Density of States and Conductivity of Granular Metal or Array of Quantum Dots

The conductivity of a granular metal or an array of quantum dots usually has the temperature dependence associated with variable range hopping within the soft Coulomb gap of density of states. This is difficult to explain because neutral dots have a hard charging gap at the Fermi level. We show that uncontrolled or intentional doping of the insulator around dots by donors leads to random charging of dots and finite bare density of states at the Fermi level. Then Coulomb interactions between electrons of distant dots results in the a soft Coulomb gap. We show that in a sparse array of dots the bare density of states oscillates as a function of concentration of donors and causes periodic changes in the temperature dependence of conductivity. In a dense array of dots the bare density of states is totally smeared if there are several donors per dot in the insulator.Comment: 13 pages, 15 figures. Some misprints are fixed. Some figures are dropped. Some small changes are given to improve the organizatio

Complexation of a polyelectrolyte with oppositely charged spherical macroions: Giant inversion of charge

Complexation of a long flexible polyelectrolyte (PE) molecule with oppositely charged spherical particles such as colloids, micelles, or globular proteins in a salty water solution is studied. PE binds spheres winding around them, while spheres repel each other and form almost periodic necklace. If the total charge of PE is larger than the total charge of spheres, repulsive correlations of PE turns on a sphere lead to inversion of the net charge of each sphere. In the opposite case, we predict another correlation effect: under-screened by PE spheres bind to PE in such a great number that they invert charge of PE. The inverted charge by absolute value can be larger than the bare charge of PE even when screening by monovalent salt is weak. At larger concentrations of monovalent salt, the inverted charge can reach giant proportions. Our theory is in qualitative agreement with recent experiments on micelles-PE systems.Comment: Various additions and corrections to the text, Figures and references. Accepted for publication in J. Chem. Phys. 200

Jumps in current-voltage characteristics in disordered films

We argue that giant jumps of current at finite voltages observed in disordered samples of InO, TiN and YSi manifest a bistability caused by the overheating of electrons. One of the stable states is overheated and thus low-resistive, while the other, high-resistive state is heated much less by the same voltage. The bistability occurs provided that cooling of electrons is inefficient and the temperature dependence of the equilibrium resistance, R(T), is steep enough. We use experimental R(T) and assume phonon mechanism of the cooling taking into account its strong suppression by disorder. Our description of details of the I-V characteristics does not involve adjustable parameters and turns out to be in a quantitative agreement with the experiments. We propose experiments for more direct checks of this physical picture.Comment: Final version, as published; 4 pages, 3 figure

Self-energy limited ion transport in sub-nanometer channels

The current-voltage characteristics of the alpha-Hemolysin protein pore during the passage of single-stranded DNA under varying ionic strength, C, are studied experimentally. We observe strong blockage of the current, weak super-linear growth of the current as a function of voltage, and a minimum of the current as a function of C. These observations are interpreted as the result of the ion electrostatic self-energy barrier originating from the large difference in the dielectric constants of water and the lipid bilayer. The dependence of DNA capture rate on C also agrees with our model.Comment: more experimental material is added. 4 pages, 7 figure

Statistics of Rare Events in Disordered Conductors

Asymptotic behavior of distribution functions of local quantities in disordered conductors is studied in the weak disorder limit by means of an optimal fluctuation method. It is argued that this method is more appropriate for the study of seldom occurring events than the approaches based on nonlinear $\sigma$-models because it is capable of correctly handling fluctuations of the random potential with large amplitude as well as the short-scale structure of the corresponding solutions of the Schr\"{o}dinger equation. For two- and three-dimensional conductors new asymptotics of the distribution functions are obtained which in some cases differ significantly from previously established results.Comment: 17 pages, REVTeX 3.0 and 1 Postscript figur

Perturbation Theory for the Rosenzweig-Porter Matrix Model

We study an ensemble of random matrices (the Rosenzweig-Porter model) which, in contrast to the standard Gaussian ensemble, is not invariant under changes of basis. We show that a rather complete understanding of its level correlations can be obtained within the standard framework of diagrammatic perturbation theory. The structure of the perturbation expansion allows for an interpretation of the level structure on simple physical grounds, an aspect that is missing in the exact analysis (T. Guhr, Phys. Rev. Lett. 76, 2258 (1996), T. Guhr and A. M\"uller-Groeling, cond-mat/9702113).Comment: to appear in PRE, 5 pages, REVTeX, 2 figures, postscrip

On the Theory of Metal-Insulator Transitions in Gated Semiconductors

It is shown that recent experiments indicating a metal-insulator transition in 2D electron systems can be interpreted in terms of a simple model, in which the resistivity is controlled by scattering at charged hole traps located in the oxide layer. The gate voltage changes the number of charged traps which results in a sharp change in the resistivity. The observed exponential temperature dependence of the resistivity in the metallic phase of the transition follows from the temperature dependence of the trap occupation number. The model naturally describes the experimentally observed scaling properties of the transition and effects of magnetic and electric fields.Comment: 4 two-column pages, 4 figures (included in the text