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

Behavior of vortices near twin boundaries in underdoped Ba(Fe1−xCox)2As2Ba(Fe_{1-x}Co_{x})_{2}As_{2}

We use scanning SQUID microscopy to investigate the behavior of vortices in the presence of twin boundaries in the pnictide superconductor Ba(Fe1-xCox)2As2. We show that the vortices avoid pinning on twin boundaries. Individual vortices move in a preferential way when manipulated with the SQUID: they tend to not cross a twin boundary, but rather to move parallel to it. This behavior can be explained by the observation of enhanced superfluid density on twin boundaries in Ba(Fe1-xCox)2As2. The observed repulsion from twin boundaries may be a mechanism for enhanced critical currents observed in twinned samples in pnictides and other superconductors

Width of percolation transition in complex networks

It is known that the critical probability for the percolation transition is not a sharp threshold, actually it is a region of non-zero width $\Delta p_c$ for systems of finite size. Here we present evidence that for complex networks $\Delta p_c \sim \frac{p_c}{l}$, where $l \sim N^{\nu_{opt}}$ is the average length of the percolation cluster, and $N$ is the number of nodes in the network. For Erd\H{o}s-R\'enyi (ER) graphs $\nu_{opt} = 1/3$, while for scale-free (SF) networks with a degree distribution $P(k) \sim k^{-\lambda}$ and $3<\lambda<4$, $\nu_{opt} = (\lambda-3)/(\lambda-1)$. We show analytically and numerically that the \textit{survivability} $S(p,l)$, which is the probability of a cluster to survive $l$ chemical shells at probability $p$, behaves near criticality as $S(p,l) = S(p_c,l) \cdot exp[(p-p_c)l/p_c]$. Thus for probabilities inside the region $|p-p_c| < p_c/l$ the behavior of the system is indistinguishable from that of the critical point

Surface superconductivity in multilayered rhombohedral graphene: Supercurrent

The supercurrent for the surface superconductivity of a flat-band multilayered rhombohedral graphene is calculated. Despite the absence of dispersion of the excitation spectrum, the supercurrent is finite. The critical current is proportional to the zero-temperature superconducting gap, i.e., to the superconducting critical temperature and to the size of the flat band in the momentum space

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

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

Critical thickness for ferromagnetism in LaAlO3/SrTiO3 heterostructures

In heterostructures of LaAlO3 (LAO) and SrTiO3 (STO), two nonmagnetic insulators, various forms of magnetism have been observed [1-7], which may [8, 9] or may not [10] arise from interface charge carriers that migrate from the LAO to the interface in an electronic reconstruction [11]. We image the magnetic landscape [5] in a series of n-type samples of varying LAO thickness. We find ferromagnetic patches that appear only above a critical thickness, similar to that for conductivity [12]. Consequently we conclude that an interface reconstruction is necessary for the formation of magnetism. We observe no change in ferromagnetism with gate voltage, and detect ferromagnetism in a non-conducting p-type sample, indicating that the carriers at the interface do not need to be itinerant to generate magnetism. The fact that the ferromagnetism appears in isolated patches whose density varies greatly between samples strongly suggests that disorder or local strain induce magnetism in a population of the interface carriers

Spontaneous Conducting Boundary Channels in 1T-TaS2_{2}

Materials that transition between metal and insulator, the two opposing states that distinguish all solids, are fascinating because they underlie many mysteries in the physics of the solid state. In 1T-TaS$_{2}$, the metal-insulator transition is linked to a series of metastable states of a chiral charge density wave whose basic nature is still an open question. In this work, we show that pulses of current through these materials create current-carrying boundary channels that distinguish the metallic and insulating states. We demonstrate electrical control of these channels' properties, suggesting their formation could be due to the complex interplay of the formation of domain walls and the viscous flow of electrons. Our findings show that physical boundaries play a key role in the properties of the metastable states of the metal-insulator transition, highlighting new possibilities for in-situ electrical design and active manipulation of electrical components

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

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