Hidden Quantum Hall Stripes in Al_{x}Ga_{1-x}As/Al_{0.24}Ga_{0.76}As Quantum Wells.

We report on transport signatures of hidden quantum Hall stripe (hQHS) phases in high (N>2) half-filled Landau levels of Al_{x}Ga_{1-x}As/Al_{0.24}Ga_{0.76}As quantum wells with varying Al mole fraction x<10^{-3}. Residing between the conventional stripe phases (lower N) and the isotropic liquid phases (higher N), where resistivity decreases as 1/N, these hQHS phases exhibit isotropic and N-independent resistivity. Using the experimental phase diagram, we establish that the stripe phases are more robust than theoretically predicted, calling for improved theoretical treatment. We also show that, unlike conventional stripe phases, the hQHS phases do not occur in ultrahigh mobility GaAs quantum wells but are likely to be found in other systems.

ZnO Nanocrystal Networks Near the Insulator-Metal Transition: Tuning Contact Radius and Electron Density with Intense Pulsed Light.

Networks of ligand-free semiconductor nanocrystals (NCs) offer a valuable combination of high carrier mobility and optoelectronic properties tunable via quantum confinement. In principle, maximizing carrier mobility entails crossing the insulator-metal transition (IMT), where carriers become delocalized. A recent theoretical study predicted that this transition occurs at nρ3 ≈ 0.3, where n is the carrier density and ρ is the interparticle contact radius. In this work, we satisfy this criterion in networks of plasma-synthesized ZnO NCs by using intense pulsed light (IPL) annealing to tune n and ρ independently. IPL applied to as-deposited NCs increases ρ by inducing sintering, and IPL applied after the NCs are coated with Al2O3 by atomic layer deposition increases n by removing electron-trapping surface hydroxyls. This procedure does not substantially alter NC size or composition and is potentially applicable to a wide variety of nanomaterials. As we increase nρ3 to at least twice the predicted critical value, we observe conductivity scaling consistent with arrival at the critical region of a continuous quantum phase transition. This allows us to determine the critical behavior of the dielectric constant and electron localization length at the IMT. However, our samples remain on the insulating side of the critical region, which suggests that the critical value of nρ3 may in fact be significantly higher than 0.3.

Metal-insulator transition in films of doped semiconductor nanocrystals.

To fully deploy the potential of semiconductor nanocrystal films as low-cost electronic materials, a better understanding of the amount of dopants required to make their conductivity metallic is needed. In bulk semiconductors, the critical concentration of electrons at the metal-insulator transition is described by the Mott criterion. Here, we theoretically derive the critical concentration nc for films of heavily doped nanocrystals devoid of ligands at their surface and in direct contact with each other. In the accompanying experiments, we investigate the conduction mechanism in films of phosphorus-doped, ligand-free silicon nanocrystals. At the largest electron concentration achieved in our samples, which is half the predicted nc, we find that the localization length of hopping electrons is close to three times the nanocrystals diameter, indicating that the film approaches the metal-insulator transition.

Percolation via Combined Electrostatic and Chemical Doping in Complex Oxide Films.

Stimulated by experimental advances in electrolyte gating methods, we investigate theoretically percolation in thin films of inhomogeneous complex oxides, such as La_{1-x}Sr_{x}CoO_{3} (LSCO), induced by a combination of bulk chemical and surface electrostatic doping. Using numerical and analytical methods, we identify two mechanisms that describe how bulk dopants reduce the amount of electrostatic surface charge required to reach percolation: (i) bulk-assisted surface percolation and (ii) surface-assisted bulk percolation. We show that the critical surface charge strongly depends on the film thickness when the film is close to the chemical percolation threshold. In particular, thin films can be driven across the percolation transition by modest surface charge densities. If percolation is associated with the onset of ferromagnetism, as in LSCO, we further demonstrate that the presence of critical magnetic clusters extending from the film surface into the bulk results in considerable enhancement of the saturation magnetization, with pronounced experimental consequences. These results should significantly guide experimental work seeking to verify gate-induced percolation transitions in such materials.

Why is the bulk resistivity of topological insulators so small?

As-grown topological insulators (TIs) are typically heavily doped n-type crystals. Compensation by acceptors is used to move the Fermi level to the middle of the band gap, but even then TIs have a frustratingly small bulk resistivity. We show that this small resistivity is the result of band bending by poorly screened fluctuations in the random Coulomb potential. Using numerical simulations of a completely compensated TI, we find that the bulk resistivity has an activation energy of just 0.15 times the band gap, in good agreement with experimental data. At lower temperatures activated transport crosses over to variable range hopping with a relatively large localization length.

Coulomb gap triptych in a periodic array of metal nanocrystals.

The Coulomb gap in the single-particle density of states (DOS) is a universal consequence of electron-electron interaction in disordered systems with localized electron states. Here we show that in arrays of monodisperse metallic nanocrystals, there is not one but three identical adjacent Coulomb gaps, which together form a structure that we call a "Coulomb gap triptych." We calculate the DOS and the conductivity in two- and three-dimensional arrays using a computer simulation. Unlike in the conventional Coulomb glass models, in nanocrystal arrays the DOS has a fixed width in the limit of large disorder. The Coulomb gap triptych can be studied via tunneling experiments.

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 A. 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.

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

Translocation of a single-stranded DNA molecule through genetically engineered alpha -hemolysin channels with positively charged walls is studied. It is predicted that transport properties of such channels are dramatically different from neutral wild-type alpha -hemolysin channels. We assume that the wall charges compensate a fraction x of the bare charge q_{b} of the DNA piece residing in the channel. Our predictions are as follows. (i) At small concentration of salt the blocked ion current decreases with x . (ii) The effective charge q_{s} of the 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 grows exponentially with x . Our theory is also applicable to translocation of a double-stranded DNA molecular in narrow solid state nanopores with positively charged walls.

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.

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.

Kinetics of viral self-assembly: role of the single-stranded RNA antenna.

Many viruses self-assemble from a large number of identical capsid proteins with long flexible N-terminal tails and single-stranded (ss) RNA. We study the role of the strong Coulomb interaction of positive N-terminal tails with ssRNA in the kinetics of in vitro virus self-assembly. Capsid proteins stick to the unassembled chain of ssRNA (which we call an "antenna") and slide on it toward the assembly site. We show that at excess of capsid proteins such one-dimensional diffusion accelerates self-assembly more than ten times. On the other hand at excess of ssRNA, the antenna slows self-assembly down. Several experiments are proposed to verify the role of the ssRNA antenna.

How does a protein search for the specific site on DNA: The role of disorder.

Proteins can locate their specific targets on DNA up to two orders of magnitude faster than the Smoluchowski three-dimensional diffusion rate. This happens due to nonspecific adsorption of proteins to DNA and subsequent one-dimensional sliding along DNA. We call such a one-dimensional route towards the target an "antenna." We studied the role of the dispersion of nonspecific binding energies within the antenna due to a quasirandom sequence of natural DNA. A random energy profile for sliding proteins slows the searching rate for the target. We show that this slowdown is different for macroscopic and mesoscopic antennas.

Ion exchange phase transitions in water-filled channels with charged walls.

Ion transport through narrow water-filled channels is impeded by a high electrostatic barrier. The latter originates from the large ratio of the dielectric constants of the water and the surrounding media. We show that "doping," i.e., immobile charges attached to the walls of the channel, substantially reduces the barrier. This explains why most of the biological ion channels are "doped." We show that at rather generic conditions the channels may undergo ion exchange phase transitions (typically of the first order). Upon such a transition a finite latent concentration of ions may either enter or leave the channel, or be exchanged between the ions of different valences. We discuss possible implications of these transitions for the Ca-vs-Na selectivity of biological Ca channels. We also show that transport of divalent Ca ions is assisted by their fractionalization into two separate excitations.

Long-range polarization attraction between two different like-charged macroions.

It is known that in a water solution with multivalent counterions (Z-ions) two likely charged macroions can attract each other due to correlations of Z-ions adsorbed on their surfaces. This "correlation" attraction is short ranged and decays exponentially with increasing distance between macroions at characteristic distance A/2pi , where A is the average distance between Z -ions on the surfaces of macroions. In this work, we show that an additional long-range "polarization" attraction exists when the bare surface charge densities of the two macroions have the same sign, but are different in absolute values. The key idea is that with adsorbed Z -ions, two insulating macroions can be considered as conductors with fixed but different electric potentials. Each potential is determined by the difference between the entropic bulk chemical potential of a Z -ion and its correlation chemical potential at the surface of the macroion determined by its bare surface charge density. When the two macroions are close enough, they get polarized in such a way that their adjacent spots form a charged capacitor, which leads to attraction. In a salt-free solution this polarization attractive force is long ranged: it decays as a power of the distance between the surfaces of two macroions, d. The polarization force decays slower than the van der Waals attraction and therefore is much larger than it in a large range of distances. In the presence of large amount of monovalent salt, the polarization attraction decays exponentially at d larger than the Debye-Hückel screening radius r(s) . Still, when A/2pi<

A simple derivation of the Gompertz law for human mortality.

The Gompertz law of dependence of human mortality rate on age is derived from a simple model of death as a result of an exponentially rare escape of abnormal cells from immunological response.

Phase diagram of aggregation of oppositely charged colloids in salty water.

Aggregation of two oppositely charged colloids in salty water is studied. We focus on the role of Coulomb interaction in strongly asymmetric systems in which the charge and size of one colloid is much larger than the other one. In the solution, each large colloid (macroion) attracts a certain number of oppositely charged small colloids (Z-ion) to form a complex. If the concentration ratio of the two colloids is such that complexes are not strongly charged, they condense in a macroscopic aggregate. As a result, the phase diagram in a plane of concentrations of two colloids consists of an aggregation domain sandwiched between two domains of stable solutions of complexes. The aggregation domain has a central part of total aggregation and two wings corresponding to partial aggregation. A quantitative theory of the phase diagram in the presence of monovalent salt is developed. It is shown that as the Debye-Hückel screening radius r(s) decreases, the aggregation domain grows, but the relative size of the partial aggregation domains becomes much smaller. As an important application of the theory, we consider solutions of long double-helix DNA with strongly charged positive spheres (artificial chromatin). We also consider implications of our theory for in vitro experiments with the natural chromatin. Finally, the effect of different shapes of macroions on the phase diagram is discussed.

Adsorption of charged particles on an oppositely charged surface: oscillating inversion of charge.

Adsorption of multivalent counterions on the charged surface of a macroion is known to lead to inversion of the macroion charge due to the strong lateral correlations of counterions. We consider a nontrivial role of the excluded volume of counterions on this effect. It is shown analytically that when the bare charge of the macroion increases, its net charge including the adsorbed counterions oscillates with the number of their layers. Charge inversion vanishes every time the top layer of counterions is completely full and becomes incompressible. These oscillations of charge inversion are confirmed by Monte Carlo simulations. Another version of this phenomenon is studied for a metallic electrode screened by multivalent counterions when the potential of the electrode is controlled instead of its charge. In this case, oscillations of the compressibility and charge inversion lead to oscillations of capacitance of this electrode with the number of adsorbed layers of multivalent counterions.

Kinetics of macroion coagulation induced by multivalent counterions.

Due to the strong correlations between multivalent counterions condensed on a macroion, the net macroion charge changes sign at some critical counterion concentration. This effect is known as the charge inversion. Near this critical concentration the macroion net charge is small. Therefore, short range attractive forces between macroions dominate Coulomb repulsion and lead to their coagulation. The kinetics of macroion coagulation in this range of counterion concentrations is studied. We calculate the Coulomb barrier between two approaching like charged macroions at a given counterion concentration. Two different macroion shapes (spherical and rodlike) are considered. A new "self-regulated" regime of coagulation is found. As the size of aggregates increases, their charge and Coulomb barrier also grow and diminish the sticking probability of aggregates. This leads to a slow, logarithmic increase of the aggregate size with time.

Persistence length of a polyelectrolyte in salty water: Monte Carlo study.

We address the long standing problem of the dependence of the electrostatic persistence length l(e) of a flexible polyelectrolyte (PE) on the screening length r(s) of the solution within the linear Debye-Hückel theory. The standard Odijk, Skolnick, and Fixman (OSF) theory suggests l(e) proportional, variant r(2)s, while some variational theories and some computer simulations suggest l(e) proportional, variant r(s). In this paper, we use Monte Carlo simulations to study the conformation of a simple polyelectrolyte. Using four times longer PEs than in previous simulations and refined methods for the treatment of the simulation data, we show that the results are consistent with the OSF dependence l(e) proportional, variant r(2)s. The linear charge density of the PE, which enters in the coefficient of this dependence is properly renormalized to take into account local fluctuations.

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 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.