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

TL;DR

This paper investigates how finite transverse band dispersion affects the spectral function of quasi-one-dimensional conductors, revealing a crossover from non-Fermi liquid to Fermi liquid behavior as inter-chain hopping increases.

Contribution

It provides a detailed analysis of the spectral function considering finite inter-chain hopping and Coulomb interactions, extending beyond low-energy Luttinger liquid models.

Findings

Appearance of a quasi-particle delta peak due to optical plasmon dispersion

Transfer of spectral weight from plasmon hump to quasi-particle peak with increasing t_perp

Quasi-particle residue Z behaves like -1/ln(t_perp) as t_perp approaches zero

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 $\delta$-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.