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

Composite fermions in periodic and random antidot lattices

The longitudinal and Hall magnetoresistance of random and periodic arrays of artificial scatterers, imposed on a high-mobility two-dimensional electron gas, were investigated in the vicinity of Landau level filling factor ν=1/2. In periodic arrays, commensurability effects between the period of the antidot array and the cyclotron radius of composite fermions are observed. In addition, the Hall resistance shows a deviation from the anticipated linear dependence, reminiscent of quenching around zero magnetic field. Both effects are absent for random antidot lattices. The relative amplitude of the geometric resonances for opposite signs of the effective magnetic field and its dependence on illumination illustrate enhanced soft wall effects for composite fermions

Classification of Higher Dimensional Spacetimes

We algebraically classify some higher dimensional spacetimes, including a number of vacuum solutions of the Einstein field equations which can represent higher dimensional black holes. We discuss some consequences of this work.Comment: 16 pages, 1 Tabl

Inference of the genetic network regulating lateral root initiation in Arabidopsis thaliana

Regulation of gene expression is crucial for organism growth, and it is one of the challenges in Systems Biology to reconstruct the underlying regulatory biological networks from transcriptomic data. The formation of lateral roots in Arabidopsis thaliana is stimulated by a cascade of regulators of which only the interactions of its initial elements have been identified. Using simulated gene expression data with known network topology, we compare the performance of inference algorithms, based on different approaches, for which ready-to-use software is available. We show that their performance improves with the network size and the inclusion of mutants. We then analyse two sets of genes, whose activity is likely to be relevant to lateral root initiation in Arabidopsis, by integrating sequence analysis with the intersection of the results of the best performing methods on time series and mutants to infer their regulatory network. The methods applied capture known interactions between genes that are candidate regulators at early stages of development. The network inferred from genes significantly expressed during lateral root formation exhibits distinct scale-free, small world and hierarchical properties and the nodes with a high out-degree may warrant further investigation

How branching can change the conductance of ballistic semiconductor devices

We demonstrate that branching of the electron flow in semiconductor nanostructures can strongly affect macroscopic transport quantities and can significantly change their dependence on external parameters compared to the ideal ballistic case even when the system size is much smaller than the mean free path. In a corner-shaped ballistic device based on a GaAs/AlGaAs two-dimensional electron gas we observe a splitting of the commensurability peaks in the magnetoresistance curve. We show that a model which includes a random disorder potential of the two-dimensional electron gas can account for the random splitting of the peaks that result from the collimation of the electron beam. The shape of the splitting depends on the particular realization of the disorder potential. At the same time magnetic focusing peaks are largely unaffected by the disorder potential.Comment: accepted for publication in Phys. Rev.

Twist Symmetry and Classical Solutions in Open String Field Theory

We construct classical solutions of open string field theory which are not invariant under ordinary twist operation. From detailed analysis of the moduli space of the solutions, it turns out that our solutions become nontrivial at boundaries of the moduli space. The cohomology of the modified BRST operator and the CSFT potential evaluated by the level truncation method strongly support the fact that our nontrivial solutions correspond to the closed string vacuum. We show that the nontrivial solutions are equivalent to the twist even solution which was found by Takahashi and Tanimoto, and twist invariance of open string field theory remains after the shift of the classical backgrounds.Comment: 19 pages, 2 figures; v2: errors fixe

Even-denominator fractional quantum Hall physics in ZnO

The fractional quantum Hall (FQH) effect emerges in high-quality two-dimensional electron systems exposed to a magnetic field when the Landau-level filling factor, ν_e, takes on a rational value. Although the overwhelming majority of FQH states have odd-denominator fillings, the physical properties of the rare and fragile even-denominator states are most tantalizing in view of their potential relevance for topological quantum computation. For decades, GaAs has been the preferred host for studying these even-denominator states, where they occur at ν_e = 5/2 and 7/2. Here we report an anomalous series of quantized even-denominator FQH states outside the realm of III–V semiconductors in the MgZnO/ZnO 2DES electron at ν_e = 3/2 and 7/2, with precursor features at 9/2; all while the 5/2 state is absent. The effect in this material occurs concomitantly with tunability of the orbital character of electrons at the chemical potential, thereby realizing a new experimental means for investigating these exotic ground states

The Kerr-Newman-Godel Black Hole

By applying a set of Hassan-Sen transformations and string dualities to the Kerr-Godel solution of minimal D=5 supergravity we derive a four parameter family of five dimensional solutions in type II string theory. They describe rotating, charged black holes in a rotating background. For zero background rotation, the solution is D=5 Kerr-Newman; for zero charge it is Kerr-Godel. In a particular extremal limit the solution describes an asymptotically Godel BMPV black hole.Comment: 12 pages, LaTeX, no figures; v2: one reference added, very minor changes; to appear in CQ

Domain Formation in v=2/3 Fractional Quantum Hall Systems

We study the domain formation in the v=2/3 fractional quantum Hall systems basing on the density matrix renormalization group (DMRG) analysis. The ground-state energy and the pair correlation functions are calculated for various spin polarizations. The results confirm the domain formation in partially spin polarized states, but the presence of the domain wall increases the energy of partially spin polarized states and the ground state is either spin unpolarized state or fully spin polarized state depending on the Zeeman energy. We expect coupling with external degrees of freedom such as nuclear spins is important to reduce the energy of partially spin polarized state.Comment: 7 pages, submitted to J. Phys. Soc. Jp