Meissner response of a bulk superconductor with an embedded sheet of reduced penetration depth

We calculate the change in susceptibility resulting from a thin sheet with reduced penetration depth embedded perpendicular to the surface of an isotropic superconductor, in a geometry applicable to scanning Superconducting QUantum Interference Device (SQUID) microscopy, by numerically solving Maxwell's and London's equations using the finite element method. The predicted stripes in susceptibility agree well in shape with the observations of Kalisky et al. of enhanced susceptibility above twin planes in the underdoped pnictide superconductor Ba(Fe1-xCox)2As2 (Ba-122). By comparing the predicted stripe amplitudes with experiment and using the London relation between penetration depth and superfluid density, we estimate the enhanced Cooper pair density on the twin planes, and the barrier force for a vortex to cross a twin plane. Fits to the observed temperature dependence of the stripe amplitude suggest that the twin planes have a higher critical temperature than the bulk, although stripes are not observed above the bulk critical temperature.Comment: 16 pages, 9 figure

Localization transition on complex networks via spectral statistics

The spectral statistics of complex networks are numerically studied. The features of the Anderson metal-insulator transition are found to be similar for a wide range of different networks. A metal-insulator transition as a function of the disorder can be observed for different classes of complex networks for which the average connectivity is small. The critical index of the transition corresponds to the mean field expectation. When the connectivity is higher, the amount of disorder needed to reach a certain degree of localization is proportional to the average connectivity, though a precise transition cannot be identified. The absence of a clear transition at high connectivity is probably due to the very compact structure of the highly connected networks, resulting in a small diameter even for a large number of sites.Comment: 6 pages, expanded introduction and referencess (to appear in PRE

Scanning SQUID Susceptometry of a paramagnetic superconductor

Scanning SQUID susceptometry images the local magnetization and susceptibility of a sample. By accurately modeling the SQUID signal we can determine the physical properties such as the penetration depth and permeability of superconducting samples. We calculate the scanning SQUID susceptometry signal for a superconducting slab of arbitrary thickness with isotropic London penetration depth, on a non-superconducting substrate, where both slab and substrate can have a paramagnetic response that is linear in the applied field. We derive analytical approximations to our general expression in a number of limits. Using our results, we fit experimental susceptibility data as a function of the sample-sensor spacing for three samples: 1) delta-doped SrTiO3, which has a predominantly diamagnetic response, 2) a thin film of LaNiO3, which has a predominantly paramagnetic response, and 3) a two-dimensional electron layer (2-DEL) at a SrTiO3/AlAlO3 interface, which exhibits both types of response. These formulas will allow the determination of the concentrations of paramagnetic spins and superconducting carriers from fits to scanning SQUID susceptibility measurements.Comment: 11 pages, 13 figure

Effect of Disorder Strength on Optimal Paths in Complex Networks

We study the transition between the strong and weak disorder regimes in the scaling properties of the average optimal path $\ell_{\rm opt}$ in a disordered Erd\H{o}s-R\'enyi (ER) random network and scale-free (SF) network. Each link $i$ is associated with a weight $\tau_i\equiv\exp(a r_i)$, where $r_i$ is a random number taken from a uniform distribution between 0 and 1 and the parameter $a$ controls the strength of the disorder. We find that for any finite $a$, there is a crossover network size $N^*(a)$ at which the transition occurs. For $N \ll N^*(a)$ the scaling behavior of $\ell_{\rm opt}$ is in the strong disorder regime, with $\ell_{\rm opt} \sim N^{1/3}$ for ER networks and for SF networks with $\lambda \ge 4$, and $\ell_{\rm opt} \sim N^{(\lambda-3)/(\lambda-1)}$ for SF networks with $3 < \lambda < 4$. For $N \gg N^*(a)$ the scaling behavior is in the weak disorder regime, with $\ell_{\rm opt}\sim\ln N$ for ER networks and SF networks with $\lambda > 3$. In order to study the transition we propose a measure which indicates how close or far the disordered network is from the limit of strong disorder. We propose a scaling ansatz for this measure and demonstrate its validity. We proceed to derive the scaling relation between $N^*(a)$ and $a$. We find that $N^*(a)\sim a^3$ for ER networks and for SF networks with $\lambda\ge 4$, and $N^*(a)\sim a^{(\lambda-1)/(\lambda-3)}$ for SF networks with $3 < \lambda < 4$.Comment: 6 pages, 6 figures. submitted to Phys. Rev.

Nanopatterning of oxide 2-dimensional electron systems using low-temperature ion milling

We present a \u27top-down\u27 patterning technique based on ion milling performed at low-temperature, for the realization of oxide two-dimensional electron system devices with dimensions down to 160 nm. Using electrical transport and scanning Superconducting QUantum Interference Device measurements we demonstrate that the low-temperature ion milling process does not damage the 2DES properties nor creates oxygen vacancies-related conducting paths in the STO substrate. As opposed to other procedures used to realize oxide 2DES devices, the one we propose gives lateral access to the 2DES along the in-plane directions, finally opening the way to coupling with other materials, including superconductors

Surface-Barrier Effects in the Microwave Second-Harmonic Response of Superconductors in the Mixed State

We report on transient effects in the microwave second-order response of different type of superconductors in the mixed state. The samples have contemporarily been exposed to a dc magnetic field, varying with a constant rate of 60 Oe/s, and a pulsed microwave magnetic field. The time evolution of the signal radiated at the second-harmonic frequency of the driving field has been measured for about 500 s from the instant in which the dc-field sweep has been stopped, with sampling time of about 0.3 s. We show that the second-harmonic signal exhibits two relaxation regimes; an initial exponential decay, which endures roughly 10 s, and a logarithmic decay in the time scale of minutes. Evidence is given that the decay in the time scale of minutes is ruled by magnetic relaxation over the surface barrier.Comment: 6 pages, 6 embedded figure

Local measurement of the penetration depth in the pnictide superconductor Ba(Fe0.95_{0.95}Co0.05_{0.05})2_2As2_2

We use magnetic force microscopy (MFM) and scanning SQUID susceptometry to measure the local superfluid density $\rho_{s}$ in Ba(Fe$_{0.95}$Co$_{0.05}$)$_2$As$_2$ single crystals from 0.4 K to the critical temperature $T_c=18.5$ K. We observe that the penetration depth $\lambda$ varies about ten times more slowly with temperature than previously published, with a dependence that can be well described by a clean two-band fully gapped model. We demonstrate that MFM can measure the important and hard-to-determine absolute value of $\lambda$, as well as obtain its temperature dependence and spatial homogeneity. We find $\rho_{s}$ to be uniform despite the highly disordered vortex pinning

In silico evolution of diauxic growth

The glucose effect is a well known phenomenon whereby cells, when presented with two different nutrients, show a diauxic growth pattern, i.e. an episode of exponential growth followed by a lag phase of reduced growth followed by a second phase of exponential growth. Diauxic growth is usually thought of as a an adaptation to maximise biomass production in an environment offering two or more carbon sources. While diauxic growth has been studied widely both experimentally and theoretically, the hypothesis that diauxic growth is a strategy to increase overall growth has remained an unconfirmed conjecture. Here, we present a minimal mathematical model of a bacterial nutrient uptake system and metabolism. We subject this model to artificial evolution to test under which conditions diauxic growth evolves. As a result, we find that, indeed, sequential uptake of nutrients emerges if there is competition for nutrients and the metabolism/uptake system is capacity limited. However, we also find that diauxic growth is a secondary effect of this system and that the speed-up of nutrient uptake is a much larger effect. Notably, this speed-up of nutrient uptake coincides with an overall reduction of efficiency. Our two main conclusions are: (i) Cells competing for the same nutrients evolve rapid but inefficient growth dynamics. (ii) In the deterministic models we use here no substantial lag-phase evolves. This suggests that the lag-phase is a consequence of stochastic gene expression

Optimal Path and Minimal Spanning Trees in Random Weighted Networks

We review results on the scaling of the optimal path length in random networks with weighted links or nodes. In strong disorder we find that the length of the optimal path increases dramatically compared to the known small world result for the minimum distance. For Erd\H{o}s-R\'enyi (ER) and scale free networks (SF), with parameter $\lambda$ ($\lambda >3$), we find that the small-world nature is destroyed. We also find numerically that for weak disorder the length of the optimal path scales logaritmically with the size of the networks studied. We also review the transition between the strong and weak disorder regimes in the scaling properties of the length of the optimal path for ER and SF networks and for a general distribution of weights, and suggest that for any distribution of weigths, the distribution of optimal path lengths has a universal form which is controlled by the scaling parameter $Z=\ell_{\infty}/A$ where $A$ plays the role of the disorder strength, and $\ell_{\infty}$ is the length of the optimal path in strong disorder. The relation for $A$ is derived analytically and supported by numerical simulations. We then study the minimum spanning tree (MST) and show that it is composed of percolation clusters, which we regard as "super-nodes", connected by a scale-free tree. We furthermore show that the MST can be partitioned into two distinct components. One component the {\it superhighways}, for which the nodes with high centrality dominate, corresponds to the largest cluster at the percolation threshold which is a subset of the MST. In the other component, {\it roads}, low centrality nodes dominate. We demonstrate the significance identifying the superhighways by showing that one can improve significantly the global transport by improving a very small fraction of the network.Comment: review, accepted at IJB

Flux-flow resistivity anisotropy in the instability regime in the a-b plane of epitaxial YBCO thin films

Measurements of the nonlinear flux-flow resistivity $\rho$ and the critical vortex velocity $\rm v^*_\phi$ at high voltage bias close to the instability regime predicted by Larkin and Ovchinnikov \cite{LO} are reported along the node and antinode directions of the d-wave order parameter in the \textit{a-b} plane of epitaxial $YBa_2Cu_3O_{7-\delta}$ films. In this pinning-free regime, $\rho$ and $\rm v^*_\phi$ are found to be anisotropic with values in the node direction larger on average by 10% than in the antinode direction. The anisotropy of $\rho$ is almost independent of temperature and field. We attribute the observed results to the anisotropic quasiparticle distribution on the Fermi surface of $YBa_2Cu_3O_{7-\delta}$.Comment: 5 figure