Showing papers on "Luttinger parameter published in 2009"

Measurements on quantum capacitance of individual single walled carbon nanotubes

Abstract: We report measurements of the quantum capacitance of individual semiconducting and small band gap single walled carbon nanotubes (SWNTs). The observed quantum capacitance, 82 aF/μm for a semiconducting SWNT with chiral index (16,8) and 10.3 aF/μm for a small band gap SWNT upon Fermi level lying at the first subband are remarkably smaller than those originating from the density of states. We attribute the discrepancy to a strong electron correlation in SWNTs and derive the Luttinger parameter g of 0.25–0.3 for the (16,8) SWNT and of 0.32 for a small band gap SWNT.

Attractively bound pairs of atoms in the Bose-Hubbard model and antiferromagnetism

Abstract: We consider a periodic lattice loaded with pairs of bosonic atoms tightly bound to each other via strong attractive on-site interaction that exceeds the intersite tunneling rate. An ensemble of such lattice dimers is accurately described by an effective Hamiltonian of hard-core bosons with strong nearest-neighbor repulsion, which is equivalent to the $XXZ$ model with Ising-like anisotropy. We calculate the ground-state phase diagram for a one-dimensional system, which exhibits incompressible phases, corresponding to an empty and a fully filled lattice (ferromagnetic phases) and a half-filled alternating density crystal (antiferromagnetic phase), separated from each other by compressible phases. In a finite lattice the compressible phases show characteristic oscillatory modulations on top of the antiferromagnetic density profile and in density-density correlations. We derive a kink model that provides simple quantitative explanation of these features. To describe the long-range correlations of the system, we employ the Luttinger-liquid theory with the relevant Luttinger parameter $K$ obtained exactly using the Bethe-ansatz solution. We calculate the density-density as well as first-order correlations and find excellent agreement with numerical results obtained with density-matrix renormalization-group methods.

Complete series for the off-diagonal correlations of a one-dimensional interacting Bose gas

Abstract: We develop a generalized harmonic-fluid approach, based on a regularization of the effective low-energy Luttinger-liquid Hamiltonian, for a one-dimensional Bose gas with repulsive contact interactions. The method enables us to compute the complete series corresponding to the large-distance, off-diagonal behavior of the one-body density matrix for any value of the Luttinger parameter K. We compare our results with the exact ones known in the Tonks-Girardeau limit of infinitely large interactions (corresponding to K=1) and, different from the usual harmonic-fluid approach, we recover the full structure of the series. The structure is conserved for arbitrary values of the interaction strength, with power laws fixed by the universal parameter K and a sequence of subleading corrections.

A Scaling Approach for Interacting Quantum Wires -a Possible Explanation for the 0.7 Anomalous Conductance

Abstract: We consider a weakly interacting finite wire with short and long range interactions. The long range interactions enhance the $4k_{F}$ scattering and renormalize the wire to a strongly interacting limit. For large screening lengths, the renormalized charge stiffness Luttinger parameter $K_{eff.}$ decreases to $K_{eff.}< {1/2}$, giving rise to a Wigner crystal at T=0 with an anomalous conductance at finite temperatures. For short screening lengths, the renormalized Luttinger parameter $K_{eff.}$ is restricted to ${1/2}\leq K_{eff.}\leq 1$. As a result, at temperatures larger than the magnetic exchange energy we find an interacting metal which for $K_{eff.}\approx {1/2}$ is equivalent to the Hubbard $U\to\infty$ model, with the anomalous conductance $G\approx\frac{e^2}{h}$ .

Effects of impurities in spin Bose-metal phase on a two-leg triangular strip

Abstract: We study the effects of nonmagnetic impurities in a spin Bose-metal (SBM) phase discovered in a two-leg triangular strip spin-1/2 model with ring exchanges (D. N. Sheng et al., arXiv:0902.4210). This phase is a quasi-one-dimensional (quasi-1D) descendant of a two-dimensional (2D) spin liquid with spinon Fermi sea and the present study aims at interpolating between the 1D and 2D cases. Different types of defects can be treated as local-energy perturbations, which we find are always relevant. As a result, a nonmagnetic impurity generically cuts the system into two decoupled parts. We calculate bond energy and local spin susceptibility near the defect, both of which can be measured in experiments. The spin Bose metal has dominant correlations at characteristic incommensurate wave vectors that are revealed near the defect. Thus, the bond energy shows a static texture oscillating as a function of distance from the defect and decaying as a slow power law. The local spin susceptibility also oscillates and actually increases as a function of distance from the defect, similar to the effect found in the 1D chain [S. Eggert and I. Affleck, Phys. Rev. Lett. 75, 934 (1995)]. We calculate the corresponding power-law exponents for the textures as a function of one Luttinger parameter of the SBM theory.

Spin-orbit mixing in III–V semiconductors at the Γ point

Abstract: The consequences of the theory of spin-orbit mixing in III–V semiconductors at the Γ point have been analyzed within the five-band model for the first time. A formula that describes the optical matrix element relating the Γ7 and Γ8 bands and expresses it through the known Luttinger parameter q is derived. Until recently, it was believed that this optical matrix element is equal to zero and that the corresponding transition is forbidden. The role of this transition in the experiment on photon absorption by free holes in the p-GaSb compound is discussed.