Optical Properties of px + ipy Superconductors with Strong Impurities

JETP Letters - We study effects of strong impurities on the optical properties of a chiral px + ipy superconductor with broken time-reversal symmetry. Potential impurities create subgap states in...     

Percolation with excluded small clusters and Coulomb blockade in a granular system

We consider dc-conductivity σ of a mixture of small conducting and insulating grains slightly below the percolation threshold, where finite clusters of conducting grains are characterized by a wide spectrum of sizes. The charge transport is controlled by tunneling of carriers between neighboring conducting clusters via short “links“ consisting of one insulating grain. Upon lowering temperature small clusters (up to some T-dependent size) become Coulomb blockaded, and are avoided, if possible, by relevant hopping paths. We introduce a relevant percolational problem of next-nearest-neighbors (NNN) conductivity with excluded small clusters and demonstrate (both numerically and analytically) that σ decreases as power law of the size of excluded clusters. As a physical consequence, the conductivity is a power-law function of temperature in a wide intermediate temperature range. We express the corresponding index through known critical indices of the perco lation theory and confirm this relation numerically.     

Quantum percolation in granular metals

Theory of quantum corrections to conductivity of granular metal films is developed for the realistic case of large randomly distributed tunnel conductances. Quantum fluctuations of intergrain voltages (at energies E much below the bare charging energy scale E(C)) suppress the mean conductance g (E) much more strongly than its standard deviation sigma(E). At sufficiently low energies E(*) any distribution becomes broad, with sigma(E(*)) approximately g (E(*)), leading to strong local fluctuations of the tunneling density of states. The percolative nature of the metal-insulator transition is established by a combination of analytic and numerical analysis of the matrix renormalization group equations.     

Drag of a plane plate in a stream of a polymer solution having variable concentration

One of the methods of reducing the frictional resistance of bodies moving in water is the discharge of a water-soluble polymer admixture into the turbulent boundary layer on the surface of the body. For dilute polymer solutions having constant concentration, existing semiempirical methods of calculation which use information on the effect of long molecules on the rearrangement of the flow in the boundary layer enable one to calculate the resistance of smooth and rough tubes [1] with sufficient accuracy and to analyze effects of the redistribution of local tangential stresses on the surface of plane plates [2]. Methods of calculating the drag of plates that have been developed up to the present time are also suitable for predicting the reduction of turbulent friction of elongated bodies by polymer admixtures. It is of interest to generalize these methods to the case of variable concentration. Below we consider the problem of calculating the turbulent boundary layer on a plane plate when a polymer solution is injected near its leading edge. For its solution we use the simplifying assumption that it is possible to replace the actual distribution of the concentration of polymer admixtures along a normal to the surface of the plate with an effective uniform distribution. This assumption enables us to estimate the discharge rate of the polymer that is required to obtain a given reduction in the frictional resistance.     

Self-trapping of hot particles

The theory of self-trapping (ST) of hot particles having non-equilibrium distribution function is presented. It is shown, that for fast particles the trapping at the adiabatic level produced by the lattice deformation is a bottleneck controlling the ST rate. As a result, the ST rate reaches its maximum for particles having a moderate energy which does not exceed the height of self-trapping barrier. This energy decreases with increasing the lattice temperature.     

Universal temperature dependence of the conductivity of a strongly disordered granular metal

A disordered array of metal grains with large and random intergrain conductances is studied within the one-loop accuracy renormalization group approach. While, at low level of disorder, the dependence of conductivity on logT is nonuniversal (it depends on the details of the array’s geometry), for strong disorder, this dependence is described by a universal nonlinear function, which depends only on the array’s dimensionality. This function is found numerically in two dimensions. The dimensional crossover in granular films is discussed. The text was submitted by the authors in English.     

Coulomb zero bias anomaly for fractal geometry and conductivity of granular systems near the percolation threshold

A granular system slightly below the percolation threshold is a collection of finite metallic clusters, characterized by wide spectrum of sizes, resistances, and charging energies. Electrons hop from cluster to clusters via short insulating “links” of high resistance. At low temperatures all clusters are Coulomb blockaded and the dc-conductivity σ is exponentially suppressed. At lowest T the leading transport mechanism is variable range cotunneling via largest (critical) clusters, leading to the modified Efros-Shklovsky law. At intermediate temperatures the principal suppression of ρ originates from the Coulomb zero bias anomaly occurring, when electron tunnels between adjacent large clusters with large resistances. Such clusters are essentially extended objects and their internal dynamics should be taken into account. In this regime the T-dependence of ρ is stretched exponential with a nontrivial index, expressed through the indices of percolation theory. Due to the fractal structure of large clusters the anomaly is strongly enhanced: it arises not only in low dimensions, but also in d = 3 case.     

“Burning and sticking” model for a porous material: suppression of the topological phase transition due to the backbone reinforcement effect

We introduce and study the “burning-and-sticking” (BS) lattice model for the porous material that involves sticking of emerging finite clusters to the mainland. In contrast with other single-cluster models, it does not demonstrate any phase transition: the backbone exists at arbitrarily low concentrations. The same is true for hybrid models, where the sticking events occur with probability q: the backbone survives at arbitrarily low q. Disappearance of the phase transition is attributed to the backbone reinforcement effect, generic for models with sticking. A relation between BS and the cluster-cluster aggregation is briefly discussed. The article is published in the original.