Optical response of the tightbinding model on the Fibonacci chain

TL;DR

This paper investigates the optical conductivity of a Fibonacci chain tightbinding model, revealing self-similar structures and the effects of disorder on optical responses due to critical wave function behavior.

Contribution

It introduces a detailed analysis of optical conductivity in Fibonacci sequence-based tightbinding models, highlighting self-similarity and disorder effects.

Findings

Self-similar structure appears in optical conductivity for large hopping integral ratios.

Optical response between high- and low-energy bands is interconnected, indicating critical wave function behavior.

Disorder destroys the self-similar optical features in the Fibonacci chain model.

Abstract

We theoretically study the optical conductivity of the tightbinding model which has two types of the hopping integrals arranged in the Fibonacci sequence. Due to the lack of the translational symmetry, many peak structures appear in the optical conductivity as well as the density of states. When the ratio of two hopping integrals is large, the self-similar structure appears in the optical conductivity. This implies that the optical response between the high-energy bands is related to that within the low-energy bands, which should originate from critical behavior in the wave functions. The effects of disorders on the optical conductivity are also analyzed in order to show the absence of the self-similarity in the tightbinding model with the random sequence.