The microscopic nature of localization in the quantum Hall effect

The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field. The effect involves exact quantization of all the electronic transport properties due to particle localization. In the conventional theory of the quantum Hall effect, strong-field localization is associated with a single-particle drift motion of electrons along contours of constant disorder potential. Transport experiments that probe the extended states in the transition regions between quantum Hall phases have been used to test both the theory and its implications for quantum Hall phase transitions. Although several experiments on highly disordered samples have affirmed the validity of the single-particle picture, other experiments and some recent theories have found deviations from the predicted universal behaviour. Here we use a scanning single-electron transistor to probe the individual localized states, which we find to be strikingly different from the predictions of single-particle theory. The states are mainly determined by Coulomb interactions, and appear only when quantization of kinetic energy limits the screening ability of electrons. We conclude that the quantum Hall effect has a greater diversity of regimes and phase transitions than predicted by the single-particle framework. Our experiments suggest a unified picture of localization in which the single-particle model is valid only in the limit of strong disorder

On fractionality of the path packing problem

In this paper, we study fractional multiflows in undirected graphs. A fractional multiflow in a graph G with a node subset T, called terminals, is a collection of weighted paths with ends in T such that the total weights of paths traversing each edge does not exceed 1. Well-known fractional path packing problem consists of maximizing the total weight of paths with ends in a subset S of TxT over all fractional multiflows. Together, G,T and S form a network. A network is an Eulerian network if all nodes in N\T have even degrees. A term "fractionality" was defined for the fractional path packing problem by A. Karzanov as the smallest natural number D so that there exists a solution to the problem that becomes integer-valued when multiplied by D. A. Karzanov has defined the class of Eulerian networks in terms of T and S, outside which D is infinite and proved that whithin this class D can be 1,2 or 4. He conjectured that D should be 1 or 2 for this class of networks. In this paper we prove this conjecture.Comment: 18 pages, 5 figures in .eps format, 2 latex files, main file is kc13.tex Resubmission due to incorrectly specified CS type of the article; no changes to the context have been mad

Compressibility of a two-dimensional hole gas in tilted magnetic field

We have measured compressibility of a two-dimensional hole gas in p-GaAs/AlGaAs heterostructure, grown on a (100) surface, in the presence of a tilted magnetic field. It turns out that the parallel component of magnetic field affects neither the spin splitting nor the density of states. We conclude that: (a) g-factor in the parallel magnetic field is nearly zero in this system; and (b) the level of the disorder potential is not sensitive to the parallel component of the magnetic field

Physics of the Insulating Phase in the Dilute Two-Dimensional Electron Gas

We propose to use the radio-frequency single-electron transistor as an extremely sensitive probe to detect the time-periodic ac signal generated by sliding electron lattice in the insulating state of the dilute two-dimensional electron gas. We also propose to use the optically-pumped NMR technique to probe the electron spin structure of the insulating state. We show that the electron effective mass and spin susceptibility are strongly enhanced by critical fluctuations of electron lattice in the vicinity of the metal-insulator transition, as observed in experiment.Comment: 5 pages, 2 figures, uses jetpl.cls (included). v.4: After publication in JETP Letters, two plots comparing theory and experiment are added, and a minor error is correcte

A self-consistent theory for graphene transport

We demonstrate theoretically that most of the observed transport properties of graphene sheets at zero magnetic field can be explained by scattering from charged impurities. We find that, contrary to common perception, these properties are not universal but depend on the concentration of charged impurities $n_{\rm imp}$. For dirty samples ($250 \times 10^{10} {\rm cm}^{-2} < n_{\rm imp} < 400 \times 10^{10} {\rm cm}^{-2}$), the value of the minimum conductivity at low carrier density is indeed $4 e^2/h$ in agreement with early experiments, with weak dependence on impurity concentration. For cleaner samples, we predict that the minimum conductivity depends strongly on $n_{\rm imp}$, increasing to $8 e^2/h$ for $n_{\rm imp} \sim 20 \times 10^{10}{\rm cm}^{-2}$. A clear strategy to improve graphene mobility is to eliminate charged impurities or use a substrate with a larger dielectric constant.Comment: To be published in Proc. Natl. Acad. Sci. US

Quantum Capacitance Extraction for Carbon Nanotube Interconnects

Electrical transport in metallic carbon nanotubes, especially the ones with diameters of the order of a few nanometers can be best described using the Tomanaga Luttinger liquid (TL) model. Recently, the TL model has been used to create a convenient transmission line like phenomenological model for carbon nanotubes. In this paper, we have characterized metallic nanotubes based on that model, quantifying the quantum capacitances of individual metallic single walled carbon nanotubes and crystalline bundles of single walled tubes of different diameters. Our calculations show that the quantum capacitances for both individual tubes and the bundles show a weak dependence on the diameters of their constituent tubes. The nanotube bundles exhibit a significantly large quantum capacitance due to enhancement of density of states at the Fermi level

A group contribution model for determining the sublimation enthalpy of organic compounds at the standard reference temperature of 298 K

Article discussing a group contribution model for determining the sublimation enthalpy of organic compounds at the standard reference temperature of 298 K

A Group Contribution Model for Determining the Vaporization Enthalpy of Organic Compounds at the Standard Reference Temperature of 298 K

Article on a group contribution model for determining the vaporization enthalpy of organic compounds at the standard reference temperature of 298 K

The nature of localization in graphene under quantum Hall conditions

Particle localization is an essential ingredient in quantum Hall physics [1,2]. In conventional high mobility two-dimensional electron systems Coulomb interactions were shown to compete with disorder and to play a central role in particle localization [3]. Here we address the nature of localization in graphene where the carrier mobility, quantifying the disorder, is two to four orders of magnitude smaller [4,5,6,7,8,9,10]. We image the electronic density of states and the localized state spectrum of a graphene flake in the quantum Hall regime with a scanning single electron transistor [11]. Our microscopic approach provides direct insight into the nature of localization. Surprisingly, despite strong disorder, our findings indicate that localization in graphene is not dominated by single particle physics, but rather by a competition between the underlying disorder potential and the repulsive Coulomb interaction responsible for screening.Comment: 18 pages, including 5 figure

On the Ground State of Electron Gases at Negative Compressibility

Two- and three-dimensional electron gases with a uniform neutralizing background are studied at negative compressibility. Parametrized expressions for the dielectric function are used to access this strong-coupling regime, where the screened Coulomb potential becomes overall attractive for like charges. Closely examining these expressions reveals that the ground state with a periodic modulation of the charge density, albeit exponentially damped, replaces the homogeneous one at positive compressibility. The wavevector characterizing the new ground state depends on the density and is complex, having a positive imaginary part, as does the homogeneous ground state, and real part, as does the genuine charge density wave.Comment: 6 double-column pages, 2 figures. 2nd version is an extension of the 1st one, giving more detail