Temperature and magnetic-field dependence of the conductivity of YBaCuO films in the vicinity of superconducting transition: Effect of Tc-inhomogeneity

Temperature and magnetic field dependences of the conductivity of YBaCuO films in the transition region are analyzed taking into account spatial inhomogeneity in transition temperature, Tc. (i) An expression for the superconducting contribution to conductivity, \sigma_s(T,H,Tc), of a homogeneous superconductor for H<<Hc2(T=0) is obtained using the solution of the Ginzburg-Landau equation in form of perturbation expansions [S.Ullah, A.T.Dorsey, PRB 44, 262 (1991)]. (ii) The error in \sigma_s(T,H,Tc) occurring due to the presence of Tc-inhomogeneity is calculated and plotted on an H-T plane diagram. These calculations use an effective medium approximation and a Gaussian distribution of Tc. (iii) Measuring the temperature dependences of a voltage, induced by a focused electron beam, we determine spatial distributions of the critical temperature for YBaCuO microbridges with a 2 micron resolution. A typical Tc-distribution dispersion is found to be approximately 1K. For such dispersion, error in \sigma_s(T,H,Tc) due to Tc-inhomogeneity exceeds 30% for magnetic fields H < 1 T and temperatures |T-Tc| < 0.5 K. (iv) Experimental R(T,H) dependences of resistance are well described by a numerical solution of a set of Kirchoff equations for the resistor network based on the measured spatial distributions of Tc and the expression for \sigma_s(T,H,Tc).Comment: REVTeX, 12 pages including 7 figures, resubmitted to Phys. Rev.

Inferring connection proximity in networks of electrically coupled cells by subthreshold frequency response analysis

Electrical synapses continuously transfer signals bi-directionally from one cell to another, directly or indirectly via intermediate cells. Electrical synapses are common in many brain structures such as the inferior olive, the subcoeruleus nucleus and the neocortex, between neurons and between glial cells. In the cortex, interneurons have been shown to be electrically coupled and proposed to participate in large, continuous cortical syncytia, as opposed to smaller spatial domains of electrically coupled cells. However, to explore the significance of these findings it is imperative to map the electrical synaptic microcircuits, in analogy with in vitro studies on monosynaptic and disynaptic chemical coupling. Since "walking" from cell to cell over large distances with a glass pipette is challenging, microinjection of (fluorescent) dyes diffusing through gap-junctions remains so far the only method available to decipher such microcircuits even though technical limitations exist. Based on circuit theory, we derive analytical descriptions of the AC electrical coupling in networks of isopotential cells. We then suggest an operative electrophysiological protocol to distinguish between direct electrical connections and connections involving one or more intermediate cells. This method allows inferring the number of intermediate cells, generalizing the conventional coupling coefficient, which provides limited information. We validate our method through computer simulations, theoretical and numerical methods and electrophysiological paired recordings. \ua9 Springer Science+Business Media, LLC 2007