Electrons and Phonons on the Square Fibonacci Tiling

TL;DR

This paper investigates the spectral properties and wave functions of electrons and phonons in a square Fibonacci quasicrystal, revealing insights into their behavior in this complex aperiodic structure.

Contribution

It provides a detailed analysis of the spectral characteristics and wave functions for both electronic and vibrational states in the square Fibonacci tiling, a less-explored quasicrystal model.

Findings

Analysis of the spectral nature of electrons and phonons.

Characterization of wave functions in the quasicrystal.

Insights into the vibrational and electronic properties of the structure.

Abstract

We study the Schroedinger equation for an off-diagonal tight-binding hamiltonian, as well as the equations of motion for out-of-plane vibrations, on the separable square Fibonacci quasicrystal. We discuss the nature of the spectra and wave functions of the solutions.