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A. S. Ioselevich

Publications and source records attributed to A. S. Ioselevich.

18 recordsLinked to original sources
arXiv2024

Coexistence of localized and extended states in the Anderson model with long-range hopping

We study states arising from fluctuations in the disorder potential in systems with long-range hopping. Here, contrary to systems with short-range hopping, the optimal fluctuations of disorder responsible for the formation of the states in the gap, are not rendered shallow and long-range when $E$ approaches the band edge ($E\to 0$). Instead, they remain deep and short-range. The corresponding electronic wave functions also remain short-range-localized for all $E<0$. This behavior has striking implications for the structure of the wave functions slightly above $E=0$. By a study of finite systems, we demonstrate that the wave functions $Ψ_E$ transform from a localized to a quasi-localized type upon crossing the $E=0$ level, forming resonances embedded in the $E>0$ continuum. The quasi-localized $Ψ_{E>0}$ consists of a short-range core that is essentially the same as $Ψ_{E=0}$ and a delocalized tail extending to the boundaries of the system. The amplitude of the tail is small, but it decreases with $r$ slowly. Its contribution to the norm of the wave function dominates for sufficiently large system sizes, $L\gg L_c(E)$; such states behave as delocalized ones. In contrast, in small systems, $L\ll L_c(E)$, quasi-localized states are overwhelmingly dominated by the localized cores and are effectively localized.

cond-mat.dis-nn↗
arXiv2021

Two-impurity scattering in quasi-one-dimensional systems

In a quasi-one-dimensional system (a tube) with low concentration of defects $n$ the resistivity $ρ$ has peaks (van-Hove singularities) as a function of Fermi-energy. We show that due to non-Born scattering effects a deep narrow gap should appear just in the center of each peak. The resistivity at the bottom of a gap ($ρ_{\min}\propto n^2$) is dominated by scattering at rare "twin" pairs of close defects, while scattering at solitary defects is suppressed. The predicted effect is characteristic for multi-channel systems, it can not be observed in strictly one-dimensional one.

cond-mat.mes-hall↗
arXiv2020

Non-Born effects in scattering of electrons in a conducting strip with low concentration of impurities

We extend the theory of non-Born effects in resistivity $ρ$ of clean conducting tubes (developed in our previous work arXiv:1810.00426) to ``strips'' -- quasi-one-dimensional structures in 2D conductors. Here also an original Van Hove singularity in dependence of $ρ$ on the position of chemical potential $\varepsilon$ is asymmetrically split in two peaks for attracting impurities. However, since amplitudes of scattering at impurities depend on their positions, these peaks are inhomogeneously broadened. Strongest broadening occurs in the left peak, arising, for attracting impurities, due to scattering at quasistationary levels. In contrast with the case of tube these levels form not a unique sharp line, but a relatively broad impurity band with a weak quasi-Van Hove feature on its lower edge. Different parts of $ρ(\varepsilon)$ are dominated by different groups of impurities: close to the minimum the most effective scatterers, paradoxically are the ``weakest'' impurities -- those, located close to nodes of the electronic wave-function, so that the bare scattering matrix elements are suppressed. The quasi-Van Hove feature at left maximum is dominated by strongest impurites, located close to antinodes.

cond-mat.mes-hall↗
arXiv2018

Non-Born effects in scattering of electrons in a clean conducting tube

Quasi-one-dimensional systems demonstrate Van Hove singularities in the density of states $ν_F$ and the resistivity $ρ$, occurring when the Fermi level $E$ crosses a bottom $E_N$ of some subband of transverse quantization. We demonstrate that the character of smearing of the singularities crucially depends on the concentration of impurities. There is a crossover concentration $n_c\propto |λ|$, $λ\ll 1$ being the dimensionless amplitude of scattering. For $n\gg n_c$ the singularities are simply rounded at $\varepsilon\equiv E-E_N\sim τ^{-1}$ -- the Born scattering rate. For $n\ll n_c$ the non-Born effects in scattering become essential despite $λ\ll 1$. The peak of the resistivity is asymmetrically split in a Fano-resonance manner (however with a more complex structure). Namely, for $\varepsilon>0$ there is a broad maximum at $\varepsilon\propto λ^2$ while for $\varepsilon<0$ there is a deep minimum at $|\varepsilon|\propto n^2\ll λ^2$. The behaviour of $ρ$ below the minimum depends on the sign of $λ$. In case of repulsion $ρ$ monotonically grows with $|\varepsilon|$ and saturates for $|\varepsilon|\gg λ^2$. In case of attraction $ρ$ has sharp maximum at $|\varepsilon|\propto λ^2$. The latter feature is due to resonant scattering by quasistationary bound states that inevitably arise just below the bottom of each subband for any attracting impurity.

cond-mat.mes-hall↗
arXiv2017

Cotunnelling and polaronic effect in granular systems

We theoretically study the conductivity in arrays of metallic grains due to the variable-range multiple cotunneling of electrons with short-range (screened) Coulomb interaction. The system is supposed to be coupled to random stray charges in the dielectric matrix that are only loosely bounded to their spatial positions by elastic forces. The flexibility of the stray charges gives rise to a polaronic effect, which leads to the onset of Arrhenius-like conductivity behavior at low temperatures, replacing conventional Mott variable-range hopping. The effective activation energy logarithmically depends on temperature due to fluctuations of the polaron barrier heights. We present the unified theory that covers both weak and strong polaron effect regimes of hopping in granular metals and describes the crossover from elastic to inelastic cotunneling.

cond-mat.dis-nn↗
arXiv2015

"Creeping conductance" in nonstationary granular systems and artificial arrays

We consider a nonstationary array of conductors, connected by resistances that fluctuate with time. The charge transfer between a particular pair of conductors is supposed to be dominated by "electrical breakdowns" -- the moments when the corresponding resistance is close to zero. An amount of charge, transferred during a particular breakdown, is controlled by the condition of minimum for the electrostatic energy of the system. We find the conductivity, relaxation rate, and fluctuations for such a system within the "classical approximation", valid, if the typical transferred charge is large compared to $e$. We discuss possible realizations of the model for colloidal systems and arrays of polymer-linked grains.

cond-mat.mes-hall↗
arXiv2009

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 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 the conductivity 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 conductivity 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.

cond-mat.mes-hall↗
arXiv2009

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 percolation theory and confirm this relation numerically.

cond-mat.dis-nn↗
arXiv2009

Universality and non-universality in behavior of self-repairing random networks

We numerically study one-parameter family of random single-cluster systems. A finite-concentration topological phase transition from the net-like to the tree-like phase (the latter is without a backbone) is present in all models of the class. Correlation radius index $ν_B$ of the backbone in the net-like phase; graph dimensions -- $d_{\min}$ of the tree-like phase, and $D_{\min}$ of the backbone in the net-like phase appear to be universal within the accuracy of our calculations, while the backbone fractal dimension $D_B$ is not universal: it depends on the parameter of a model.

cond-mat.dis-nn↗
arXiv2009

"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.

cond-mat.dis-nn↗
arXiv2009

Charge relaxation resistance in the Coulomb blockade problem

We study the dissipation in a system consisting of a small metallic island coupled to a gate electrode and to a massive reservoir via single tunneling junction. The dissipation of energy is caused by a slowly oscillating gate voltage. We compute it in the regimes of weak and strong Coulomb blockade. We focus on the regime of not very low temperatures when electron coherence can be neglected but quantum fluctuations of charge are strong due to Coulomb interaction. The answers assume a particularly transparent form while expressed in terms of specially chosen physical observables. We discovered that the dissipation rate is given by a universal expression in both limiting cases.

cond-mat.mes-hall↗
arXiv2008

Inelastic cotunneling through a long diffusive wire

We show that electron transport through a long multichannel wire, connected to leads by tunnel junctions, at low temperatures and voltages is dominated by inelastic cotunnelling. This mechanism results in experimentally observed power-law dependence of conductance on temperature and voltage, in the diffusive regime where usual Coulomb anomaly theory leads to exponentially low conductance. The power-law exponent is proportional to the distance between contacts.

cond-mat.mes-hall↗
arXiv2006

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 log T is nonuniversal (it depends on 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. In two dimensions this function is found numerically. The dimensional crossover in granular films is discussed.

cond-mat.mes-hall↗
arXiv2005

Variable range cotunneling and conductivity of a granular metal

The Efros-Shklovskii law for the conductivity of granular metals is interpreted as a result of a variable range cotunneling process. The cotunneling between distant resonant grains is predominantly elastic at low T << T_c, while it is inelastic (i.e., accompanied by creation of electron-hole pairs on a string of intermediate non-resonant grains) at T > T_c. The corresponding E-S temperature T_ES in the latter case is slightly (logarithmically) T-dependent. The magnetoresistance in the two cases is different: it may be relatively strong and negative at T much below T_c, while at T>T_c it is suppressed due to inelastic processes which destroy the interference.

cond-mat.mes-hall↗
arXiv2004

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 bare charging energy scale E_C) suppress the mean conductance \bar{g}(E) much stronger than its standard deviation σ(E). At sufficiently low energies E_* any distribution becomes broad, with σ(E_*) ~ \bar{g}(E_*), leading to strong local fluctuations of the tunneling density of states. Percolative nature of metal-insulator transition is established by combination of analytic and numerical analysis of the matrix renormalization group equations.

cond-mat.mes-hall↗
arXiv2004

Protected Qubits and Chern Simons theories in Josephson Junction Arrays

We present general symmetry arguments that show the appearance of doubly denerate states protected from external perturbations in a wide class of Hamiltonians. We construct the simplest spin Hamiltonian belonging to this class and study its properties both analytically and numerically. We find that this model generally has a number of low energy modes which might destroy the protection in the thermodynamic limit. These modes are qualitatively different from the usual gapless excitations as their number scales as the linear size (instead of volume) of the system. We show that the Hamiltonians with this symmetry can be physically implemented in Josephson junction arrays and that in these arrays one can eliminate the low energy modes with a proper boundary condition. We argue that these arrays provide fault tolerant quantum bits. Further we show that the simplest spin model with this symmetry can be mapped to a very special Z_2 Chern-Simons model on the square lattice. We argue that appearance of the low energy modes and the protected degeneracy is a natural property of lattice Chern-Simons theories. Finally, we discuss a general formalism for the construction of discrete Chern-Simons theories on a lattice.

cond-mat.supr-con↗
arXiv2003

Phase Transition in a Self-repairing Random Network

We consider a network, bonds of which are being sequentially removed; that is done at random, but conditioned on the system remaining connected (Self-Repairing Bond Percolation SRBP). This model is the simplest representative of a class of random systems for which forming of isolated clusters is forbidden. It qualitatively describes the process of fabrication of artificial porous materials and degradation of strained polymers. We find a phase transition at a finite concentration of bonds $p=p_c$, at which the backbone of the system vanishes; for all $p<p_c$ the network is a dense fractal.

cond-mat.dis-nn↗