Universal Scaling of Strong-Field Localization in an Integer Quantum Hall Liquid

We study the Landau level localization and scaling properties of a disordered two-dimensional electron gas in the presence of a strong external magnetic field. The impurities are treated as random distributed scattering centers with parameterized potentials. Using a transfer matrix for a finite-width strip geometry, we calculate the localization length as a function of system size and electron energy. The finite-size localization length is determined by calculating the Lyapunov exponents of the transfer matrix. A detailed finite-size scaling analysis is used to study the critical behavior near the center of the Landau bands. The influence of varying the impurity concentration, the scattering potential range and its nature, and the Landau level index on the scaling behavior and on the critical exponent is systematically investigated. Particular emphasis is put on studying the effects of finite range of the disorder potential and Landau level coupling on the quantum localization behavior. Our numerical results, which are carried out on systems much larger than those studied before, indicate that pure $\delta$-function disorder in the absence of any Landau level coupling gives rise to non-universal localization properties with the critical exponents in the lowest two Landau levels being substantially different. Inclusion of a finite potential range and/or Landau level mixing may be essential in producing universality in the localization.Comment: 28 pages, Latex, 17 figures (available upon request), #phd0

Scaling Behavior of the Activated Conductivity in a Quantum Hall Liquid

We propose a scaling model for the universal longitudinal conductivity near the mobility edge for the integer quantum Hall liquid. We fit our model with available experimental data on exponentially activated conductance near the Landau level tails in the integer quantum Hall regime. We obtain quantitative agreement between our scaling model and the experimental data over a wide temperature and magnetic field range.Comment: 9 pages, Latex, 2 figures (available upon request), #phd0

Isoselenocyanates derived from Boc/Z-amino acids: Synthesis, isolation, characterization, and application to the efficient synthesis of unsymmetrical selenoureas and selenoureidopeptidomimetics

Isoselenocyanates derived from Boc/Z-amino acids are prepared by the reaction of the corresponding isonitriles with selenium powder in presence of triethylamine at reflux. The utility of these new classes of isoselenocyanates in the preparation of selenoureidodipeptidomimetics possessing both amino as well as carboxy termini has been accomplished. The 1H NMR analysis confirmed that the protocol involving the conversion of isonitriles to isoselenocyanates and their use as coupling agents in assembling selenoureido derivatives is free from racemization. © 2010 Elsevier Ltd. All rights reserved

Electron Localization in a 2D System with Random Magnetic Flux

Using a finite-size scaling method, we calculate the localization properties of a disordered two-dimensional electron system in the presence of a random magnetic field. Below a critical energy $E_c$ all states are localized and the localization length $\xi$ diverges when the Fermi energy approaches the critical energy, {\it i.e.} $\xi(E)\propto |E-E_c|^{-\nu}$. We find that $E_c$ shifts with the strength of the disorder and the amplitude of the random magnetic field while the critical exponent ($\nu\approx 4.8$) remains unchanged indicating universality in this system. Implications on the experiment in half-filling fractional quantum Hall system are also discussed.Comment: 4 pages, RevTex 3.0, 5 figures(PS files available upon request), #phd1

Short-Range Interactions and Scaling Near Integer Quantum Hall Transitions

We study the influence of short-range electron-electron interactions on scaling behavior near the integer quantum Hall plateau transitions. Short-range interactions are known to be irrelevant at the renormalization group fixed point which represents the transition in the non-interacting system. We find, nevertheless, that transport properties change discontinuously when interactions are introduced. Most importantly, in the thermodynamic limit the conductivity at finite temperature is zero without interactions, but non-zero in the presence of arbitrarily weak interactions. In addition, scaling as a function of frequency, $\omega$, and temperature, $T$, is determined by the scaling variable $\omega/T^p$ (where $p$ is the exponent for the temperature dependence of the inelastic scattering rate) and not by $\omega/T$, as it would be at a conventional quantum phase transition described by an interacting fixed point. We express the inelastic exponent, $p$, and the thermal exponent, $z_T$, in terms of the scaling dimension, $-\alpha < 0$, of the interaction strength and the dynamical exponent $z$ (which has the value $z=2$), obtaining $p=1+2\alpha/z$ and $z_T=2/p$.Comment: 9 pages, 4 figures, submitted to Physical Review

Focus Point SUSY at the LHC Revisited

The estimation of the backgrounds for gluino signals in focus point supersymmetry is extended by including the backgrounds from the production of four third generation quarks in the analysis. We find that these backgrounds are negligible if one uses the strong selection criteria proposed in the literature (including this analysis) for heavy gluino searches. Softer selection criteria often recommended for lighter gluino searches yield backgrounds which are small but numerically significant. We have also repeated the more conventional background calculations and compared our results with the other groups. We find that the size of the total residual background estimated by different groups using different event generators and hard kinematical cuts agree approximately. In view of the theoretical uncertainties in the leading order signal and background cross sections mainly due to the choice of the QCD scale, the gluino mass reach at the LHC cannot be pinpointed. However, requiring a signal with $\rm\geq 3$ tagged b-jets (instead of the standard choice of $\rm\geq 2$) it is shown that gluino masses close to 2 TeV can be probed at the LHC for a range of reasonable choices of the QCD scale for an integrated luminosity of 300 fb$^{-1}$.Comment: 17 pages, 4 figures, minor typos correctio

Probing R-parity violating models of neutrino mass at the Tevatron via top Squark decays

We have estimated the limiting branching ratio of the R-parity violating (RPV) decay of the lighter top squark, \tilde t_1 \ar l^+ d ($l=e$ or $\mu$ and d is a down type quark of any flavor), as a function of top squark mass(\MST) for an observable signal in the di-lepton plus di-jet channel at the Tevatron RUN-II experiment with 2 fb$^{-1}$ luminosity. Our simulations indicate that the lepton number violating nature of the underlying decay dynamics can be confirmed via the reconstruction of \MST. The above decay is interesting in the context of RPV models of neutrino mass where the RPV couplings ($\lambda'_{i3j}$) driving the above decay are constrained to be small (\lsim 10^{-3} - 10^{-4} ). If $\tilde t_1$ is the next lightest super particle - a theoretically well motivated scenario - then the RPV decay can naturally compete with the R-parity conserving (RPC) modes which also have suppressed widths. The model independent limiting BR can delineate the parameter space in specific supersymmetric models, where the dominating RPV decay is observable and predict the minimum magnitude of the RPV coupling that will be sensitive to Run-II data. We have found it to be in the same ballpark value required by models of neutrino mass, for a wide range of \MST. A comprehensive future strategy for linking top squark decays with models of neutrino mass is sketched.Comment: 28 pages, 14 Figure

Fragmentation Function and Hadronic Production of the Heavy Supersymmetric Hadrons

The light top-squark \sto may be the lightest squark and its lifetime may be `long enough' in a kind of SUSY models which have not been ruled out yet experimentally, so colorless `supersymmetric hadrons (superhadrons)' (\sto \bar{q}) ($q$ is a quark except $t$-quark) may be formed as long as the light top-squark \sto can be produced. Fragmentation function of \sto to heavy `supersymmetric hadrons (superhadrons)' (\sto \bar{Q}) ($\bar{Q}=\bar{c}$ or $\bar{b}$) and the hadronic production of the superhadrons are investigated quantitatively. The fragmentation function is calculated precisely. Due to the difference in spin of the SUSY component, the asymptotic behavior of the fragmentation function is different from those of the existent ones. The fragmentation function is also applied to compute the production of heavy superhadrons at hadronic colliders Tevatron and LHC under the so-called fragmentation approach. The resultant cross-section for the heavy superhadrons is too small to observe at Tevatron, but great enough at LHC, even when all the relevant parameters in the SUSY models are taken within the favored region for the heavy superhadrons. The production of `light superhadrons' (\sto \bar{q}) ($q=u, d, s$) is also roughly estimated. It is pointed out that the production cross-sections of the light superhadrons (\sto \bar{q}) may be much greater than those of the heavy superhadrons, so that even at Tevatron the light superhadrons may be produced in great quantities.Comment: 20 pages, 9 figure

Top-squark searches at the Tevatron in models of low-energy supersymmetry breaking

We study the production and decays of top squarks (stops) at the Tevatron collider in models of low-energy supersymmetry breaking. We consider the case where the lightest Standard Model (SM) superpartner is a light neutralino that predominantly decays into a photon and a light gravitino. Considering the lighter stop to be the next-to-lightest Standard Model superpartner, we analyze stop signatures associated with jets, photons and missing energy, which lead to signals naturally larger than the associated SM backgrounds. We consider both 2-body and 3-body decays of the top squarks and show that the reach of the Tevatron can be significantly larger than that expected within either the standard supergravity models or models of low-energy supersymmetry breaking in which the stop is the lightest SM superpartner. For a modest projection of the final Tevatron luminosity, L = 4 fb-1, stop masses of order 300 GeV are accessible at the Tevatron collider in both 2-body and 3-body decay modes. We also consider the production and decay of ten degenerate squarks that are the supersymmetric partners of the five light quarks. In this case we find that common squark masses up to 360 GeV are easily accessible at the Tevatron collider, and that the reach increases further if the gluino is light.Comment: 32 pages, 9 figures; references adde

Non-zero temperature transport near quantum critical points

We describe the nature of charge transport at non-zero temperatures ($T$) above the two-dimensional ($d$) superfluid-insulator quantum critical point. We argue that the transport is characterized by inelastic collisions among thermally excited carriers at a rate of order $k_B T/\hbar$. This implies that the transport at frequencies $\omega \ll k_B T/\hbar$ is in the hydrodynamic, collision-dominated (or `incoherent') regime, while $\omega \gg k_B T/\hbar$ is the collisionless (or `phase-coherent') regime. The conductivity is argued to be $e^2 / h$ times a non-trivial universal scaling function of $\hbar \omega / k_B T$, and not independent of $\hbar \omega/k_B T$, as has been previously claimed, or implicitly assumed. The experimentally measured d.c. conductivity is the hydrodynamic $\hbar \omega/k_B T \to 0$ limit of this function, and is a universal number times $e^2 / h$, even though the transport is incoherent. Previous work determined the conductivity by incorrectly assuming it was also equal to the collisionless $\hbar \omega/k_B T \to \infty$ limit of the scaling function, which actually describes phase-coherent transport with a conductivity given by a different universal number times $e^2 / h$. We provide the first computation of the universal d.c. conductivity in a disorder-free boson model, along with explicit crossover functions, using a quantum Boltzmann equation and an expansion in $\epsilon=3-d$. The case of spin transport near quantum critical points in antiferromagnets is also discussed. Similar ideas should apply to the transitions in quantum Hall systems and to metal-insulator transitions. We suggest experimental tests of our picture and speculate on a new route to self-duality at two-dimensional quantum critical points.Comment: Feedback incorporated into numerous clarifying remarks; additional appendix discusses relationship to transport in dissipative quantum mechanics and quantum Hall edge state tunnelling problems, stimulated by discussions with E. Fradki