The Fractional Quantum Hall effect in an array of quantum wires

We demonstrate the emergence of the quantum Hall (QH) hierarchy in a 2D model of coupled quantum wires in a perpendicular magnetic field. At commensurate values of the magnetic field, the system can develop instabilities to appropriate inter-wire electron hopping processes that drive the system into a variety of QH states. Some of the QH states are not included in the Haldane-Halperin hierarchy. In addition, we find operators allowed at any field that lead to novel crystals of Laughlin quasiparticles. We demonstrate that any QH state is the groundstate of a Hamiltonian that we explicitly construct.Comment: Revtex, 4 pages, 2 figure

Multiple-quasiparticle agglomerates at \nu=2/5

We investigate the dynamics of quasiparticle agglomerates in edge states of the Jain sequence for \nu=2/5. Comparison of the Fradkin-Lopez model with the Wen one is presented within a field theoretical construction, focusing on similarities and differences. We demonstrate that both models predict the same universal role for the multiple-quasiparticle agglomerates that dominate on single quasiparticles at low energy. This result is induced by the presence of neutral modes with finite velocity and is essential to explain the anomalous behavior of tunneling conductance and noise through a point contact.Comment: 6 pages, in press Physica E as proceedings of FQMT0

Many-body dispersions in interacting ballistic quantum wires

We have measured the collective excitation spectrum of interacting electrons in one-dimension. The experiment consists of controlling the energy and momentum of electrons tunneling between two clean and closely situated, parallel quantum wires in a GaAs/AlGaAs heterostructure while measuring the resulting conductance. We measure excitation spectra that clearly deviate from the non-interacting spectrum, attesting to the importance of Coulomb interactions. Notable is an observed 30% enhancement of the velocity of the main excitation branch relative to non-interacting electrons with the same density. In short wires, finite size effects resulting from broken translational invariance are observed. Spin - charge separation is manifested through moire patterns, reflecting different spin and charge excitation velocities.Comment: 14 pages, 6 eps figures. To be published in NANOWIRE, a special issue of Solid State Communication

Contacts and Edge State Equilibration in the Fractional Quantum Hall Effect

We develop a simple kinetic equation description of edge state dynamics in the fractional quantum Hall effect (FQHE), which allows us to examine in detail equilibration processes between multiple edge modes. As in the integer quantum Hall effect (IQHE), inter-mode equilibration is a prerequisite for quantization of the Hall conductance. Two sources for such equilibration are considered: Edge impurity scattering and equilibration by the electrical contacts. Several specific models for electrical contacts are introduced and analyzed. For FQHE states in which edge channels move in both directions, such as $\nu=2/3$, these models for the electrical contacts {\it do not} equilibrate the edge modes, resulting in a non-quantized Hall conductance, even in a four-terminal measurement. Inclusion of edge-impurity scattering, which {\it directly} transfers charge between channels, is shown to restore the four-terminal quantized conductance. For specific filling factors, notably $\nu =4/5$ and $\nu=4/3$, the equilibration length due to impurity scattering diverges in the zero temperature limit, which should lead to a breakdown of quantization for small samples at low temperatures. Experimental implications are discussed.Comment: 14 pages REVTeX, 6 postscript figures (uuencoded and compressed

The HD 192263 system: planetary orbital period and stellar variability disentangled

As part of the Transit Ephemeris Refinement and Monitoring Survey (TERMS), we present new radial velocities and photometry of the HD 192263 system. Our analysis of the already available Keck-HIRES and CORALIE radial velocity measurements together with the five new Keck measurements we report in this paper results in improved orbital parameters for the system. We derive constraints on the size and phase location of the transit window for HD 192263b, a Jupiter-mass planet with a period of 24.3587 \pm 0.0022 days. We use 10 years of Automated Photoelectric Telescope (APT) photometry to analyze the stellar variability and search for planetary transits. We find continuing evidence of spot activity with periods near 23.4 days. The shape of the corresponding photometric variations changes over time, giving rise to not one but several Fourier peaks near this value. However, none of these frequencies coincides with the planet's orbital period and thus we find no evidence of star-planet interactions in the system. We attribute the ~23-day variability to stellar rotation. There are also indications of spot variations on longer (8 years) timescales. Finally, we use the photometric data to exclude transits for a planet with the predicted radius of 1.09 RJ, and as small as 0.79 RJ.Comment: 9 pages, 6 tables, 6 figures; accepted to Ap

Experiments on the Fermi to Tomonaga-Luttinger liquid transition in quasi-1D systems

We present experimental results on the tunneling into the edge of a two dimensional electron gas (2DEG) obtained with GaAs/AlGaAs cleaved edge overgrown structures. The electronic properties of the edge of these systems can be described by a one-dimensional chiral Tomonaga-Luttinger liquid when the filling factor of the 2DEG is very small. Here we focus on the region where the Tomonaga-Luttinger liquid breaks down to form a standard Fermi liquid close to $\nu=1$ and show that we recover a universal curve, which describes all existing data.Comment: 5 pages, localisation 2002, conference proceeding

Hyperelliptic curves for multi-channel quantum wires and the multi-channel Kondo problem

We study the current in a multi-channel quantum wire and the magnetization in the multi-channel Kondo problem. We show that at zero temperature they can be written simply in terms of contour integrals over a (two-dimensional) hyperelliptic curve. This allows one to easily demonstrate the existence of weak-coupling to strong-coupling dualities. In the Kondo problem, the curve is the same for under- and over-screened cases; the only change is in the contour.Comment: 7 pages, 1 figure, revte

Magnetic Response in Quantized Spin Hall Phase of Correlated Electrons

We investigate the magnetic response in the quantized spin Hall (SH) phase of layered-honeycomb lattice system with intrinsic spin-orbit coupling lambda_SO and on-site Hubbard U. The response is characterized by a parameter g= 4 U a^2 d / 3, where a and d are the lattice constant and interlayer distance, respectively. When g< (sigma_{xy}^{s2} mu)^{-1}, where sigma_{xy}^{s} is the quantized spin Hall conductivity and mu is the magnetic permeability, the magnetic field inside the sample oscillates spatially. The oscillation vanishes in the non-interacting limit U -> 0. When g > (sigma_{xy}^{s2} mu)^{-1}, the system shows perfect diamagnetism, i.e., the Meissner effect occurs. We find that superlattice structure with large lattice constant is favorable to see these phenomena. We also point out that, as a result of Zeeman coupling, the topologically-protected helical edge states shows weak diamagnetism which is independent of the parameter g.Comment: 7 pages, the final version will be published in J. Phys. Soc. Jp