Electronic energy spectra and wave functions on the square Fibonacci tiling

TL;DR

This paper investigates the electronic energy spectra and wave functions on the square Fibonacci tiling using a tight-binding model to understand spectral transitions and the emergence of extended states as the system dimension increases.

Contribution

It provides an analysis of spectral behavior and wave function nature on the square Fibonacci tiling, highlighting the role of degeneracy and dimensionality in electronic properties.

Findings

Identification of spectral transition behaviors

Scaling analysis of total bandwidth

Role of degeneracy in wave function extension

Abstract

We study the electronic energy spectra and wave functions on the square Fibonacci tiling, using an off-diagonal tight-binding model, in order to determine the exact nature of the transitions between different spectral behaviors, as well as the scaling of the total bandwidth as it becomes finite. The macroscopic degeneracy of certain energy values in the spectrum is invoked as a possible mechanism for the emergence of extended electronic Bloch wave functions as the dimension changes from one to two.