Linear and nonlinear transport across carbon nanotube quantum dots

We present a low energy-theory for non-linear transport in finite-size interacting single-wall carbon nanotubes. It is based on a microscopic model for the interacting p_z electrons and successive bosonization. We consider weak coupling to the leads and derive equations of motion for the reduced density matrix. We focus on the case of large-diameter nanotubes where exchange effects can be neglected. In this situation the energy spectrum is highly degenerate. Due to the multiple degeneracy, diagonal as well as off-diagonal (coherences) elements of the density matrix contribute to the nonlinear transport. At low bias, a four-electron periodicity with a characteristic ratio between adjacent peaks is predicted. Our results are in quantitative agreement with recent experiments.     

Luttinger liquid with asymmetric dispersion

We present an extension of the Tomonaga-Luttinger model in which left and right-moving particles have different Fermi velocities. We derive expressions for one-particle Green's functions, momentum-distributions, density of states, charge compressibility and conductivity as functions of both the velocity difference ε and the strength of the interaction β. This allows us to identify a novel restricted region in the parameter space in which the system keeps the main features of a Luttinger liquid but with an unusual behavior of the density of states and the static charge compressibility κ. In particular κ diverges on the boundary of the restricted region, indicating the occurrence of a phase transition. Received 20 May 2002 / Received in final form 23 August 2002 Published online 19 November 2002     

Damping of zero sound in Luttinger liquids

We calculate the damping γ_q of collective density oscillations (zero sound) in a one-dimensional Fermi gas with dimensionless forward scattering interaction F and quadratic energy dispersion k² / 2 m at zero temperature. Using standard many-body perturbation theory, we obtain γ_q from the expansion of the inverse irreducible polarization to first order in the effective screened (RPA) interaction. For wave-vectors | q| /k_F ≪F (where k_F = m v_F is the Fermi wave-vector) we find to leading order γ_q ∝| q |³ /(v_F m²). On the other hand, for F ≪| q| /k_F most of the spectral weight is carried by the particle-hole continuum, which is distributed over a frequency interval of the order of q²/m. We also show that zero sound damping leads to a finite maximum proportional to |k - k_F | ^{-2 + 2 η} of the charge peak in the single-particle spectral function, where η is the anomalous dimension. Our prediction agrees with photoemission data for the blue bronze K_0.3MoO₃. We comment on other recent calculations of γ_q.     

Tails of the dynamical structure factor of 1D spinless fermions beyond the Tomonaga approximation

We consider one-dimensional (1D) interacting spinless fermions with a non-linear spectrum in a clean quantum wire (non-linear bosonization). We compute diagrammatically the 1D dynamical structure factor, S(ω,q), beyond the Tomonaga approximation focusing on it's tails, |ω| ≫vq, i.e. the 2-pair excitation continuum due to forward scattering. Our methodology reveals three classes of diagrams: two “chiral” classes which bring divergent contributions in the limits ω→±vq, i.e. near the single-pair excitation continuum, and a “mixed” class (so-called Aslamasov-Larkin or Altshuler-Shklovskii type diagrams) which is crucial for the f-sum rule to be satisfied. We relate our approach to the T=0 ones present in the literature. We also consider the case and show that the 2-pair excitation continuum dominates the single-pair one in the range: |q|T/k_F ≪ω±vq ≪T (substantial for q ≪k_F). As applications we first derive the small-momentum optical conductivity due to forward scattering: σ∼1/ω for T ≪ω and σ∼T/ω² for T ≫ω. Next, within the 2-pair excitation continuum, we show that the attenuation rate of a coherent mode of dispersion Ω_q crosses over from , e.g. γ_q ∼|q|³ for an acoustic mode, to , independent of Ω_q, as temperature increases. Finally, we show that the 2-pair excitation continuum yields subleading curvature corrections to the electron-electron scattering rate: , where V is the dimensionless strength of the interaction.     

The asymptotic behaviour of the exact and approximative ν = 1/2 Chern-Simons Green's functions

We consider the asymptotic behaviour of the Chern-Simons Green's function of the ν = 1/ system for an infinite area in position-time representation. We calculate explicitly the asymptotic form of the Green's function of the interaction free Chern-Simons system for small times. The calculated Green's function vanishes exponentially with the logarithm of the area. Furthermore, we discuss the form of the divergence for all τ and also for the Coulomb interacting Chern-Simons system. We compare the asymptotics of the exact Chern-Simons Green's function with the asymptotics of the Green's function in the Hartree-Fock as well as the random-phase approximation (RPA). The asymptotics of the Hartree-Fock Green's function correspondence well with the exact Green's function. In the case of the RPA Green's function we do not get the correct asymptotics. At last, we calculate the self consistent Hartree-Fock Green's function. Received 5 July 2001 and Received in final form 30 November 2001     

Determination of the chemical potential and the energy of the ν=1/2 FQHE system for low temperatures

We consider the energy density of a spin polarized ν = 1/2 system for low temperatures. We show that due to the elimination of the magnetic field and the field of the positive background charge in the calculation of the grand canonical potential of Chern-Simons systems through a mean field formalism one gets corrections to the well known equations which determine the chemical potential and the energy from the grand canonical potential. We use these corrected equations to calculate the chemical potential and the energy of the ν = 1/2 system at low temperatures in two different approximations. Received 14 March 2001     

Charge localization in organic conductors (TM)X: The influence of anion ordering

An investigation of the different contributions leading to charge localization in a 1/2 or 1/4 filled band 1D conductor has been conducted through a study of transport properties in the solid solution [(TMTSF)_1-x (TMTTF) _x]₂ReO₄. The existence of an ordering transition of the anions allows to identify two contributions to the electronic potential with wave vector 4k_F. A dominant on-site 4k_F potential besides the bond contribution is revealed when Umklapp scattering is pertinent via the weakening of the localization arising at the (0, 1/2, 1/2) anion ordering which is stabilized under pressure in the compound [(TMTSF) _0.5 (TMTTF)_0.5]₂ReO₄ at variance with the enhancement of localization observed in the homomolecular (TMTTF)₂ReO ₄ material. Received: 13 May 1998 / Revised: 8 July 1998 / Accepted: 9 July 1998     

to -12pt [-12pt]to 16ptRapid Note Wavefunctions for the Luttinger liquid

Standard bosonization techniques lead to phonon-like excitations in a Luttinger liquid (LL), reflecting the absence of Landau quasiparticles in these systems. Yet in addition to the above excitations some LL are known to possess solitonic states carrying fractional quantum numbers (e.g. the spin 1/2 Heisenberg chain). We have reconsidered the zero modes in the low-energy spectrum of the Gaussian boson LL Hamiltonian both for fermionic and bosonic LL: in the spinless case we find that two elementary excitations carrying fractional quantum numbers allow to generate all the charge and current excited states of the LL. We explicitly compute the wavefunctions of these two objects and show that one of them can be identified with the 1D version of the Laughlin quasiparticle introduced in the context of the Fractional Quantum Hall effect. For bosons, the other quasiparticle corresponds to a spinon excitation. The eigenfunctions of Wen's chiral LL Hamiltonian are also derived: they are quite simply the one dimensional restrictions of the 2D bulk Laughlin wavefunctions. Received 26 January 1999 and Received in final form 21 April 1999     

Single hole dynamics in the one-dimensional - model

We present a new finite-temperature quantum Monte Carlo algorithm to compute imaginary-time Green functions for a single hole in the t-J model on non-frustrated lattices. Spectral functions are obtained with the Maximum Entropy method. Simulations of the one-dimensional case show that a simple charge-spin separation Ansatz is able to describe the overall features of the spectral function such as the bandwidth and the compact support of the spectral function, over the whole energy range for values of J / t from 1/3 to 4. This is contrasted with the two-dimensional case. The quasiparticle weight Z_k is computed on lattices up to L =128 sites in one dimension, and scales as . Received 15 February 2000     

Photoconductance of a one-dimensional quantum dot

The ac-transport properties of a one-dimensional quantum dot with non-Fermi liquid correlations are investigated. It is found that the linear photoconductance is drastically influenced by the interaction. While for weak interaction it shows peak-like resonances, in the strong interaction regime it assumes a step-like behavior. In both cases the photo-transport provides precise informations about the quantized plasmon modes in the dot. Temperature and voltage dependences of the sideband peaks are treated in detail. Characteristic Luttinger liquid power laws are found. Received 23 October 2001     

Random-phase approximation for the grand-canonical potential of composite fermions in the half-filled lowest Landau level

We reconsider the theory of the half-filled lowest Landau level using the Chern-Simons formulation and study the grand-canonical potential in the random-phase approximation (RPA). Calculating the unperturbed response functions for current- and charge-density exactly, without any expansion with respect to frequency or wave vector, we find that the integral for the ground-state energy converges rapidly (algebraically) at large wave vectors k, but exhibits a logarithmic divergence at small k. This divergence originates in the k^-2 singularity of the Chern-Simons interaction and it is already present in lowest-order perturbation theory. A similar divergence appears in the chemical potential. Beyond the RPA, we identify diagrams for the grand-canonical potential (ladder-type, maximally crossed, or a combination of both) which diverge with powers of the logarithm. We expand our result for the RPA ground-state energy in the strength of the Coulomb interaction. The linear term is finite and its value compares well with numerical simulations of interacting electrons in the lowest Landau level. Received: 19 February 1998 / Revised: 25 March 1998 / Accepted: 17 April 1998     

The Fermi-sea-like limit of the composite fermion wave function

The experimentally observed filling factors of the fractional quantum Hall effect can be described in terms of the composite fermion wave function of the Jastrow-Slater form [0pt] fully projected into the lowest Landau level. The Slater determinant of the above composite fermion wave function represents the filled Landau levels of composite fermions evaluated at the corresponding reduced magnetic field. For a system of fermions studied in the thermodynamic limit, we prove that in the even-denominator-filled state limit (when the number of filled Landau levels of composite fermions becomes infinite), the above composite fermion wave function exactly transforms into the Rezayi-Read Fermi-sea-like wave function [0pt] constructed by attaching 2m flux quanta to the Slater determinant of two-dimensional free fermions at the density corresponding to that filling. We study the composite fermion wave function and its evolution into the Fermi-sea-like wave function for a range of filling factors very close to the even-denominator-filled state. Received 19 March 1999     

Luttinger liquids with boundaries: Power-laws and energy scales

We present a study of the one-particle spectral properties for a variety of models of Luttinger liquids with open boundaries. We first consider the Tomonaga-Luttinger model using bosonization. For weak interactions the boundary exponent of the power-law suppression of the spectral weight close to the chemical potential is dominated by a term linear in the interaction. This motivates us to study the spectral properties also within the Hartree-Fock approximation. It already gives power-law behavior and qualitative agreement with the exact spectral function. For the lattice model of spinless fermions and the Hubbard model we present numerically exact results obtained using the density-matrix renormalization-group algorithm. We show that many aspects of the behavior of the spectral function close to the boundary can again be understood within the Hartree-Fock approximation. For the repulsive Hubbard model with interaction U the spectral weight is enhanced in a large energy range around the chemical potential. At smaller energies a power-law suppression, as predicted by bosonization, sets in. We present an analytical discussion of the crossover and show that for small U it occurs at energies exponentially (in -1/U) close to the chemical potential, i.e. that bosonization only holds on exponentially small energy scales. We show that such a crossover can also be found in other models. Received 8 February 2000 and Received in final form 25 April 2000     

Charge density waves and bond order waves in a quarter filled extended Hubbard ladder

We investigate the phase diagram of a quarter filled Hubbard ladder with nearest-neighbor Coulomb repulsion using bosonization and renormalization group approach. Focusing on the strong-repulsion regime, we discuss the effect of an interchain exchange interaction J and interchain repulsion V on the possible ground states of the system and charge order configurations. Since the spin excitations always possess a gap, we find competing bond-order wave and charge density wave phases as possible ground states of the ladder model. We discuss the elementary excitations in these various phases and point an analogy between the excitations on some of these phases and those of a Kondo-Heisenberg insulator. We also study the order of the quantum phase transitions between the different ground states of the system. We obtain second order transitions in the Ising or SU(2)₂ universality class or first order transitions. We map the complete phase diagram in the J –V plane by integrating perturbative renormalization-group equations. Finally, we discuss the effect of doping away from half-filling and the effect of an applied magnetic field.     

Spectral broadening due to long-range Coulomb interactions in the molecular metal TTF-TCNQ

We employ density-functional theory to calculate realistic parameters for an extended Hubbard model of the molecular metal TTF-TCNQ. Considering both intra- and intermolecular screening in the crystal, we confirm the importance of the suspected longer-range Coulomb interactions along the molecular stacks, as well as inter-stack coupling. Contrary to past belief, these terms do not lead to the formation of a Wigner lattice, but simply broaden the spectral function.     

Competition of disorder and interchain hopping in a two-chain Hubbard model

We study the interplay of Anderson localization and interaction in a two chain Hubbard ladder allowing for arbitrary ratio of disorder strength to interchain coupling. We obtain three different types of spin gapped localized phases depending on the strength of disorder: a pinned 4k _F Charge Density Wave (CDW) for weak disorder, a pinned 2k _F CDW^π for intermediate disorder and two independently pinned single chain 2k _F CDW for strong disorder. Confinement of electrons can be obtained as a result of strong disorder or strong attraction. We give the full phase diagram as a function of disorder, interaction strength and interchain hopping. We also study the influence of interchain hopping on localization length and show that localization is enhanced by a small interchain hopping but suppressed by a large interchain hopping. Received 6 April 2001     

Density-functional theory of inhomogeneous electron systems in thin quantum wires

Motivated by current interest in strongly correlated quasi-one-dimensional (1D) Luttinger liquids subject to axial confinement, we present a novel density-functional study of few-electron systems confined by power-low external potentials inside a short portion of a thin quantum wire. The theory employs the 1D homogeneous Coulomb liquid as the reference system for a Kohn-Sham treatment and transfers the Luttinger ground-state correlations to the inhomogeneous electron system by means of a suitable local-density approximation (LDA) to the exchange-correlation energy functional. We show that such 1D-adapted LDA is appropriate for fluid-like states at weak coupling, but fails to account for the transition to a “Wigner molecules” regime of electron localization as observed in thin quantum wires at very strong coupling. A detailed analyzes is given for the two-electron problem under axial harmonic confinement.     

Spin susceptibility of interacting electrons in one dimension: Luttinger liquid and lattice effects

The temperature-dependent uniform magnetic susceptibility of interacting electrons in one dimension is calculated using several methods. At low temperature, the renormalization group reveals that the Luttinger liquid spin susceptibility approaches zero temperature with an infinite slope in striking contrast with the Fermi liquid result and with the behavior of the compressibility in the absence of umklapp scattering. This effect comes from the leading marginally irrelevant operator, in analogy with the Heisenberg spin 1/2 antiferromagnetic chain. Comparisons with Monte Carlo simulations at higher temperature reveal that non-logarithmic terms are important in that regime. These contributions are evaluated from an effective interaction that includes the same set of diagrams as those that give the leading logarithmic terms in the renormalization group approach. Comments on the third law of thermodynamics as well as reasons for the failure of approaches that work in higher dimensions are given. Received 2 March 1999     

Non perturbative calculations for three particles in a linear chain within the generalized Hubbard model

A real-space method has been introduced to study the pairing problem within the generalized Hubbard Hamiltonian. This method includes the bond-charge interaction term as an extension of the previously proposed mapping method [1] for the Hubbard model. The generalization of the method is based on mapping the correlated many-body problem onto an equivalent site- and bond-impurity tight-binding one in a higher dimensional space, where the problem can be solved exactly. In a one-dimensional lattice, we analyzed the three particle correlation by calculating the binding energy at the ground state, using different values of the bond-charge, the on-site (U) and the nearest-neighbor (V) interactions. A pairing asymmetry is found between electrons and holes for the generalized hopping amplitude, where the hole pairing is not always easier than the electron case. For some special values of the hopping parameters and for all kinds of interactions in the Hubbard Hamiltonian, an analytical solution is obtained. Received 21 January 2000 and Received in final form 18 July 2000