Specific heat evidence for two-gap superconductivity in ternary-iron silicide Lu2_{2}Fe3_{3}Si5_{5}

We report low-temperature specific heat studies on single-crystalline ternary-iron silicide superconductor Lu$_{2}$Fe$_{3}$Si$_{5}$ with$T_c$ = 6.1 K down to $\sim T_c/20$. We confirm a reduced normalized jump in specific heat at $T_c$, and find that the specific heat divided by temperature $C/T$ shows sudden drop at $\sim T_c/5$ and goes to zero with further decreasing temperature. These results indicate the presence of two distinct superconducting gaps in Lu$_{2}$Fe$_{3}$Si$_{5}$, similar to a typical two-gap superconductor MgB$_{2}$. We also report Hall coefficients, band structure calculation, and the anisotropy of upper critical fields for Lu$_{2}$Fe$_{3}$Si$_{5}$, which support the anisotropic multiband nature and reinforce the existence of two superconducting gaps in Lu$_{2}$Fe$_{3}$Si$_{5}$.Comment: 5 pages, 5 figure

Disorder-sensitive superconductivity in the iron silicide Lu2_2Fe3_3Si5_5 studied by the Lu-site substitutions

We studied effect of non-magnetic and magnetic impurities on superconductivity in Lu$_2$Fe$_3$Si$_5$ by small amount substitution of the Lu site, which investigated structural, magnetic, and electrical properties of non-magnetic (Lu$_{1-x}$Sc$_x$)$_2$Fe$_3$Si$_5$, (Lu$_{1-x}$Y$_x$)$_2$Fe$_3$Si$_5$, and magnetic (Lu$_{1-x}$Dy$_x$)$_2$Fe$_3$Si$_5$. The rapid depression of $T_c$ by non-magnetic impurities in accordance with the increase of residual resistivity reveals the strong pair breaking dominated by disorder. We provide compelling evidence for the sign reversal of the superconducting order parameter in Lu$_2$Fe$_3$Si$_5$.Comment: 4 pages, 5 figure

Pfaffian representations of cubic surfaces

Let K be a field of characteristic zero. We describe an algorithm which requires a homogeneous polynomial F of degree three in K[x_0,x_1,x_2,x_3] and a zero A of F in P^3_K and ensures a linear pfaffian representation of V(F) with entries in K[x_0,x_1,x_2,x_3], under mild assumptions on F and A. We use this result to give an explicit construction of (and to prove the existence of) a linear pfaffian representation of V(F), with entries in K'[x_0,x_1,x_2,x_3], being K' an algebraic extension of K of degree at most six. An explicit example of such a construction is given.Comment: 17 pages. Expanded with some remarks. Published with minor corrections in Geom. Dedicat

Shear-induced quench of long-range correlations in a liquid mixture

A static correlation function of concentration fluctuations in a (dilute) binary liquid mixture subjected to both a concentration gradient and uniform shear flow is investigated within the framework of fluctuating hydrodynamics. It is shown that a well-known $|\nabla c|^2/k^4$ long-range correlation at large wave numbers $k$ crosses over to a weaker divergent one for wave numbers satisfying $k<(\dot{\gamma}/D)^{1/2}$, while an asymptotic shear-controlled power-law dependence is confirmed at much smaller wave numbers given by $k\ll (\dot{\gamma}/\nu)^{1/2}$, where $c$, $\dot{\gamma}$, $D$ and $\nu$ are the mass concentration, the rate of the shear, the mass diffusivity and the kinematic viscosity of the mixture, respectively. The result will provide for the first time the possibility to observe the shear-induced suppression of a long-range correlation experimentally by using, for example, a low-angle light scattering technique.Comment: 8pages, 2figure

Surfaces containing a family of plane curves not forming a fibration

We complete the classification of smooth surfaces swept out by a 1-dimensional family of plane curves that do not form a fibration. As a consequence, we characterize manifolds swept out by a 1-dimensional family of hypersurfaces that do not form a fibration.Comment: Author's post-print, final version published online in Collect. Mat

Variety of idempotents in nonassociative algebras

In this paper, we study the variety of all nonassociative (NA) algebras from the idempotent point of view. We are interested, in particular, in the spectral properties of idempotents when algebra is generic, i.e. idempotents are in general position. Our main result states that in this case, there exist at least $n-1$ nontrivial obstructions (syzygies) on the Peirce spectrum of a generic NA algebra of dimension $n$. We also discuss the exceptionality of the eigenvalue $\lambda=\frac12$ which appears in the spectrum of idempotents in many classical examples of NA algebras and characterize its extremal properties in metrised algebras.Comment: 27 pages, 1 figure, submitte

Tracking Cooper Pairs in a Cuprate Superconductor by Ultrafast Angle-Resolved Photoemission

In high-temperature superconductivity, the process that leads to the formation of Cooper pairs, the fundamental charge carriers in any superconductor, remains mysterious. We use a femtosecond laser pump pulse to perturb superconducting Bi2Sr2CaCu2O8+{\delta}, and study subsequent dynamics using time- and angle-resolved photoemission and infrared reflectivity probes. Gap and quasiparticle population dynamics reveal marked dependencies on both excitation density and crystal momentum. Close to the d-wave nodes, the superconducting gap is sensitive to the pump intensity and Cooper pairs recombine slowly. Far from the nodes pumping affects the gap only weakly and recombination processes are faster. These results demonstrate a new window into the dynamical processes that govern quasiparticle recombination and gap formation in cuprates.Comment: 22 pages, 9 figure

On Invariant Notions of Segre Varieties in Binary Projective Spaces

Invariant notions of a class of Segre varieties \Segrem(2) of PG(2^m - 1, 2) that are direct products of $m$ copies of PG(1, 2), $m$ being any positive integer, are established and studied. We first demonstrate that there exists a hyperbolic quadric that contains \Segrem(2) and is invariant under its projective stabiliser group \Stab{m}{2}. By embedding PG(2^m - 1, 2) into \PG(2^m - 1, 4), a basis of the latter space is constructed that is invariant under \Stab{m}{2} as well. Such a basis can be split into two subsets whose spans are either real or complex-conjugate subspaces according as $m$ is even or odd. In the latter case, these spans can, in addition, be viewed as indicator sets of a \Stab{m}{2}-invariant geometric spread of lines of PG(2^m - 1, 2). This spread is also related with a \Stab{m}{2}-invariant non-singular Hermitian variety. The case $m=3$ is examined in detail to illustrate the theory. Here, the lines of the invariant spread are found to fall into four distinct orbits under \Stab{3}{2}, while the points of PG(7, 2) form five orbits.Comment: 18 pages, 1 figure; v2 - version accepted in Designs, Codes and Cryptograph