arXiv subjects

B. I. Shklovskii

Publications and source records attributed to B. I. Shklovskii.

At least 73 records · Page 4Linked to original sources

arXiv2011

Cooperative Charging in a Nanocrystal Assembly Gated By Ionic Liquid

In order to make a densely packed assembly of undoped semiconductor nanocrystals conductive, it is usually gated by a room temperature ionic liquid. The ionic liquid enters the pores of the super-crystal assembly under the influence of an applied voltage. We study the capacitance of such a device as a function of the gate voltage. We show that, counter-intuitively, the capacitance of the system is the sum of delta-functions located at a sequence of critical gate voltages. At each critical voltage every nanocrystal acquires one additional electron.

cond-mat.mes-hall↗

arXiv2011

Coulomb gap in the one-particle density of states in three-dimensional systems with localized electrons

The one-particle density of states (1P-DOS) in a system with localized electron states vanishes at the Fermi level due to the Coulomb interaction between electrons. Derivation of the Coulomb gap uses stability criteria of the ground state. The simplest criterion is based on the excitonic interaction of an electron and a hole and leads to a quadratic 1P-DOS in the three-dimensional (3D) case. In 3D, higher stability criteria, including two or more electrons, were predicted to exponentially deplete the 1P-DOS at energies close enough to the Fermi level. In this paper we show that there is a range of intermediate energies where this depletion is strongly compensated by the excitonic interaction between single-particle excitations, so that the crossover from quadratic to exponential behavior of the 1P-DOS is retarded. This is one of the reasons why such exponential depletion was never seen in computer simulations.

cond-mat.dis-nn↗

arXiv2011

Theory of volumetric capacitance of an electric double-layer supercapacitor

Electric double layer supercapacitors are a fast-rising class of high-power energy storage devices based on porous electrodes immersed in a concentrated electrolyte or ionic liquid. As of yet there is no microscopic theory to describe their surprisingly large capacitance per unit volume (volumetric capacitance) of ~ 100 F/cm^3, nor is there a good understanding of the fundamental limits on volumetric capacitance. In this paper we present a non-mean-field theory of the volumetric capacitance of a supercapacitor that captures the discrete nature of the ions and the exponential screening of their repulsive interaction by the electrode. We consider analytically and via Monte-Carlo simulations the case of an electrode made from a good metal and show that in this case the volumetric capacitance can reach the record values. We also study how the capacitance is reduced when the electrode is an imperfect metal characterized by some finite screening radius. Finally, we argue that a carbon electrode, despite its relatively large linear screening radius, can be approximated as a perfect metal because of its strong nonlinear screening. In this way the experimentally-measured capacitance values of ~ 100 F/cm^3 may be understood.

cond-mat.mtrl-sci↗

arXiv2010

Non-mean-field theory of anomalously large double-layer capacitance

Mean-field theories claim that the capacitance of the double-layer formed at a metal/ionic conductor interface cannot be larger than that of the Helmholtz capacitor, whose width is equal to the radius of an ion. However, in some experiments the apparent width of the double-layer capacitor is substantially smaller. We propose an alternate, non-mean-field theory of the ionic double-layer to explain such large capacitance values. Our theory allows for the binding of discrete ions to their image charges in the metal, which results in the formation of interface dipoles. We focus primarily on the case where only small cations are mobile and other ions form an oppositely-charged background. In this case, at small temperature and zero applied voltage dipoles form a correlated liquid on both contacts. We show that at small voltages the capacitance of the double-layer is determined by the transfer of dipoles from one electrode to the other and is therefore limited only by the weak dipole-dipole repulsion between bound ions, so that the capacitance is very large. At large voltages the depletion of bound ions from one of the capacitor electrodes triggers a collapse of the capacitance to the much smaller mean-field value, as seen in experimental data. We test our analytical predictions with a Monte Carlo simulation and find good agreement. We further argue that our ``one-component plasma" model should work well for strongly asymmetric ion liquids. We believe that this work also suggests an improved theory of pseudo-capacitance.

cond-mat.soft↗

arXiv2010

Anomalously large capacitance of an ionic liquid described by the restricted primitive model

We use Monte Carlo simulations to examine the simplest model of an ionic liquid, called the restricted primitive model, at a metal surface. We find that at moderately low temperatures the capacitance of the metal/ionic liquid interface is so large that the effective thickness of the electrostatic double-layer is up to 3 times smaller than the ion radius. To interpret these results we suggest an approach which is based on the interaction between discrete ions and their image charges in the metal surface and which therefore goes beyond the mean-field approximation. When a voltage is applied across the interface, the strong image attraction causes counterions to condense onto the metal surface to form compact ion-image dipoles. These dipoles repel each other to form a correlated liquid. When the surface density of these dipoles is low, the insertion of an additional dipole does not require much energy. This leads to a large capacitance $C$ that decreases monotonically with voltage $V$, producing a "bell-shaped" curve $C(V)$. We also consider what happens when the electrode is made from a semi-metal rather than a perfect metal. In this case, the finite screening radius of the electrode shifts the reflection plane for image charges to the interior of the electrode and we arrive at a "camel-shaped" $C(V)$. These predictions seem to be in qualitative agreement with experiment.

physics.chem-ph↗

arXiv2010

Capacitance of the Double Layer Formed at the Metal/Ionic-Conductor Interface: How Large Can It Be?

The capacitance of the double layer formed at a metal/ionic-conductor interface can be remarkably large, so that the apparent width of the double layer is as small as 0.3 Å. Mean-field theories fail to explain such large capacitance. We propose an alternate theory of the ionic double layer which allows for the binding of discrete ions to their image charges in the metal. We show that at small voltages the capacitance of the double layer is limited only by the weak dipole-dipole repulsion between bound ions, and is therefore very large. At large voltages the depletion of bound ions from one of the capacitor electrodes triggers a collapse of the capacitance to the mean-field value.

cond-mat.soft↗

arXiv2009

Ionic conductivity on a wetting surface

Recent experiments measuring the electrical conductivity of DNA molecules highlight the need for a theoretical model of ion transport along a charged surface. Here we present a simple theory based on the idea of unbinding of ion pairs. The strong humidity dependence of conductivity is explained by the decrease in the electrostatic self-energy of a separated pair when a layer of water (with high dielectric constant) is adsorbed to the surface. We compare our prediction for conductivity to experiment, and discuss the limits of its applicability.

cond-mat.soft↗

arXiv2009

Non-monotonic swelling of a macroion due to correlation-induced charge inversion

It is known that a large, charged body immersed in a solution of multivalent counterions may undergo charge inversion as the counterions adsorb to its surface. We use the theory of charge inversion to examine the case of a deformable, porous macroion which may adsorb multivalent ions into its bulk to form a three-dimensional strongly-correlated liquid. This adsorption may lead to non-monotonic changes in the size of the macroion as multivalent ions are added to the solution. The macroion first shrinks as its bare charge is screened and then reswells as the adsorbed ions invert the sign of the net charge. We derive a value for the outward pressure experienced by such a macroion as a function of the ion concentration in solution. We find that for small deviations in the concentration of multivalent ions away from the neutral point (where the net charge of the body is zero), the swollen size grows parabolically with the logarithm of the ratio of multivalent ion concentration to the concentration at the neutral point.

cond-mat.soft↗

arXiv2009

Non-mean-field screening by multivalent counterions

Screening of a strongly charged macroion by its multivalent counterions can not be described in the framework of mean field Poisson-Boltzmann (PB) theory because multivalent counterions form a strongly correlated liquid (SCL) on the surface of the macroion. It was predicted that a distant counterion polarizes the SCL as if it were a metallic surface and creates an electrostatic image. The attractive potential energy of the image is the reason why the charge density of counterions decreases faster with distance from the charged surface than in PB theory. Using the Monte Carlo method to find the equilibrium distribution of counterions around the macroion, we confirm the existence of the image potential energy. It is also shown that due to the negative screening length of the SCL, $-2ξ$, the effective metallic surface is actually above the SCL by $|ξ|$.

cond-mat.soft↗

arXiv2008

Theory of DNA translocation through narrow ion channels and nanopores with charged walls

Translocation of a single stranded DNA through genetically engineered $α$-hemolysin channels with positively charged walls is studied. It is predicted that transport properties of such channels are dramatically different from neutral wild type $α$-hemolysin channel. We assume that the wall charges compensate the fraction $x$ of the bare charge $q_{b}$ of the DNA piece residing in the channel. Our prediction are as follows (i) At small concentration of salt the blocked ion current decreases with $x$. (ii) The effective charge $q$ of DNA piece, which is very small at $x = 0$ (neutral channel) grows with $x$ and at $x=1$ reaches $q_{b}$. (iii) The rate of DNA capture by the channel exponentially grows with $x$. Our theory is also applicable to translocation of a double stranded DNA in narrow solid state nanopores with positively charged walls.

q-bio.SC↗

arXiv2008

Variable range hopping in thin film with large dielectric constant

In a film with large dielectric constant $κ$ the electric field of an electron spreads inside the film before exiting the film at large distances of order of $κd$ ($d$ is the film width). This leads to the logarithmic Coulomb repulsion between electrons and modifies the shape of the Coulomb gap in the density of localized states in a doped film. As a result the variable range hopping conductivity in such a film has a peculiar temperature dependence, where the domain of the $\ln σ(T) \propto (T_0/T)^{p}$ dependence, with the index $p \simeq 0.7$, is sandwiched between the two domains with $p = 1/2$.

cond-mat.dis-nn↗

arXiv2008

Effective charge and free energy of DNA inside an ion channel

Translocation of a single stranded DNA (ssDNA) through an alpha-hemolysin channel in a lipid membrane driven by applied transmembrane voltage V was extensively studied recently. While the bare charge of the ssDNA piece inside the channel is approximately 12 (in units of electron charge) measurements of different effective charges resulted in values between one and two. We explain these challenging observations by a large self-energy of a charge in the narrow water filled gap between ssDNA and channel walls, related to large difference between dielectric constants of water and lipid, and calculate effective charges of ssDNA. We start from the most fundamental stall charge $q_s$, which determines the force $F_s= q_s V/L$ stalling DNA against the voltage V (L is the length of the channel). We show that the stall charge $q_s$ is proportional to the ion current blocked by DNA, which is small due to the self-energy barrier. Large voltage V reduces the capture barrier which DNA molecule should overcome in order to enter the channel by $|q_c|V$, where $q_c$ is the effective capture charge. We expressed it through the stall charge $q_s$. We also relate the stall charge $q_s$ to two other effective charges measured for ssDNA with a hairpin in the back end: the charge $q_u$ responsible for reduction of the barrier for unzipping of the hairpin and the charge $q_e$ responsible for DNA escape in the direction of hairpin against the voltage. At small V we explain reduction of the capture barrier with the salt concentration.

cond-mat.soft↗

arXiv2008

Effect of disorder on a graphene p-n junction

We propose the theory of transport in a gate-tunable graphene p-n junction, in which the gradient of the carrier density is controlled by the gate voltage. Depending on this gradient and on the density of charged impurities, the junction resistance is dominated by either diffusive or ballistic contribution. We find the conditions for observing ballistic transport and show that in existing devices they are satisfied only marginally. We also simulate numerically the trajectories of charge carriers and illustrate challenges in realizing more delicate ballistic effects, such as Veselago lensing.

cond-mat.mes-hall↗

arXiv2007

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.

cond-mat.supr-con↗

arXiv2007

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.

cond-mat.mes-hall↗

arXiv2007

Superfluid-insulator transition and BCS-BEC crossover in dirty ultracold Fermi gas

Superfluid-insulator transition in an ultracold Fermi gas in the external disorder potential of the amplitude $V_0$ is studied as a function of the concentration of the gas $n$ and magnetic field $B$ in the presence of the Feshbach resonance. We find the zero temperature phase diagrams in the plane ($B,n$) at a given $V_0$ and in the plane $(V_0, n)$ at a given $B$. Our results for BEC side of the diagram are also valid for the superfluid-insulator transition in a Bose gas.

cond-mat.dis-nn↗

arXiv2007

Screening of a hypercritical charge in graphene

Screening of a large external charge in graphene is studied. The charge is assumed to be displaced away or smeared over a finite region of the graphene plane. The initial decay of the screened potential with distance is shown to follow the 3/2 power. It gradually changes to the Coulomb law outside of a hypercritical core whose radius is proportional to the external charge.

cond-mat.mes-hall↗

arXiv2007

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.

q-bio.BM↗