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

Neoplasia renal con extensión a la vena cava

La neoplasia renal con extensión a la vena cava es relativamente rara (4-10%). Cualquiera que sea la terapia coadjuvante (radioterapia, hormonal, quimioterapia e inmunoterapia), la exéresis completa del trombo tumoral de la vena cava continúa siendo la mejor forma de tratamiento. El valor pronóstico de la extensión cefálica de un trombo tumoral en la vena cava inferior en enfermos con carcinoma de células renales es controvertido. Es posible conseguir una larga supervivencia después del tratamiento quirúrgico en enfermos con carcinoma de células renales localizado (supervivencia de 50% en 5 años). Los autores describen un caso de carcinoma de células renales con extensión a la vena cava en un enfermo del sexo masculino, de 70 años de edad. El enfermo presentaba una historia de lumbalgia derecha y edema del miembro inferior homolateral. La resonancia magnética demostró la presencia y el nivel del trombo tumoral. El enfermo fue sometido a nefrectomía radical derecha y exéresis completa del trombo tumoral de la vena cava. Renal cancer with vena cava tumour thrombus is relatively rare (4 to 10%). Because of the poor results obtained with any kind of alternative therapy (e.g. radiation, hormonal, chemotherapy and immunotherapy) operation with complete removal of the vena cava tumour thrombus continues to be the better method of treatment. The prognostic significance of the cephalic extent of an inferior vena caval tumor thrombus associated with renal cell carcinoma is controversial. Long-term survival after surgical treatment is possible in patients with localized renal cell carcinoma (survival 50% at five years). The authors report a case of vena caval extension of renal cell carcinoma in a 70-years-old man. The patient presented with a history of right lombar pain and pedal edema. Magnetic Ressonance demonstrated the presence and the level of tumoral thrombus. The patient was submitted to a radical nefrectomy and complete removal of tumor thrombus from vena caval

Multiple Invaded Consolidating Materials

We study a multiple invasion model to simulate corrosion or intrusion processes. Estimated values for the fractal dimension of the invaded region reveal that the critical exponents vary as function of the generation number $G$, i.e., with the number of times the invasion process takes place. The averaged mass $M$ of the invaded region decreases with a power-law as a function of $G$, $M\sim G^{\beta}$, where the exponent $\beta\approx 0.6$. We also find that the fractal dimension of the invaded cluster changes from $d_{1}=1.887\pm0.002$ to $d_{s}=1.217\pm0.005$. This result confirms that the multiple invasion process follows a continuous transition from one universality class (NTIP) to another (optimal path). In addition, we report extensive numerical simulations that indicate that the mass distribution of avalanches $P(S,L)$ has a power-law behavior and we find that the exponent $\tau$ governing the power-law $P(S,L)\sim S^{-\tau}$ changes continuously as a function of the parameter $G$. We propose a scaling law for the mass distribution of avalanches for different number of generations $G$.Comment: 8 pages and 16 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