Quantized Thermal Transport in the Fractional Quantum Hall Effect

We analyze thermal transport in the fractional quantum Hall effect (FQHE), employing a Luttinger liquid model of edge states. Impurity mediated inter-channel scattering events are incorporated in a hydrodynamic description of heat and charge transport. The thermal Hall conductance, $K_H$, is shown to provide a new and universal characterization of the FQHE state, and reveals non-trivial information about the edge structure. The Lorenz ratio between thermal and electrical Hall conductances {\it violates} the free-electron Wiedemann-Franz law, and for some fractional states is predicted to be {\it negative}. We argue that thermal transport may provide a unique way to detect the presence of the elusive upstream propagating modes, predicted for fractions such as $\nu=2/3$ and $\nu=3/5$.Comment: 6 pages REVTeX, 2 postscript figures (uuencoded and compressed

Randomness at the Edge: Theory of Quantum Hall transport at filling ν=2/3\nu=2/3

Current Luttinger liquid edge state theories for filling $\nu=2/3$ predict a non-universal Hall conductance, in disagreement with experiment. Upon inclusion of random edge tunnelling we find a phase transition into a new disordered-dominated edge phase. An exact solution of the random model in this phase gives a quantized Hall conductance of 2/3 and a neutral mode propagating upstream. The presence of the neutral mode changes the predicted temperature dependence for tunnelling through a point contact from $T^{2/\nu -2}$ to $T^2$.Comment: 12 pages 1 postscript figure appended, REVTEX 3.

Edge Dynamics in Quantum Hall Bilayers II: Exact Results with Disorder and Parallel Fields

We study edge dynamics in the presence of interlayer tunneling, parallel magnetic field, and various types of disorder for two infinite sequences of quantum Hall states in symmetric bilayers. These sequences begin with the 110 and 331 Halperin states and include their fractional descendants at lower filling factors; the former is easily realized experimentally while the latter is a candidate for the experimentally observed quantum Hall state at a total filling factor of 1/2 in bilayers. We discuss the experimentally interesting observables that involve just one chiral edge of the sample and the correlation functions needed for computing them. We present several methods for obtaining exact results in the presence of interactions and disorder which rely on the chiral character of the system. Of particular interest are our results on the 331 state which suggest that a time-resolved measurement at the edge can be used to discriminate between the 331 and Pfaffian scenarios for the observed quantum Hall state at filling factor 1/2 in realistic double-layer systems.Comment: revtex+epsf; two-up postscript at http://www.sns.ias.edu/~leonid/ntwoup.p

Impurity scattering and transport of fractional Quantum Hall edge state

We study the effects of impurity scattering on the low energy edge state dynamic s for a broad class of quantum Hall fluids at filling factor $\nu =n/(np+1)$, for integer $n$ and even integer $p$. When $p$ is positive all $n$ of the edge modes are expected to move in the same direction, whereas for negative $p$ one mode moves in a direction opposite to the other $n-1$ modes. Using a chiral-Luttinger model to describe the edge channels, we show that for an ideal edge when $p$ is negative, a non-quantized and non-universal Hall conductance is predicted. The non-quantized conductance is associated with an absence of equilibration between the $n$ edge channels. To explain the robust experimental Hall quantization, it is thus necessary to incorporate impurity scattering into the model, to allow for edge equilibration. A perturbative analysis reveals that edge impurity scattering is relevant and will modify the low energy edge dynamics. We describe a non-perturbative solution for the random $n-$channel edge, which reveals the existence of a new disorder-dominated phase, characterized by a stable zero temperature renormalization group fixed point. The phase consists of a single propagating charge mode, which gives a quantized Hall conductance, and $n-1$ neutral modes. The neutral modes all propagate at the same speed, and manifest an exact SU(n) symmetry. At finite temperatures the SU(n) symmetry is broken and the neutral modes decay with a finite rate which varies as $T^2$ at low temperatures. Various experimental predictions and implications which follow from the exact solution are described in detail, focusing on tunneling experiments through point contacts.Comment: 19 pages (two column), 5 post script figures appended, 3.0 REVTE

Single Spin Measurement using Single Electron Transistors to Probe Two Electron Systems

We present a method for measuring single spins embedded in a solid by probing two electron systems with a single electron transistor (SET). Restrictions imposed by the Pauli Principle on allowed two electron states mean that the spin state of such systems has a profound impact on the orbital states (positions) of the electrons, a parameter which SET's are extremely well suited to measure. We focus on a particular system capable of being fabricated with current technology: a Te double donor in Si adjacent to a Si/SiO2 interface and lying directly beneath the SET island electrode, and we outline a measurement strategy capable of resolving single electron and nuclear spins in this system. We discuss the limitations of the measurement imposed by spin scattering arising from fluctuations emanating from the SET and from lattice phonons. We conclude that measurement of single spins, a necessary requirement for several proposed quantum computer architectures, is feasible in Si using this strategy.Comment: 22 Pages, 8 Figures; revised version contains updated references and small textual changes. Submitted to Phys. Rev.

An NMR-based nanostructure switch for quantum logic

We propose a nanostructure switch based on nuclear magnetic resonance (NMR) which offers reliable quantum gate operation, an essential ingredient for building a quantum computer. The nuclear resonance is controlled by the magic number transitions of a few-electron quantum dot in an external magnetic field.Comment: 4 pages, 2 separate PostScript figures. Minor changes included. One reference adde

Voltage-tunable singlet-triplet transition in lateral quantum dots

Results of calculations and high source-drain transport measurements are presented which demonstrate voltage-tunable entanglement of electron pairs in lateral quantum dots. At a fixed magnetic field, the application of a judiciously-chosen gate voltage alters the ground-state of an electron pair from an entagled spin singlet to a spin triplet.Comment: 8.2 double-column pages, 10 eps figure

Vacuum structure of Toroidal Carbon Nanotubes

Low energy excitations in carbon nanotubes can be described by an effective field theory of two components spinor. It is pointed out that the chiral anomaly in 1+1 dimensions should be observed in a metallic toroidal carbon nanotube on a planar geometry with varying magnetic field. We propose an experimental setup for studying this quantum effect. We also analyze the vacuum structure of the metallic toroidal carbon nanotube including the Coulomb interactions and discuss some effects of external charges on the vacuum.Comment: 10 pages, 11 figure

Double quantum dot turnstile as an electron spin entangler

We study the conditions for a double quantum dot system to work as a reliable electron spin entangler, and the efficiency of a beam splitter as a detector for the resulting entangled electron pairs. In particular, we focus on the relative strengths of the tunneling matrix elements, the applied bias and gate voltage, the necessity of time-dependent input/output barriers, and the consequence of considering wavepacket states for the electrons as they leave the double dot to enter the beam splitter. We show that a double quantum dot turnstile is, in principle, an efficient electron spin entangler or entanglement filter because of the exchange coupling between the dots and the tunable input/output potential barriers, provided certain conditions are satisfied in the experimental set-up.Comment: published version; minor error correcte

RHESSI Results -- Time For a Rethink?

Hard X-rays and gamma-rays are the most direct signatures of energetic electrons and ions in the sun's atmosphere which is optically thin at these energies and their radiation involves no coherent processes. Being collisional they are complementary to gyro-radiation in probing atmospheric density as opposed to magnetic field and the electrons are primarily 10--100 keV in energy, complementing the (>100 keV) electrons likely responsible for microwave bursts. The pioneering results of the Ramaty High Energy Solar Spectroscopic Imager (RHESSI) are raising the first new major questions concerning solar energetic particles in many years. Some highlights of these results are discussed -- primarily around RHESSI topics on which the authors have had direct research involvement -- particularly when they are raising the need for re-thinking of entrenched ideas. Results and issues are broadly divided into discoveries in the spatial, temporal and spectral domains, with the main emphasis on flare hard X-rays/fast electrons but touching also on gamma-rays/ions, non-flare emissions, and the relationship to radio bursts.Comment: Proceedings CESRA Workshop 2004: "The High Energy Solar Corona: Waves, Eruptions, Particles", Lecture Notes in Physics, 2006 (accepted