferred system state. Moreover, we make specific predictions concerning the heat capacity for a ferromagnetic superconductor. In particular, we report a nonuniversal relative jump in the specific heat, depending on the magnetization of the system, at the uppermost superconducting phase transition. [Shortened abstract due to arXiv submission.]Comment: 19 pages, 15 figures (high quality figures available in published version). Accepted for publication in Phys. Rev.

On the Lifshitz tail in the density of states of a superconductor with magnetic impurities

We argue that any superconductor with magnetic impurities is gapless due to a Lifshitz tail in the density of states extending to zero energy. At low energy the density of states $\nu(E \to 0)$ remains finite. We show that fluctuations in the impurity distribution produce regions of suppressed superconductivity, which are responsible for the low energy density of states.Comment: 4 pages, uuencoded latex file + ps figure file

A quantization procedure based on completely positive maps and Markov operators

We describe $\omega$-limit sets of completely positive (CP) maps over finite-dimensional spaces. In such sets and in its corresponding convex hulls, CP maps present isometric behavior and the states contained in it commute with each other. Motivated by these facts, we describe a quantization procedure based on CP maps which are induced by Markov (transfer) operators. Classical dynamics are described by an action over essentially bounded functions. A non-expansive linear map, which depends on a choice of a probability measure, is the centerpiece connecting phenomena over function and matrix spaces

OpenSPIM - an open access platform for light sheet microscopy

Light sheet microscopy promises to revolutionize developmental biology by enabling live in toto imaging of entire embryos with minimal phototoxicity. We present detailed instructions for building a compact and customizable Selective Plane Illumination Microscopy (SPIM) system. The integrated OpenSPIM hardware and software platform is shared with the scientific community through a public website, thereby making light sheet microscopy accessible for widespread use and optimization to various applications.Comment: 7 pages, 3 figures, 6 supplementary videos, submitted to Nature Methods, associated public website http://openspim.or