Coulomb gap in one-dimensional disordered electron systems

The density of states of one-dimensional disordered electron systems with long range Coulomb interaction is studied in the weak pinning limit. The density of states is found to follow a power law with an exponent determined by localization length, and this power law behavior is consistent with the existing numerical results.Comment: RevTeX4 file, 5 pages, no figures To appear in Physical Reviews

Nonlinear spectral calculus and super-expanders

Nonlinear spectral gaps with respect to uniformly convex normed spaces are shown to satisfy a spectral calculus inequality that establishes their decay along Cesaro averages. Nonlinear spectral gaps of graphs are also shown to behave sub-multiplicatively under zigzag products. These results yield a combinatorial construction of super-expanders, i.e., a sequence of 3-regular graphs that does not admit a coarse embedding into any uniformly convex normed space.Comment: Typos fixed based on referee comments. Some of the results of this paper were announced in arXiv:0910.2041. The corresponding parts of arXiv:0910.2041 are subsumed by the current pape

Charging effects in quantum wires

We investigate the role of charging effects in a voltage-biased quantum wire. Both the finite range of the Coulomb interaction and the long-ranged nature of the Friedel oscillation imply a finite capacitance, leading to a charging energy. While observable Coulomb blockade effects are absent for a single impurity, they are crucial if islands are present. For a double barrier, we give the resonance condition, fully taking into account the charging of the island.Comment: 6 Pages RevTeX, no figures, Phys. Rev. B (in press

Influence of thermal fluctuations on quantum phase transitions in one-dimensional disordered systems: Charge density waves and Luttinger liquids

The low temperature phase diagram of 1D weakly disordered quantum systems like charge or spin density waves and Luttinger liquids is studied by a \emph{full finite temperature} renormalization group (RG) calculation. For vanishing quantum fluctuations this approach is amended by an \emph{exact} solution in the case of strong disorder and by a mapping onto the \emph{Burgers equation with noise} in the case of weak disorder, respectively. At \emph{zero} temperature we reproduce the quantum phase transition between a pinned (localized) and an unpinned (delocalized) phase for weak and strong quantum fluctuations, respectively, as found previously by Fukuyama or Giamarchi and Schulz. At \emph{finite} temperatures the localization transition is suppressed: the random potential is wiped out by thermal fluctuations on length scales larger than the thermal de Broglie wave length of the phason excitations. The existence of a zero temperature transition is reflected in a rich cross-over phase diagram of the correlation functions. In particular we find four different scaling regions: a \emph{classical disordered}, a \emph{quantum disordered}, a \emph{quantum critical} and a \emph{thermal} region. The results can be transferred directly to the discussion of the influence of disorder in superfluids. Finally we extend the RG calculation to the treatment of a commensurate lattice potential. Applications to related systems are discussed as well.Comment: 19 pages, 7 figure

Electronic Spectral Functions for Quantum Hall Edge States

We have evaluated wavevector-dependent electronic spectral functions for integer and fractional quantum Hall edge states using a chiral Luttinger liquid model. The spectral functions have a finite width and a complicated line shape because of the long-range of the Coulomb interaction. We discuss the possibility of probing these line shapes in vertical tunneling experiments.Comment: 4 pages, RevTex, two figures included, to appear as a Rapid Communication in PRB; we updated references which have recently appeared in print and were cited as preprints in our ealier submissio

Variational theory of elastic manifolds with correlated disorder and localization of interacting quantum particles

We apply the gaussian variational method (GVM) to study the equilibrium statistical mechanics of the two related systems: (i) classical elastic manifolds, such as flux lattices, in presence of columnar disorder correlated along the $\tau$ direction (ii) interacting quantum particles in a static random potential. We find localization by disorder, the localized phase being described by a replica symmetry broken solution confined to the mode $\omega=0$. For classical systems we compute the correlation function of relative displacements. In $d=2+1$, in the absence of dislocations, the GVM allows to describes the Bose glass phase. Along the columns the displacements saturate at a length $l_{\perp}$ indicating flux-line localization. Perpendicularly to the columns long range order is destroyed. We find divergent tilt modulus $c_{44}=\infty$ and a $x \sim \tau^{1/2}$ scaling. Quantum systems are studied using the analytic continuation from imaginary to real time $\tau \to i t$. We compute the conductivity and find that it behaves at small frequency as $\sigma(\omega) \approx \omega^2$ in all dimensions ($d < 4$) for which disorder is relevant. We compute the quantum localization length $\xi$. In $d=1$, where the model also describes interacting fermions in a static random potential, we find a delocalization transition and obtain analytically both the low and high frequency behavior of the conductivity for any value of the interaction. We show that the marginality condition appears as the condition to obtain the correct physical behavior. Agreement with renormalization group results is found whenever it can be compared.Comment: 34 pages, REVTeX, no figure

A novel homozygous KCNQ3 loss-of-function variant causes non-syndromic intellectual disability and neonatal-onset pharmacodependent epilepsy

OBJECTIVE: Heterozygous variants in KCNQ2 or, more rarely, KCNQ3 genes are responsible for early-onset developmental/epileptic disorders characterized by heterogeneous clinical presentation and course, genetic transmission, and prognosis. While familial forms mostly include benign epilepsies with seizures starting in the neonatal or early-infantile period, de novo variants in KCNQ2 or KCNQ3 have been described in sporadic cases of early-onset encephalopathy (EOEE) with pharmacoresistant seizures, various age-related pathological EEG patterns, and moderate/severe developmental impairment. All pathogenic variants in KCNQ2 or KCNQ3 occur in heterozygosity. The aim of this work was to report the clinical, molecular, and functional properties of a new KCNQ3 variant found in homozygous configuration in a 9-year-old girl with pharmacodependent neonatal-onset epilepsy and non-syndromic intellectual disability. METHODS: Exome sequencing was used for genetic investigation. KCNQ3 transcript and subunit expression in fibroblasts was analyzed with quantitative real-time PCR and Western blotting or immunofluorescence, respectively. Whole-cell patch-clamp electrophysiology was used for functional characterization of mutant subunits. RESULTS: A novel single-base duplication in exon 12 of KCNQ3 (NM_004519.3:c.1599dup) was found in homozygous configuration in the proband born to consanguineous healthy parents; this frameshift variant introduced a premature termination codon (PTC), thus deleting a large part of the C-terminal region. Mutant KCNQ3 transcript and protein abundance was markedly reduced in primary fibroblasts from the proband, consistent with nonsense-mediated mRNA decay. The variant fully abolished the ability of KCNQ3 subunits to assemble into functional homomeric or heteromeric channels with KCNQ2 subunits. SIGNIFICANCE: The present results indicate that a homozygous KCNQ3 loss-of-function variant is responsible for a severe phenotype characterized by neonatal-onset pharmacodependent seizures, with developmental delay and intellectual disability. They also reveal difference in genetic and pathogenetic mechanisms between KCNQ2- and KCNQ3-related epilepsies, a crucial observation for patients affected with EOEE and/or developmental disabilities

Dynamical response of a pinned two-dimensional Wigner crystal

We re-examine a long-standing problem of a finite-frequency conductivity of a weakly pinned two-dimensional classical Wigner crystal. In this system an inhomogeneously broadened absorption line (pinning mode) centered at disorder and magnetic field dependent frequency $\omega_p$ is known to appear. We show that the relative linewidth $\Delta \omega_p / \omega_p$ of the pinning mode is of the order of one in weak magnetic fields, exhibits a power-law decrease in intermediate fields, and eventually saturates at a small value in strong magnetic fields. The linewidth narrowing is due to a peculiar mechanism of mixing between the stiffer longitudinal and the softer transverse components of the collective excitations. The width of the high-field resonance proves to be related to the density of states in the low-frequency tail of the zero-field phonon spectrum. We find a qualitative agreement with recent experiments and point out differences from the previous theoretical work on the subject.Comment: 19 pages, 11 figures. Supersedes cond-mat/990424

Transport of interacting electrons through a double barrier in quantum wires

We generalize the fermionic renormalization group method to describe analytically transport through a double barrier structure in a one-dimensional system. Focusing on the case of weakly interacting electrons, we investigate thoroughly the dependence of the conductance on the strength and the shape of the double barrier for arbitrary temperature T. Our approach allows us to systematically analyze the contributions to renormalized scattering amplitudes from different characteristic scales absent in the case of a single impurity, without restricting the consideration to the model of a single resonant level. Both a sequential resonant tunneling for high T and a resonant transmission for T smaller than the resonance width are studied within the unified treatment of transport through strong barriers. For weak barriers, we show that two different regimes are possible. Moderately weak impurities may get strong due to a renormalization by interacting electrons, so that transport is described in terms of theory for initially strong barriers. The renormalization of very weak impurities does not yield any peak in the transmission probability; however, remarkably, the interaction gives rise to a sharp peak in the conductance, provided asymmetry is not too high.Comment: 18 pages, 8 figures; figures added, references updated, extended discussio

Plasmon Modes and Correlation Functions in Quantum Wires and Hall Bars

We present microscopic derivations of the one-dimensional low-energy boson effective Hamiltonians of quantum wire and quantum Hall bar systems. The quantum Hall system is distinguished by its spatial separation of oppositely directed electrons. We discuss qualitative differences in the plasmon collective mode dispersions and the ground state correlation functions of the two systems which are consequences of this difference. The slowly-decaying quasi-solid correlations expected in a quantum wire are strongly suppressed in quantum Hall bar systems.Comment: 7 pages, RevTex, 3 figures and 1 table included; references updated and minor typos correcte