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arXiv:0808.3091 · Journal of Physics Condensed Matter

Spectral properties of quasi-one-dimensional conductors with a finite transverse band dispersion

Željana Bonačić Lošić, A. Bjeliš, Paško Županović

Published Jul 21, 2008• 6 citations
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Abstract

We determine the one-particle spectral function and the corresponding derived quantities for the conducting chain lattice with the finite inter-chain hopping $t_\perp$ and the three-dimensional long-range Coulomb electron-electron interaction. The standard $G_{0}W_{0}$ approximation is used. It is shown that, due to the optical character of the anisotropic plasmon dispersion caused by the finite $t_\perp$, the low energy quasi-particle $δ$-peak appears in the spectral function in addition to the hump present at the energies of the order of plasmon energy. The particular attention is devoted to the continuous cross-over from the non-Fermi liquid to the Fermi liquid regime by increasing $t_\perp$. It is shown that the spectral weight of the hump transfers to the quasi-particle as the optical gap in the plasmon dispersion increases together with $t_\perp$, with the quasi-particle residuum $Z$ behaving like $- (\ln t_{\perp})^{-1}$ in the limit $t_{\perp}\to 0$. Our approach is appropriate for the wide range of energy scales given by the plasmon energy and the width of the conduction band, and is complementary to the Luttinger liquid techniques that are limited to the low energy regime close to the Fermi surface.

DOI
10.1088/0953-8984/20/32/325239

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We determine the one-particle spectral function and the corresponding derived quantities for the conducting chain lattice with the finite inter-chain hopping t⊥t_\perpt⊥​ and the three-dimensional long-range Coulomb electron-electron interaction. The standard G0W0G_{0}W_{0}G0​W0​ approximation is used. It is shown that, due to the optical character of the anisotropic plasmon dispersion caused by the finite t⊥t_\perpt⊥​, the low energy quasi-particle δδδ-peak appears in the spectral function in addition to the hump present at the energies of the order of plasmon energy. The particular attention is devoted to the continuous cross-over from the non-Fermi liquid to the Fermi liquid regime by increasing t⊥t_\perpt⊥​. It is shown that the spectral weight of the hump transfers to the quasi-particle as the optical gap in the plasmon dispersion increases together with t⊥t_\perpt⊥​, with the quasi-particle residuum ZZZ behaving like −(ln⁡t⊥)−1- (\ln t_{\perp})^{-1}−(lnt⊥​)−1 in the limit t⊥→0t_{\perp}\to 0t⊥​→0. Our approach is appropriate for the wide range of energy scales given by the plasmon energy and the width of the conduction band, and is complementary to the Luttinger liquid techniques that are limited to the low energy regime close to the Fermi surface.
We compute the finite-temperature single-particle spectral function of a one-dimensional Luttinger liquid coupled to an optical phonon band. The calculation is performed exactly for the case in which electron-phonon coupling is purely forward scattering. We extend the results to include backward scattering with a renormalization group treatment. The dispersion contains a change in velocity at the phonon energy, qualitatively similar to the case of electron-phonon coupling in a Fermi liquid. If the backward scattering part of the the electron-phonon interaction is not too strong compared to the forward scattering part, coupling to phonons also produces a pronounced peak in the spectral function at low energies. The calculated spectral function is remarkably similar to the angle-resolved photoemission spectra of the high-temperature superconductors, including the apparent presence of ``nodal quasiparticles,'' the presence of a ``kink'' in the dispersion, and the non-Fermi-liquid frequency and temperature dependencies. Although a microscopic justification has not been established for treating the electronic dynamics of the cuprates as quasi-one-dimensional, at the very least we take the quality of the comparison as evidence of the non-Fermi-liquid character of the measured spectra.
Accurate expressions, valid in experimentally relevant regimes, are presented for the effect of a long-ranged Coulomb interaction on the low-energy properties (momentum distribution function, density of states, electron spectral function, and 4kF{4k}_{F}4kF​ correlation function) of one-dimensional electron systems. The importance of plasmon dispersion (as opposed to exponent) effects in the spectral function is demonstrated.
We use higher-dimensional bosonization to study the normal state of electrons in weakly coupled metallic chains interacting with long-range Coulomb forces. Particular attention is paid to the crossover between Luttinger and Fermi-liquid behavior as the interchain hopping ${t}_{\ensuremath{\perp}}$ is varied. Although in the physically interesting case of finite but small ${t}_{\ensuremath{\perp}}$ the quasiparticle residue does not vanish, the single-particle Green's function exhibits the signature of Luttinger-liquid behavior (i.e., anomalous scaling and spin-charge separation) in a large intermediate parameter regime. Using realistic parameters, we find that the scaling behavior in this regime is characterized by an anomalous dimension of the order of unity, as suggested by recent experiments on quasi-one-dimensional conductors. Our calculation also gives insights into the approximations inherent in higher-dimensional bosonization; in particular, we show that the replacement of a curved Fermi surface by a finite number MMM of flat patches can give rise to unphysical nesting singularities in the single-particle Green's function, which disappear only in the limit $M\ensuremath{\rightarrow}\ensuremath{\infty}$ or if curvature effects are included. We also compare our approach with other methods. This work extends our recent letter [Phys. Rev. Lett. 74, 2997 (1995)].
We compute the spectral function rho (q, omega ) of the one-dimensional Luttinger model. We discuss the distinct influences of charge-spin separation and of the anomalous dimensions of the fermion operators and their evolution with correlation strength. Charge-spin separation shows up in finite spectral weight at frequencies between v sigma q and v rho q, where v sigma and v rho are the velocities of spin and charge fluctuations, while spectral weight above v rho q and below -v rho q is generated by the hybridization of the Fermi surface at +or-k F by interactions. There are non-universal power-law singularities at these special frequencies. We discuss the consistency of recent photoemission experiments on low-dimensional conductors with a Luttinger-liquid picture, which then would suggest very strong long-range interactions. It is pointed out that many-particle correlation functions in principle exhibit similar singularities, but they probe different and complementary aspects of the Fermi-surface interactions.
We study the problem of the crossover from one- to higher-dimensional metals by considering an array of Luttinger liquids (one-dimensional chains) coupled by a weak interchain hopping ${t}_{\ensuremath{\perp}}.$ We evaluate the exact asymptotic low-energy behavior of the self-energy in the anisotropic infinite-dimension limit. This limit extends the dynamical mean-field concept to the case of a chain embedded in a self-consistent medium. The system flows to a Fermi-liquid fixed point for energies below the dimensional crossover temperature, and the anomalous exponent \ensuremath{\alpha} renormalizes to zero, in the case of equal spin and charge velocities. In particular, the single-particle spectral function shows sharp quasiparticle peaks with nonvanishing weight along the whole Fermi surface, in contrast to the lowest-order result. Our result is obtained by carrying out a resummation of all diagrams of the expansion in ${t}_{\ensuremath{\perp}}$ contributing to the anisotropic $\stackrel{\ensuremath{\rightarrow}}{D}\ensuremath{\infty}$ limit. This is done by solving, in an almost completely analytic way, an asymptotically exact recursive equation for the renormalized vertices, within a skeleton expansion. Our outcome shows that perturbation expansions in ${t}_{\ensuremath{\perp}}$ restricted to lowest orders are unreliable below the crossover temperature. The extension to finite dimensions is discussed. This work extends our recent letter [Phys. Rev. Lett. 83, 128 (1999)], and includes all mathematical details.
The validity of the quasiparticle picture for electrons in weakly coupled linear chains is investigated using for a single chain the Tomonaga-Luttinger model of interacting one-dimensional electrons. For interchain coupling without jumps between the chains it is proved exactly that no stable quasiparticles exist. The excitation spectrum is exhausted by density oscillations and the single-particle occupation number shows a power-law behavior. For finite-interchain hopping, lowest-order-perturbation theory yields a quasiparticle peak in the spectral density. Its weight is $z={[1\ensuremath{-}2\ensuremath{\alpha}\mathrm{ln}(\frac{{W}_{\ensuremath{\perp}}}{{W}_{\ensuremath{\parallel}}})]}^{\ensuremath{-}1}$, where $\ensuremath{\alpha}$ is the interaction parameter and ${W}_{\ensuremath{\parallel}}$ and ${W}_{\ensuremath{\perp}}$ are the widths of the conduction band in momentum direction parallel and perpendicular to the chains. The relevance of our results for real quasi-one-dimensional conductors will be discussed.