DC--Transport in Quantum Wires

The influence of electron--electron interaction on two terminal DC conductance of one--dimensional quantum wires is studied. A cancelation between the effect of the electron--electron interaction on the current and on the external electric field is the reason for the universal value, $e^2/2\pi\hbar$ per mode, of the DC conductance of a clean wire. The effect of the renormalization of the electric field on the DC conductance in the presence of an interplay between the electron--electron interaction and backward scattering due to an impurity is considered.Comment: 11 Pages, Revte

Transport theory of carbon nanotube Y junctions

We describe a generalization of Landauer-B\"uttiker theory for networks of interacting metallic carbon nanotubes. We start with symmetric starlike junctions and then extend our approach to asymmetric systems. While the symmetric case is solved in closed form, the asymmetric situation is treated by a mix of perturbative and non-perturbative methods. For N>2 repulsively interacting nanotubes, the only stable fixed point of the symmetric system corresponds to an isolated node. Detailed results for both symmetric and asymmetric systems are shown for N=3, corresponding to carbon nanotube Y junctions.Comment: submitted to New Journal of Physics, Focus Issue on Carbon Nanotubes, 15 pages, 3 figure

Coulomb drag of Luttinger liquids and quantum-Hall edges

We study the transconductance for two coupled one-dimensional wires or edge states described by Luttinger liquid models. The wires are assumed to interact over a finite segment. We find for the interaction parameter $g=1/2$ that the drag rate is finite at zero temperature, which cannot occur in a Fermi-liquid system. The zero temperature drag is, however, cut off at low temperature due to the finite length of the wires. We also consider edge states in the fractional quantum Hall regime, and we suggest that the low temperature enhancement of the drag effect might be seen in the fractional quantum Hall regime.Comment: 5 pages, 2 figures; to appear in Phys. Rev. Let

Renormalization group study of the conductances of interacting quantum wire systems with different geometries

We examine the effect of interactions between the electrons on the conductances of some systems of quantum wires with different geometries. The systems include a wire with a stub in the middle, a wire containing a ring which can enclose a magnetic flux, and a system of four wires which are connected in the middle through a fifth wire. Each of the wires is taken to be a weakly interacting Tomonaga-Luttinger liquid, and scattering matrices are introduced at all the junctions. Using a renormalization group method developed recently for studying the flow of scattering matrices for interacting systems in one dimension, we compute the conductances of these systems as functions of the temperature and the wire lengths. We present results for all three regimes of interest, namely, high, intermediate and low temperature. These correspond respectively to the thermal coherence length being smaller than, comparable to and larger than the smallest wire length in the different systems, i.e., the length of the stub or each arm of the ring or the fifth wire. The renormalization group procedure and the formulae used to compute the conductances are different in the three regimes. We present a phenomenologically motivated formalism for studying the conductances in the intermediate regime where there is only partial coherence. At low temperatures, we study the line shapes of the conductances versus the electron energy near some of the resonances; the widths of the resonances go to zero with decreasing temperature. Our results show that the conductances of various systems of experimental interest depend on the temperature and lengths in a non-trivial way when interactions are taken into account.Comment: Revtex, 17 pages including 15 figure

Transport of a Luttinger liquid in the presence of a time dependent impurity

We show that the macroscopic current and charge can be formulated as a Quantum Mechanical zero mode problem. We find that the current is given by the velocity operator of a particle restricted to move around a circle. As an explicit example we investigate a Luttinger liquid of length $L$ which is perturbed by a time dependent impurity. Using the statistical mechanics of zero modes we computed the non-equilibrium current. In particular we show that in the low temperature limit, $L_T/L>1$, the zero mode method introduced here becomes essential for computing the current

Transport in quantum wires

With a brief introduction to one-dimensional channels and conductance quantisation in mesoscopic systems, we discuss some recent experimental puzzles in these systems, which include reduction of quantised conductances and an interesting {\it odd-even} effect in the presence of an in-plane magnetic field. We then discuss a recent non-homogeneous Luttinger liquid model proposed by us, which addresses and gives an explanation for the reduced conductances and the {\it odd-even} effect. We end with a brief summary and discussion of future projects.Comment: Talk presented at the International Discussion Meeting on Mesoscopic and Disordered systems, December, 2000, 16 pages, 2 figure

A Broadband X-Ray Study of the Supernova Remnant 3C 397

We present an X-ray study of the radio bright supernova remnant (SNR) 3C 397 with ROSAT, ASCA, and RXTE. A central X-ray spot seen with the ROSAT High-Resolution Imager hints at the presence of a pulsar-powered component, and gives this SNR a composite X-ray morphology. Combined ROSAT and ASCA imaging show that the remnant is highly asymmetric, with its hard X-ray emission peaking at the western lobe. The spectrum of 3C 397 is heavily absorbed, and dominated by thermal emission with emission lines evident from Mg, Si, S, Ar and Fe. Single-component models fail to describe the spectrum, and at least two components are required. We use a set of non-equilibrium ionization (NEI) models (Borkowski et al. in preparation). The temperatures from the soft and hard components are 0.2 keV and 1.6 keV respectively. The corresponding ionization time-scales $n_0 t$ ($n_0$ being the pre-shock hydrogen density) are 6 $\times 10^{12}$ cm$^{-3}$ s and 6 $\times$ 10$^{10}$ cm$^{-3}$ s, respectively. The spectrum obtained with the Proportional Counter Array (PCA) of RXTE is contaminated by emission from the Galactic ridge, with only $\sim$ 15% of the count rate originating from 3C 397 in the 5-15 keV range. The PCA spectrum allowed us to confirm the thermal nature of the hard X-ray emission. A third component originating from a pulsar-driven component is possible, but the contamination of the source signal by the Galactic ridge did not allow us to find pulsations from any hidden pulsar. We discuss the X-ray spectrum in the light of two scenarios: a young ejecta-dominated remnant of a core-collapse SN, and a middle-aged SNR expanding in a dense ISM. Spatially resolved spectroscopy (with CHANDRA and XMM) is needed to differentiate between the two scenarios, and address the nature of the mysterious radio-quiet X-ray hot spot.Comment: 21 pages including 8 figures and 5 tables. Accepted for publication in the Astrophysical journa

Charge Density Wave Behaviour of the Integer Quantum Hall Effect Edge States

We analyze the effect that the Coulomb interaction has on the edge excitations of an electron gas confined in a bar of thickness $W$, and in presence of a magnetic field corresponding to filling factor 1 Quantum Hall effect. We find that the long-range interaction between the edges leads the system to a ground state with a quasi-long range order, similar to a Charge Density Wave. The spectral density of states vanishes at zero frequency, and increases with frequency faster than any power law, being the conductance of a infinite long system zero.Comment: 10 pages, latex, 3 figures available by FAX upon request from [email protected]

Applying voltage sources to a Luttinger liquid with arbitrary transmission

The Landauer approach to transport in mesoscopic conductors has been generalized to allow for strong electronic correlations in a single-channel quantum wire. We describe in detail how to account for external voltage sources in adiabatic contact with a quantum wire containing a backscatterer of arbitrary strength. Assuming that the quantum wire is in the Luttinger liquid state, voltage sources lead to radiative boundary conditions applied to the displacement field employed in the bosonization scheme. We present the exact solution of the transport problem for arbitrary backscattering strength at the special Coulomb interaction parameter g=1/2.Comment: 9 pages REVTeX, incl 2 fig