Universalities in One-electron Properties of Limit Quasi-periodic Lattices

TL;DR

This paper explores the universal one-electron spectral properties of limit quasi-periodic lattices, revealing their multifractal spectra and the existence of marginal critical states, which differ from traditional quasi-periodic systems.

Contribution

It introduces the nonconservative trace map for limit quasi-periodic lattices and uncovers universal multifractal spectral features and marginal critical states.

Findings

Multifractal characters of energy spectra are universal.

Supports of the f(α)-spectra extend over [0,1].

Existence of marginal critical states.

Abstract

We investigate one-electron properties of one-dimensional self-similar structures called limit quasi-periodic lattices. The trace map of such a lattice is nonconservative in contrast to the quasi-periodic case, and we can determine the structure of its attractor. It allows us to obtain the three new features of the present system: 1) The multi-fractal characters of the energy spectra are {\it universal}. 2) The supports of the $f(\alpha)$-spectra extend over the whole unit interval, $[0, 1]$. 3) There exist marginal critical states.