Three-Dimensional Effects on the Electronic Structure of Quasiperiodic Systems

TL;DR

This paper presents a theoretical analysis of how three-dimensional interactions influence the electronic structure of quasiperiodic systems, revealing complex spectral properties and extending one-dimensional models to three dimensions.

Contribution

It introduces a solvable model for 3D quasiperiodic systems using nonlocal potentials, extending spectral analysis from 1D to 3D.

Findings

Systems exhibit highly fragmented, self-similar spectra

Spectra become singular continuous in the thermodynamic limit

Model applicable to chain polymer systems

Abstract

We report on a theoreticl study of the electronic structure of quasiperiodic, quasi-one-dimensional systems where fully three dimensional interaction potentials are taken into account. In our approach, the actual physical potential acting upon the electrons is replaced by a set of nonlocal separable potentials, leading to an exactly solvable Schrodinger equation. By choosing an appropriate trial potential, we obtain a discrete set of algebraic equations that can be mapped onto a general tight-binding-like equation. We introduce a Fibonacci sequence either in the strength of the on-site potentials or in the nearest-neighbor distances, and we find numerically that these systems present a highly fragmented, self-similar electronic spectrum, which becomes singular continuous in the thermodynamical limit. In this way we extend the results obtained so far in one-dimensional models to the three-dimensional case. As an example of the application of the model we consider the chain polymer case.