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

TL;DR

This paper calculates the spectral function of a Luttinger liquid coupled to phonons, revealing features similar to high-temperature superconductor spectra, and highlights the non-Fermi-liquid behavior in these materials.

Contribution

It provides an exact calculation of the spectral function for a Luttinger liquid with electron-phonon coupling, including backward scattering effects, and compares results to ARPES data in cuprates.

Findings

Spectral features show a velocity change at phonon energy.

Pronounced low-energy peak appears with moderate backward scattering.

Results resemble ARPES spectra of high-Tc 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.