Transport in Double-Crossed Luttinger Liquids

We study transport through two Luttinger liquids (one-dimensional electrons interacting through a Coulomb repulsion in a metal) coupled together at {\it two} points. External voltage biases are incorporated through boundary conditions. We include density-density couplings as well as single-particle hops at the contacts. For weak repulsive interactions, transport through the wires remains undisturbed by the inter-wire couplings, which renormalise to zero. For strong repulsive interactions, the inter-wire couplings become strong. For symmetric barriers and no external voltage bias, a single gate voltage is sufficient to tune for resonance transmission in both wires. However, for asymmetric couplings or for finite external biases, the system is insulating.Comment: Latex file, 11 pages, one eps figur

Tunneling exponents in realistic quantum wires using the mean field approximation

It is demonstrated that the charge Tomonaga-Luttinger parameter $K_\rho$ of quantum wires can be estimated accurately using the Hartree-Fock approximation if carried out self consistently. The dependence of $K_\rho$ on the carrier density distinguishes different regimes of importance of correlations

Oscillator Strength of Metallic Carbon Nanotubes

Based on the tight binding method with hopping integral between the nearest-neighbor atoms, an oscillator strength \int_0^{\infty} \d \omega {\rm Re} \sigma (\omega) is discussed for armchair and metallic zigzag carbon nanotubes. The formulae of the oscillator strength are derived for both types of nanotubes and are compared with the result obtained by a linear chain model. In addition, the doping dependence is investigated in the absence of Coulomb interaction. It is shown that the oscillator strength of each carbon nanotube shows qualitatively the same doping dependence, but the fine structure is different due to it's own peculiar band structure. Some relations independent of the radius of the tube are derived, and a useful formula for determining the amount of doping is proposed.Comment: 4 pages, 4 figures, submitted to J. Phys. Soc. Jpn. at June 30, 200

Field emission from Luttinger liquids and single-wall carbon nanotubes

We develop a theory for the field emission effect in Luttinger liquids and single-wall carbon nanotubes at the level of the energy resolved current distribution. We generalise Fowler-Nordheim relations. Just below the Fermi edge, we find a power-law vanishing current distribution with the density of states exponent. The current distribution above the Fermi edge owes its existence to a peculiar interplay of interactions and correlated tunnelling. It displays a non-trivial power-law divergence just above the Fermi energy.Comment: 4 pages, 2 figures (eps files

Interaction Constants and Dynamic Conductance of a Gated Wire

We show that the interaction constant governing the long-range electron-electron interaction in a quantum wire coupled to two reservoirs and capacitively coupled to a gate can be determined by a low frequency measurement. We present a self-consistent, charge and current conserving theory of the full conductance matrix. The collective excitation spectrum consists of plasma modes with a relaxation rate which increases with the interaction strength and is inversely proportional to the length of the wire. The interaction parameter is determined by the first two coefficients of the out-of-phase component of the dynamic conductance measured at the gate.Comment: 4 pages, LaTeX, 2 figure

Spin and Charge Luttinger-Liquid Parameters of the One-Dimensional Electron Gas

Low-energy properties of the homogeneous electron gas in one dimension are completely described by the group velocities of its charge (plasmon) and spin collective excitations. Because of the long range of the electron-electron interaction, the plasmon velocity is dominated by an electrostatic contribution and can be estimated accurately. In this Letter we report on Quantum Monte Carlo simulations which demonstrate that the spin velocity is substantially decreased by interactions in semiconductor quantum wire realizations of the one-dimensional electron liquid.Comment: 13 pages, figures include

Multi-particle effects in non-equilibrium electron tunnelling and field emission

We investigate energy resolved electric current from various correlated host materials under out-of-equilibrium conditions. We find that, due to a combined effect of electron-electron interactions, non-equilibrium and multi-particle tunnelling, the energy resolved current is finite even above the Fermi edge of the host material. In most cases, the current density possesses a singularity at the Fermi level revealing novel manifestations of correlation effects in electron tunnelling. By means of the Keldysh non-equilibrium technique, the current density is calculated for one-dimensional interacting electron systems and for two-dimensional systems, both in the pure limit and in the presence of disorder. We then specialise to the field emission and provide a comprehensive theoretical study of this effect in carbon nanotubes.Comment: 22 pages, 8 figures (eps files

Crossover from Fermi liquid to Wigner molecule behavior in quantum dots

The crossover from weak to strong correlations in parabolic quantum dots at zero magnetic field is studied by numerically exact path-integral Monte Carlo simulations for up to eight electrons. By the use of a multilevel blocking algorithm, the simulations are carried out free of the fermion sign problem. We obtain a universal crossover only governed by the density parameter $r_s$. For $r_s>r_c$, the data are consistent with a Wigner molecule description, while for $r_s<r_c$, Fermi liquid behavior is recovered. The crossover value $r_c \approx 4$ is surprisingly small.Comment: 4 pages RevTeX, 3 figures, corrected Tabl

Ground-state energy and spin in disordered quantum dots

We investigate the ground-state energy and spin of disordered quantum dots using spin-density-functional theory. Fluctuations of addition energies (Coulomb-blockade peak spacings) do not scale with average addition energy but remain proportional to level spacing. With increasing interaction strength, the even-odd alternation of addition energies disappears, and the probability of non-minimal spin increases, but never exceeds 50%. Within a two-orbital model, we show that the off-diagonal Coulomb matrix elements help stabilize a ground state of minimal spin.Comment: 10 pages, 2 figure

Quantum-dot lithium in zero magnetic field: Electronic properties, thermodynamics, and a liquid-solid transition in the ground state

Energy spectra, electron densities, pair correlation functions and heat capacity of a quantum-dot lithium in zero external magnetic field (a system of three interacting two-dimensional electrons in a parabolic confinement potential) are studied using the exact diagonalization approach. A particular attention is given to a Fermi-liquid -- Wigner-solid transition in the ground state of the dot, induced by the intra-dot Coulomb interaction.Comment: 12 pages, incl. 16 figure