Hall resistance in the hopping regime, a "Hall Insulator"?

The Hall conductivity and resistivity of strongly localized electrons at low temperatures and at small magnetic fields are obtained. It is found that the results depend on whether the conductivity or the resistivity tensors are averaged to obtain the macroscopic Hall resistivity. In the second case the Hall resistivity always {\it diverges} exponentially as the temperature tends to zero. But when the Hall resistivity is derived from the averaged conductivity, the resulting temperature dependence is sensitive to the disorder configuration. Then the Hall resistivity may approach a constant value as $T\to 0$. This is the Hall insulating behavior. It is argued that for strictly dc conditions, the transport quantity that should be averaged is the resistivity.Comment: Late

Spectral Boundary of Positive Random Potential in a Strong Magnetic Field

We consider the problem of randomly distributed positive delta-function scatterers in a strong magnetic field and study the behavior of density of states close to the spectral boundary at $E=\hbar\omega_{c}/2$ in both two and three dimensions. Starting from dimensionally reduced expression of Brezin et al. and using the semiclassical approximation we show that the density of states in the Lifshitz tail at small energies is proportio- nal to $e^{f-2}$ in two dimensions and to $\exp(-3.14f\ln(3.14f/\pi e)/ \sqrt(2me))$ in three dimensions, where $e$ is the energy and $f$ is the density of scatterers in natural units.Comment: 12 pages, LaTex, 5 figures available upon request, to appear in Phys. Rev.

Electron-Electron Interactions and the Hall-Insulator

Using the Kubo formula, we show explicitly that a non-interacting electron system can not behave like a Hall-insulator, {\it ie.,} a DC resistivity matrix $\rho_{xx}\rightarrow\infty$ and $\rho_{xy}=$finite in the zero temperature limit, as has been observed recently in experiment. For a strongly interacting electron system in a magnetic field, we illustrate, by constructing a specific form of correlations between mobile and localized electrons, that the Hall resistivity can approximately equal to its classical value. A Hall-insulator is realized in this model when the density of mobile electrons becomes vanishingly small. It is shown that in non-interacting electron systems, the zero-temperature frequency-dependent conductacnce generally does not give the DC conductance.Comment: 11 pages, RevTeX3.

The Quantized Hall Insulator: A New Insulator in Two-Dimensions

Quite generally, an insulator is theoretically defined by a vanishing conductivity tensor at the absolute zero of temperature. In classical insulators, such as band insulators, vanishing conductivities lead to diverging resistivities. In other insulators, in particular when a high magnetic field (B) is added, it is possible that while the magneto-resistance diverges, the Hall resistance remains finite, which is known as a Hall insulator. In this letter we demonstrate experimentally the existence of another, more exotic, insulator. This insulator, which terminates the quantum Hall effect series in a two-dimensional electron system, is characterized by a Hall resistance which is approximately quantized in the quantum unit of resistance h/e^2. This insulator is termed a quantized Hall insulator. In addition we show that for the same sample, the insulating state preceding the QHE series, at low-B, is of the HI kind.Comment: 4 page

Phenomenological Understanding of a Transport Regime with Reflection Symmetry in the Quantum Hall System in a Composite Fermion Picture

In this paper, we present a phenomenological picture based on the composite fermion theory, in responding to the recent discovery by Shahar et al. of a new transport regime near the transition from a $\nu=1$ quantum Hall liquid to a Hall insulator(ref[8]). In this picture, the seemingly unexpected reflection symmetry in the longitudinal resistivity $\rho_{xx}$ can be understood clearly as due to the symmetry of the gapful excitations which dominate $\sigma_{xx}$ across the transition, and the abrupt change in $\sigma_{xy}$ at the transition. The parameter $\alpha$ in the linear fit of $\nu_0(T)$ in ref[8] is also given a simple physical meaning and the effective mass can be calculated from $\alpha$, which gives a reasonable value of several electron band mass. When taking into account the result of network model, the almost invariant Hall resistivity $\rho_{xy}$ across the transition is also well-understood.Comment: 4 pages, RevTex, final version to appear in Phys.Rev.

Tail States in a Superconductor with Magnetic Impurities

A field theoretic approach is developed to investigate the profile and spectrum of sub-gap states in a superconductor subject to a weak magnetic impurity potential. Such states are found to be associated with inhomogeneous supersymmetry broken instanton configurations of the action.Comment: 4 pages, 2 eps figure

Superconductors with Magnetic Impurities: Instantons and Sub-gap States

When subject to a weak magnetic impurity potential, the order parameter and quasi-particle energy gap of a bulk singlet superconductor are suppressed. According to the conventional mean-field theory of Abrikosov and Gor'kov, the integrity of the energy gap is maintained up to a critical concentration of magnetic impurities. In this paper, a field theoretic approach is developed to critically analyze the validity of the mean field theory. Using the supersymmetry technique we find a spatially homogeneous saddle-point that reproduces the Abrikosov-Gor'kov theory, and identify instanton contributions to the density of states that render the quasi-particle energy gap soft at any non-zero magnetic impurity concentration. The sub-gap states are associated with supersymmetry broken field configurations of the action. An analysis of fluctuations around these configurations shows how the underlying supersymmetry of the action is restored by zero modes. An estimate of the density of states is given for all dimensionalities. To illustrate the universality of the present scheme we apply the same method to study `gap fluctuations' in a normal quantum dot coupled to a superconducting terminal. Using the same instanton approach, we recover the universal result recently proposed by Vavilov et al. Finally, we emphasize the universality of the present scheme for the description of gap fluctuations in d-dimensional superconducting/normal structures.Comment: 18 pages, 9 eps figure

Sliding motion of a two-dimensional Wigner crystal in a strong magnetic field

We study the sliding state of a two-dimensional Wigner crystal in a strong magnetic field and a random impurity potential. Using a high-velocity perturbation theory, we compute the nonlinear conductivity, various correlation functions, and the interference effects arising in combined AC + DC electric effects, including the Shapiro anomaly and the linear response to an AC field. Disorder is found to induce mainly transverse distortions in the sliding state of the lattice. The Hall resistivity retains its classical value. We find that, within the large velocity perturbation theory, free carriers which affect the longitudinal phonon modes of the Wigner crystal do not change the form of the nonlinear conductivity. We compare the present sliding Wigner crystal in a strong magnetic field to the conventional sliding charge-density wave systems. Our result for the nonlinear conductivity agrees well with the $I-V$ characteristics measured in some experiments at low temperatures or large depinning fields, for the insulating phases near filling factor $\nu$ = 1/5. We summarize the available experimental data, and point out the differences among them.Comment: appeared in RPB vol. 50, 4600 (1994); LaTex file; 3 figures available from [email protected]

Shoot chloride exclusion and salt tolerance in grapevine is associated with differential ion transporter expression in roots

BACKGROUND: Salt tolerance in grapevine is associated with chloride (Cl-) exclusion from shoots; the rate-limiting step being the passage of Cl- between the root symplast and xylem apoplast. Despite an understanding of the physiological mechanism of Cl- exclusion in grapevine, the molecular identity of membrane proteins that control this process have remained elusive. To elucidate candidate genes likely to control Cl- exclusion, we compared the root transcriptomes of three Vitis spp. with contrasting shoot Cl- exclusion capacities using a custom microarray. RESULTS: When challenged with 50 mM Cl-, transcriptional changes of genotypes 140 Ruggeri (shoot Cl- excluding rootstock), K51-40 (shoot Cl- including rootstock) and Cabernet Sauvignon (intermediate shoot Cl- excluder) differed. The magnitude of salt-induced transcriptional changes in roots correlated with the amount of Cl- accumulated in shoots. Abiotic-stress responsive transcripts (e.g. heat shock proteins) were induced in 140 Ruggeri, respiratory transcripts were repressed in Cabernet Sauvignon, and the expression of hypersensitive response and ROS scavenging transcripts was altered in K51-40. Despite these differences, no obvious Cl- transporters were identified. However, under control conditions where differences in shoot Cl- exclusion between rootstocks were still significant, genes encoding putative ion channels SLAH3, ALMT1 and putative kinases SnRK2.6 and CPKs were differentially expressed between rootstocks, as were members of the NRT1 (NAXT1 and NRT1.4), and CLC families. CONCLUSIONS: These results suggest that transcriptional events contributing to the Cl- exclusion mechanism in grapevine are not stress-inducible, but constitutively different between contrasting varieties. We have identified individual genes from large families known to have members with roles in anion transport in other plants, as likely candidates for controlling anion homeostasis and Cl- exclusion in Vitis species. We propose these genes as priority candidates for functional characterisation to determine their role in chloride transport in grapevine and other plants.Sam W Henderson, Ute Baumann, Deidre H Blackmore, Amanda R Walker, Rob R Walker and Matthew Gilliha