Spectral function of a Luttinger liquid coupled to phonons and angle-resolved photoemission measurements in the cuprate superconductors

Abstract

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.

Phase diagram and isotope effects of the quasi-one-dimensional electron gas coupled to phonons

“…However, the high-temperature superconductors, as well as some other materials of current interest, exhibit manifestly non-Fermi liquid behavior. 3,4,5,6,7 Compared to conventional metals, much less is known about the influence of an el-ph interaction in non-Fermi liquids. One such system, where much analytic progress can be made, 8,9,10,11,12 is the interacting one-dimensional electron gas (1DEG), where the system is strongly correlated even for weak interactions.…”

“…The same technique is employed to compute the doping dependent superconducting susceptibilities, charge density wave susceptibility, and isotope effects. In a separate paper, 7 we have studied the influence of the el-ph interaction on the electron dynamics of an interacting 1DEG, expressed via the single particle spectral function. The strategy in the present paper is to start with a microscopic electron-phonon model with many parameters (el-el interactions, electron bandwidth, el-ph interactions, and phonon frequency), and then to integrate out high-energy degrees of freedom to produce a low-energy effective field theory with a known phase diagram-the continuum 1DEG-whose only parameters are the renormalized el-el interactions and bandwidth.…”

Phonon Effects on Spin-Charge Separation in One Dimension

“…[11,12,13,14] Because both electron-electron and electron-phonon interactions exist in many low-dimensional materials, it is important to address the role of these interactions on the spin-charge separation. [6,15,16,17,18,19] The one-dimensional Holstein-Hubbard model (HHM), which is the simplest model involving both electronphonon (e-p) and electron-electron (e-e) interactions, has been used extensively to describe some low-dimensional materials. Since electrons in these materials are strongly correlated, the interplay between electron-phonon interaction and Coulomb repulsion should have profound effect on the spin-charge separation, and we expect to observe these effects by investigating the single-particle excitation spectra.…”