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Physical Review B

Nonquasiparticle behavior in momentum-dependent spectral functions of the many-electron Frohlich model

Hongxing Zheng, Keiichirō Nasu

Published Sep 5, 2007• 0 citations
Publisher

Abstract

We have developed a new approach, starting from the Frohlich Hamiltonian and by means of the unitary transformation with the perturbation treatment, to deal with the momentum-dependent spectral functions (MDSF) of electron-phonon coupling system. The approach takes care of the fact that only those electrons near the Fermi surface within a layer of width ${\ensuremath{\omega}}_{ph}$ (phonon frequency) are scattered by phonons strongly. Our results show that the MDSF is mainly composed of two parts: the zero-phonon part and the one-phonon one. When the bare electron energy ${ϵ}_{\mathbf{k}}$ is close to the Fermi energy ${E}_{F}$, $\ensuremath{\mid}{ϵ}_{\mathbf{k}}\ensuremath{-}{E}_{F}\ensuremath{\mid}\ensuremath{\simeq}{\ensuremath{\omega}}_{ph}$, the one-phonon part is quite significant and the MDSF shows a two-headed peak. However, for $\ensuremath{\mid}{ϵ}_{\mathbf{k}}\ensuremath{-}{E}_{F}\ensuremath{\mid}⪢{\ensuremath{\omega}}_{ph}$, the one-phonon part disappears gradually and the MDSF shows a single broad peak. Our calculation for MDSF is qualitatively in agreement with recent measurement of angle-resolved photoemission spectroscopy on the Be(0001) surface and ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8}$. Besides, the two-headed structure of MDSF indicates the ``hybridization'' between electrons and phonons.

DOI
10.1103/physrevb.76.104301

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Using a new path-integral theory [1], we study the angle resolved photoemission spectra (ARPES) of one - and two-dimensional metallic many-electron systems coupled with Einstein phonons. The multiple scatterings of electrons due to phonons are shown to completely dominate the ARPES, even if the electron-phonon coupling strength is intermediate. These multiple scatterings result in spectral evolution from a broad Gaussian to a two-headed asymmetric Lorentzian as the momentum changes from the band bottom to the Fermi one ( ≡ pF ), as shown in Fig. 1. We have also found that this two-headed structure near pF becomes most distinct in the two dimensional non-half-filled cases with no charge density wave gap. These results qualitatively agree with recent experiments of ARPES on the Be(0001) surface and Bi2Sr2CaCu2O8. In terms of nonlinear couplings between the electrons and the phonons, we also show the microscopic origin of anomalous isotopic band shift appeared in the ARPES of Bi2Sr2CaCu2O8, in good agreement with the recently discovery by Gweon et al. [2].
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.
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Using an efficient variational exact diagonalization method, we computed the electron removal spectral function within the framework of the Holstein-Hubbard model containing two electrons with opposite spins coupled to dispersive quantum optical phonons. We focus on how the interplay between the electron-phonon coupling and on-site Coulomb repulsion shapes the spectral function, a quantity directly relevant to angle-resolved photoemission spectroscopy (ARPES). Tuning the strengths of the electron-phonon coupling and the Hubbard interaction allows us to examine the evolution of the spectral properties of the system as it crosses over from a bound bipolaron to separate polarons. We find that phonon dispersion plays an important role: It substantially redistributes the spectral weight across the low- and the high-energy features and controls the emergence and the structure of distinct multiphonon continua. In regimes of strong electron-phonon coupling and low Coulomb repulsion, the spectral function exhibits a broad distribution reflecting bound bipolaronic states. Increasing the Coulomb repulsion weakens bipolaron binding, shifts the primary quasiparticle peak closer to polaronic behavior and confines the spectral weight near the Brillouin-zone center. Our results provide a framework for interpreting ARPES measurements in systems where phonon–mediated attraction competes with direct Coulomb repulsion.
Using a recently developed perturbative approach, which considers Hubbard operators as fundamental excitations, we have performed electronic self-energy and spectral function calculations for the $t\text{\ensuremath{-}}J$ model on the square lattice. We have found that the spectral functions along the Fermi surface are isotropic, even close to the critical doping where the ddd density wave phase occurs. Fermi liquid behavior with scattering rate $\ensuremath{\sim}{\ensuremath{\omega}}^{2}$ and a finite quasiparticle weight ZZZ was obtained. ZZZ decreases with decreasing doping taking low values for low doping. Results are compared with others obtained by analytical and numerical methods like the slave-boson and Lanczos diagonalization approaches, finding agreement. We discuss our results in the light of recent angle-resolved photoemission spectroscopy experiments in cuprates.
A model with d-wave pairing symmetry is studied by employing a nonperturbative sum-rule approach. At low temperature the magnitude of a normal-state pseudogap shows strong $\stackrel{\ensuremath{\rightarrow}}{k}$ or angle dependence well fitted by $\mathrm{cos}2\ensuremath{\varphi}$ form. With increasing temperature, the pseudogap closes at some critical angle ${\ensuremath{\varphi}}_{c},$ and beyond this angle a single quasiparticlelike peak appears. The resulting Fermi surface is strongly temperature dependent. Both in the spectral function and the density of states, the pseudogap disappears in a manner that the spectral weight fills in the pseudogap instead of closing it with increasing temperature. All these features are qualitatively consistent with angle resolved photoemission spectroscopy for underdoped cuprates.