Superconductor-insulator transition in Coulomb disorder

Superconductor-insulator transition driven by the decreasing concentration of electrons $n$ is studied in the case of the disorder potential created by randomly positioned charged impurities. Electrons and Cooper pairs (formed by an non-Coulomb attraction) nonlinearly screen the random potential of impurities. Both electrons and Cooper pairs can be delocalized or localized in the resulting self-consistent potential. The border separating the superconductor and insulator phases in the plane of the concentration of electrons and the length of the Cooper pair is found. For a strong disorder the central segment of this border follows the BEC-BCS crossover line defined for a clean sample.Comment: 4.5 pages, introduction rewritten, a dozen of references added, 2D case adde

Hopping conductivity of a suspension of nanowires in an insulator

We study the hopping conduction in a composite made of straight metallic nanowires randomly and isotropically suspended in an insulator. Uncontrolled donors and acceptors in the insulator lead to random charging of wires and hence finite bare density of states at the Fermi level. Then the Coulomb interactions between electrons of distant wires result in the soft Coulomb gap. At low temperatures the conductivity is due to variable range hopping of electrons between wires and obeys the Efros-Shklovskii (ES) law $\ln\sigma \propto -(T_{ES}/T)^{1/2}$. We show that $T_{ES} \propto 1/(nL^3)^2$, where $n$ is the concentration of wires and $L$ is the wire length. Due to enhanced screening of Coulomb potentials, at large enough $nL^3$, the ES law is replaced by the Mott law.Comment: 5 pages, 5 figure

A simple model of Coulomb disorder and screening in graphene

We suggest a simple model of disorder in graphene assuming that there are randomly distributed positive and negative centers with equal concentration $N/2$ in the bulk of silicon oxide substrate. We show that at zero gate voltage such disorder creates two-dimensional concentration $n_0 \sim N^{2/3}$ of electrons and holes in graphene. Electrons and holes reside in alternating in space puddles of the size $R_0 \sim N^{-1/3}$. A typical puddle has only one or two carriers in agreement with recent scanning single electron transistor experiment.Comment: 2.5 pages, twice longer than previous versio

Conductance noise in interacting Anderson insulators driven far from equilibrium

The combination of strong disorder and many-body interactions in Anderson insulators lead to a variety of intriguing non-equilibrium transport phenomena. These include slow relaxation and a variety of memory effects characteristic of glasses. Here we show that when such systems are driven with sufficiently high current, and in liquid helium bath, a peculiar type of conductance noise can be observed. This noise appears in the conductance versus time traces as downward-going spikes. The characteristic features of the spikes (such as typical width) and the threshold current at which they appear are controlled by the sample parameters. We show that this phenomenon is peculiar to hopping transport and does not exist in the diffusive regime. Observation of conductance spikes hinges also on the sample being in direct contact with the normal phase of liquid helium; when this is not the case, the noise exhibits the usual 1/f characteristics independent of the current drive. A model based on the percolative nature of hopping conductance explains why the onset of the effect is controlled by current density. It also predicts the dependence on disorder as confirmed by our experiments. To account for the role of the bath, the hopping transport model is augmented by a heuristic assumption involving nucleation of cavities in the liquid helium in which the sample is immersed. The suggested scenario is analogous to the way high-energy particles are detected in a Glaser's bubble chamber.Comment: 15 pages 22 figure

How a protein searches for its specific site on DNA: the role of intersegment transfer

Proteins are known to locate their specific targets on DNA up to two orders of magnitude faster than predicted by the Smoluchowski three-dimensional diffusion rate. One of the mechanisms proposed to resolve this discrepancy is termed "intersegment transfer". Many proteins have two DNA binding sites and can transfer from one DNA segment to another without dissociation to water. We calculate the target search rate for such proteins in a dense globular DNA, taking into account intersegment transfer working in conjunction with DNA motion and protein sliding along DNA. We show that intersegment transfer plays a very important role in cases where the protein spends most of its time adsorbed on DNA.Comment: 9 pages, 7 figure

Coulomb gap triptychs, 2\sqrt{2} effective charge, and hopping transport in periodic arrays of superconductor grains

In granular superconductors, individual grains can contain bound Cooper pairs while the system as a whole is strongly insulating. In such cases the conductivity is determined by electron hopping between localized states in individual grains. Here we examine a model of hopping conductivity in such an insulating granular superconductor, where disorder is assumed to be provided by random charges embedded in the insulating gaps between grains. We use computer simulations to calculate the single-electron and electron pair density of states at different values of the superconducting gap $\Delta$, and we identify "triptych" symmetries and scaling relations between them. At a particular critical value of $\Delta$, one can define an effective charge $\sqrt{2}e$ that characterizes the density of states and the hopping transport. We discuss the implications of our results for magnetoresistance and tunneling experiments.Comment: 11 pages, 7 figure

Coulomb gap and variable range hopping in a pinned Wigner crystal

It is shown that pinning of an electron Wigner crystal by a small concentration of charged impurities creates the finite density of charged localized states near the Fermi level. In the case of residual impurities in the spacer this density of states is related to nonlinear screening of a close acceptor by a Wigner crystal vacancy. On the other hand, intentional doping by a remote layer of donors is a source of a long range potential, which generates dislocations in Wigner crystal. Dislocations in turn create charged localized states near the Fermi level. In both cases Coulomb interaction of localized states leads to the soft Coulomb gap and ES variable range hopping at low enough temperatures.Comment: To be published in proceedings of 10th conference on hopping and related phenomena in Physica Status Solid

Suppression of inelastic electron-electron scattering in Anderson Insulators

We report on measurements of absorption from applied ac fields in Anderson-localized indium-oxide films. The absorption shows a roll-off at a frequency that is much smaller than the electron-electron scattering rate measured at the same temperature in diffusive samples of this material. These results are interpreted as evidence for discreteness of the energy spectrum.Comment: 4 figure

Electron Transport in Nanogranular Ferromagnets

We study electronic transport properties of ferromagnetic nanoparticle arrays and nanodomain materials near the Curie temperature in the limit of weak coupling between the grains. We calculate the conductivity in the Ohmic and non-Ohmic regimes and estimate the magnetoresistance jump in the resistivity at the transition temperature. The results are applicable for many emerging materials, including artificially self-assembled nanoparticle arrays and a certain class of manganites, where localization effects within the clusters can be neglected.Comment: 4 pages, 2 figure