Hall conductivity as bulk signature of topological transitions in superconductors

Topological superconductors may undergo transitions between phases with different topological numbers which, like the case of topological insulators, are related to the presence of gapless (Majorana) edge states. In $\mathbb{Z}$ topological insulators the charge Hall conductivity is quantized, being proportional to the number of gapless states running at the edge. In a superconductor, however, charge is not conserved and, therefore, $\sigma_{xy}$ is not quantized, even in the case of a $\mathbb{Z}$ topological superconductor. Here it is shown that while the $\sigma_{xy}$ evolves continuously between different topological phases of a $\mathbb{Z}$ topological superconductor, its derivatives display sharp features signaling the topological transitions. We consider in detail the case of a triplet superconductor with p-wave symmetry in the presence of Rashba spin-orbit (SO) coupling and externally applied Zeeman spin splitting. Generalization to the cases where the pairing vector is not aligned with that of the SO coupling is given. We generalize also to the cases where the normal system is already topologically non-trivial.Comment: 10 pages, 10 figure

Gaussian model of explosive percolation in three and higher dimensions

The Gaussian model of discontinuous percolation, recently introduced by Ara\'ujo and Herrmann [Phys. Rev. Lett., 105, 035701 (2010)], is numerically investigated in three dimensions, disclosing a discontinuous transition. For the simple-cubic lattice, in the thermodynamic limit, we report a finite jump of the order parameter, $J=0.415 \pm 0.005$. The largest cluster at the threshold is compact, but its external perimeter is fractal with fractal dimension $d_A = 2.5 \pm 0.2$. The study is extended to hypercubic lattices up to six dimensions and to the mean-field limit (infinite dimension). We find that, in all considered dimensions, the percolation transition is discontinuous. The value of the jump in the order parameter, the maximum of the second moment, and the percolation threshold are analyzed, revealing interesting features of the transition and corroborating its discontinuous nature in all considered dimensions. We also show that the fractal dimension of the external perimeter, for any dimension, is consistent with the one from bridge percolation and establish a lower bound for the percolation threshold of discontinuous models with finite number of clusters at the threshold

Theory of Andreev reflection in a two-orbital model of iron-pnictide superconductors

A recently developed theory for the problem of Andreev reflection between a normal metal (N) and a multiband superconductor (MBS) assumes that the incident wave from the normal metal is coherently transmitted through several bands inside the superconductor. Such splitting of the probability amplitude into several channels is the analogue of a quantum waveguide. Thus, the appropriate matching conditions for the wave function at the N/MBS interface are derived from an extension of quantum waveguide theory. Interference effects between the transmitted waves inside the superconductor manifest themselves in the conductance. We provide results for a FeAs superconductor, in the framework of a recently proposed effective two-band model and two recently proposed gap symmetries: in the sign-reversed s-wave ($\Delta\cos(k_x)\cos(k_y)$) scenario resonant transmission through surface Andreev bound states (ABS) at nonzero energy is found as well as destructive interference effects that produce zeros in the conductance; in the extended s-wave ($\Delta[\cos(k_x)+\cos(k_y)]$) scenario no ABS at finite energy are found.Comment: 4 pages, 5 figure

Enhancement of the critical temperature in iron-pnictide superconductors by finite size effects

Recent experiments have shown that, in agreement with previous theoretical predictions, superconductivity in metallic nanostructures can be enhanced with respect to the bulk limit. Motivated by these results we study finite size effects (FSE) in an iron-pnictide superconductor. For realistic values of the bulk critical temperature Tc ~ 20-50K, we find that, in the nanoscale region L ~ 10 nm, Tc(L) has a complicated oscillating pattern as a function of the system size L. A substantial enhancement of Tc with respect to the bulk limit is observed for different boundary conditions, geometries and two microscopic models of superconductivity. Thermal fluctuations, which break long range order, are still small in this region. Finally we show that the differential conductance, an experimental observable, is also very sensitive to FSE.Comment: 4 pages, 3 figure

From optical tracking to tactical performance via Voronoi diagrams: Team formation and players’ roles constrain interpersonal linkages in high-level football

Football performance behaviour relies on the individual and collective perceptual attunement to the opportunities for action (affordances) available in a given competitive environment. Such perception–action coupling is constrained by players’ spatial dominance. Aiming to understand the influence of team formation and players’ roles in their dynamic interaction (interpersonal linkages), Voronoi diagrams were used to assess the differences in players’ spatial dominance resulting from their interactions according to ball-possession status in high-performance football. Notational (i.e., team formation, players’ role, and ball-possession status) and positional data (from optical sensors) from ten matches of the men’s French main football league were analysed. Voronoi diagrams were computed from players’ positional data for both teams. Probability density functions of the players’ Voronoi cell areas were then computed and compared, using the Kolmogorov–Smirnov test, for the different variables (i.e., team formation, player role, and ball-possession status) and their classes. For these variables, the players’ Voronoi cell areas presented statistical differences, which were sensitive to team formation classes (i.e., defenders, midfielders, and forwards) and relative pitch location (interior or exterior in the effective play space). Differences were also found between players with similar roles when in different team formations. Our results showed that team formation and players’ roles constrain their interpersonal linkages, resulting in different spatial dominance patterns. Using positional data captured by optical sensors, Voronoi diagrams can be computed into compound variables, which are meaningful for understanding the match and thus offer information to the design representative training tasks.info:eu-repo/semantics/publishedVersio

Gender gap in the ERASMUS mobility program

Studying abroad has become very popular among students. The ERASMUS mobility program is one of the largest international student exchange programs in the world, which has supported already more than three million participants since 1987. We analyzed the mobility pattern within this program in 2011-12 and found a gender gap across countries and subject areas. Namely, for almost all participating countries, female students are over-represented in the ERASMUS program when compared to the entire population of tertiary students. The same tendency is observed across different subject areas. We also found a gender asymmetry in the geographical distribution of hosting institutions, with a bias of male students in Scandinavian countries. However, a detailed analysis reveals that this latter asymmetry is rather driven by subject and consistent with the distribution of gender ratios among subject areas