Mesoscopic effects in tunneling between parallel quantum wires

We consider a phase-coherent system of two parallel quantum wires that are coupled via a tunneling barrier of finite length. The usual perturbative treatment of tunneling fails in this case, even in the diffusive limit, once the length L of the coupling region exceeds a characteristic length scale L_t set by tunneling. Exact solution of the scattering problem posed by the extended tunneling barrier allows us to compute tunneling conductances as a function of applied voltage and magnetic field. We take into account charging effects in the quantum wires due to applied voltages and find that these are important for 1D-to-1D tunneling transport.Comment: 8 pages, 7 figures, improved Figs., added Refs. and appendix, to appear in Phys. Rev.

Charge Screening Effect in Metallic Carbon Nanotubes

Charge screening effect in metallic carbon nanotubes is investigated in a model including the one-dimensional long-range Coulomb interaction. It is pointed out that an external charge which is being fixed spatially is screened by internal electrons so that the resulting object becomes electrically neutral. We found that the screening length is given by about the diameter of a nanotube.Comment: 11 pages, 6 figure

Hopping Conduction in Disordered Carbon Nanotubes

We report electrical transport measurements on individual disordered carbon nanotubes, grown catalytically in a nanoporous anodic aluminum oxide template. In both as-grown and annealed types of nanotubes, the low-field conductance shows as exp[-(T_{0}/T)^{1/2}] dependence on temperature T, suggesting that hopping conduction is the dominant transport mechanism, albeit with different disorder-related coefficients T_{0}. The field dependence of low-temperature conductance behaves an exp[-(xi_{0}/xi)^{1/2}] with high electric field xi at sufficiently low T. Finally, both annealed and unannealed nanotubes exhibit weak positive magnetoresistance at low T = 1.7 K. Comparison with theory indicates that our data are best explained by Coulomb-gap variable range hopping conduction and permits the extraction of disorder-dependent localization length and dielectric constant.Comment: 10 pages, 5 figure

Superconductor coupled to two Luttinger liquids as an entangler for electron spins

We consider an s-wave superconductor (SC) which is tunnel-coupled to two spatially separated Luttinger liquid (LL) leads. We demonstrate that such a setup acts as an entangler, i.e. it creates spin-singlets of two electrons which are spatially separated, thereby providing a source of electronic Einstein-Podolsky-Rosen pairs. We show that in the presence of a bias voltage, which is smaller than the energy gap in the SC, a stationary current of spin-entangled electrons can flow from the SC to the LL leads due to Andreev tunneling events. We discuss two competing transport channels for Cooper pairs to tunnel from the SC into the LL leads. On the one hand, the coherent tunneling of two electrons into the same LL lead is shown to be suppressed by strong LL correlations compared to single-electron tunneling into a LL. On the other hand, the tunneling of two spin-entangled electrons into different leads is suppressed by the initial spatial separation of the two electrons coming from the same Cooper pair. We show that the latter suppression depends crucially on the effective dimensionality of the SC. We identify a regime of experimental interest in which the separation of two spin-entangled electrons is favored. We determine the decay of the singlet state of two electrons injected into different leads caused by the LL correlations. Although the electron is not a proper quasiparticle of the LL, the spin information can still be transported via the spin density fluctuations produced by the injected spin-entangled electrons.Comment: 15 pages, 2 figure

Low-temperature nonequilibrium transport in a Luttinger liquid

The temperature-dependent nonlinear conductance for transport of a Luttinger liquid through a barrier is calculated in the nonperturbative regime for $g=1/2-\epsilon$, where $g$ is the dimensionless interaction constant. To describe the low-energy behavior, we perform a leading-log summation of all diagrams contributing to the conductance which is valid for $|\epsilon| << 1$. With increasing external voltage, the asymptotic low-temperature behavior displays a turnover from the $T^{2/g-2}$ to a universal $T^2$ law.Comment: 13 pages RevTeX 3.0, accepted by Physical Review

Dagger Categories of Tame Relations

Within the context of an involutive monoidal category the notion of a comparison relation is identified. Instances are equality on sets, inequality on posets, orthogonality on orthomodular lattices, non-empty intersection on powersets, and inner product on vector or Hilbert spaces. Associated with a collection of such (symmetric) comparison relations a dagger category is defined with "tame" relations as morphisms. Examples include familiar categories in the foundations of quantum mechanics, such as sets with partial injections, or with locally bifinite relations, or with formal distributions between them, or Hilbert spaces with bounded (continuous) linear maps. Of one particular example of such a dagger category of tame relations, involving sets and bifinite multirelations between them, the categorical structure is investigated in some detail. It turns out to involve symmetric monoidal dagger structure, with biproducts, and dagger kernels. This category may form an appropriate universe for discrete quantum computations, just like Hilbert spaces form a universe for continuous computation

Small Fermi surface in the one-dimensional Kondo lattice model

We study the one-dimensional Kondo lattice model through the density matrix renormalization group (DMRG). Our results for the spin correlation function indicate the presence of a small Fermi surface in large portions of the phase diagram, in contrast to some previous studies that used the same technique. We argue that the discrepancy is due to the open boundary conditions, which introduce strong charge perturbations that strongly affect the spin Friedel oscillations.Comment: 5 pages, 7 figure

Dynamical electron transport through a nanoelectromechanical wire in a magnetic field

We investigate dynamical transport properties of interacting electrons moving in a vibrating nanoelectromechanical wire in a magnetic field. We have built an exactly solvable model in which electric current and mechanical oscillation are treated fully quantum mechanically on an equal footing. Quantum mechanically fluctuating Aharonov-Bohm phases obtained by the electrons cause nontrivial contribution to mechanical vibration and electrical conduction of the wire. We demonstrate our theory by calculating the admittance of the wire which are influenced by the multiple interplay between the mechanical and the electrical energy scales, magnetic field strength, and the electron-electron interaction

Functional Integral Bosonization for Impurity in Luttinger Liquid

We use a functional integral formalism developed earlier for the pure Luttinger liquid (LL) to find an exact representation for the electron Green function of the LL in the presence of a single backscattering impurity. This allows us to reproduce results (well known from the bosonization techniques) for the suppression of the electron local density of states (LDoS) at the position of the impurity and for the Friedel oscillations at finite temperature. In addition, we have extracted from the exact representation an analytic dependence of LDoS on the distance from the impurity and shown how it crosses over to that for the pure LL.Comment: 7 pages, 1 LaTeX produced figur

Spin- and charge-density oscillations in spin chains and quantum wires

We analyze the spin- and charge-density oscillations near impurities in spin chains and quantum wires. These so-called Friedel oscillations give detailed information about the impurity and also about the interactions in the system. The temperature dependence of these oscillations explicitly shows the renormalization of backscattering and conductivity, which we analyze for a number of different impurity models. We are also able to analyze screening effects in one dimension. The relation to the Kondo effect and experimental consequences are discussed.Comment: Final published version. 15 pages in revtex format including 22 epsf-embedded figures. The latest version in PDF format is available from http://fy.chalmers.se/~eggert/papers/density-osc.pd