Nonequilibrium electron spectroscopy of Luttinger liquids

Understanding the effects of nonequilibrium on strongly interacting quantum systems is a challenging problem in condensed matter physics. In dimensions greater than one, interacting electrons can often be understood within Fermi-liquid theory where low-energy excitations are weakly interacting quasiparticles. On the contrary, electrons in one dimension are known to form a strongly-correlated phase of matter called a Luttinger liquid (LL), whose low-energy excitations are collective density waves, or plasmons, of the electron gas. Here we show that spectroscopy of locally injected high-energy electrons can be used to probe energy relaxation in the presence of such strong correlations. For detection energies near the injection energy, the electron distribution is described by a power law whose exponent depends in a continuous way on the Luttinger parameter, and energy relaxation can be attributed to plasmon emission. For a chiral LL as realized at the edge of a fractional quantum Hall state, the distribution function grows linearly with the distance to the injection energy, independent of filling fraction.Comment: 4+ pages, 3 figure

Bulk-edge coupling in the non-abelian ν=5/2\nu=5/2 quantum Hall interferometer

Recent schemes for experimentally probing non-abelian statistics in the quantum Hall effect are based on geometries where current-carrying quasiparticles flow along edges that encircle bulk quasiparticles, which are localized. Here we consider one such scheme, the Fabry-Perot interferometer, and analyze how its interference patterns are affected by a coupling that allows tunneling of neutral Majorana fermions between the bulk and edge. While at weak coupling this tunneling degrades the interference signal, we find that at strong coupling, the bulk quasiparticle becomes essentially absorbed by the edge and the intereference signal is fully restored.Comment: 5 pages, 1 figur

Interference, Coulomb blockade, and the identification of non-abelian quantum Hall states

We examine the relation between different electronic transport phenomena in a Fabry-Perot interferometer in the fractional quantum Hall regime. In particular, we study the way these phenomena reflect the statistics of quantum Hall quasi-particles. For two series of states we examine, one abelian and one non-abelian, we show that the information that may be obtained from measurements of the lowest order interference pattern in an open Fabry-Perot interferometer is identical to the one that may be obtained from the temperature dependence of Coulomb blockade peaks in a closed interferometer. We argue that despite the similarity between the experimental signatures of the two series of states, interference and Coulomb blockade measurements are likely to be able to distinguish between abelian and non-abelian states, due to the sensitivity of the abelian states to local perturbations, to which the non-abelian states are insensitive.Comment: 10 pages. Published versio

Partition Functions of Non-Abelian Quantum Hall States

Partition functions of edge excitations are obtained for non-Abelian Hall states in the second Landau level, such as the anti-Read-Rezayi state, the Bonderson-Slingerland hierarchy and the Wen non-Abelian fluid, as well as for the non-Abelian spin-singlet state. The derivation is straightforward and unique starting from the non-Abelian conformal field theory data and solving the modular invariance conditions. The partition functions provide a complete account of the excitation spectrum and are used to describe experiments of Coulomb blockade and thermopower.Comment: 42 pages, 3 figures; published version; minor corrections to sect. 4.

Scanning Gate Spectroscopy of transport across a Quantum Hall Nano-Island

We explore transport across an ultra-small Quantum Hall Island (QHI) formed by closed quan- tum Hall edge states and connected to propagating edge channels through tunnel barriers. Scanning gate microscopy and scanning gate spectroscopy are used to first localize and then study a single QHI near a quantum point contact. The presence of Coulomb diamonds in the spectroscopy con- firms that Coulomb blockade governs transport across the QHI. Varying the microscope tip bias as well as current bias across the device, we uncover the QHI discrete energy spectrum arising from electronic confinement and we extract estimates of the gradient of the confining potential and of the edge state velocity.Comment: 13 pages, 3 figure

Nonlinear ac conductivity of one-dimensional Mott insulators

We discuss a semiclassical calculation of low energy charge transport in one-dimensional (1d) insulators with a focus on Mott insulators, whose charge degrees of freedom are gapped due to the combination of short range interactions and a periodic lattice potential. Combining RG and instanton methods, we calculate the nonlinear ac conductivity and interpret the result in terms of multi-photon absorption. We compare the result of the semiclassical calculation for interacting systems to a perturbative, fully quantum mechanical calculation of multi-photon absorption in a 1d band insulator and find good agreement when the number of simultaneously absorbed photons is large.Comment: Dedicated to Thomas Nattermann on the occasion of his 60th birthday. To appear in JSTAT. 5 pages, 2 figure