Density of states and magnetic susceptibilities on the octagonal tiling

TL;DR

This paper investigates the electronic and magnetic properties of electrons on an octagonal quasiperiodic tiling, revealing characteristic density of states, site-dependent susceptibilities, and non-local spin interactions, with implications for understanding quasiperiodic materials.

Contribution

It provides a detailed analysis of electronic density of states and magnetic susceptibilities on the octagonal tiling, including the discovery of non-local spin correlations and local magnetic moment formation.

Findings

Six characteristic forms of density of states identified.

Site-dependent magnetic susceptibilities with six characteristic patterns.

Existence of non-local spin susceptibility decaying as the square of the distance.

Abstract

We study electronic properties as a function of the six types of local environments found in the octagonal tiling. The density of states has six characteristic forms, although the detailed structure differs from site to site since no two sites are equivalent in a quasiperiodic tiling. We present the site-dependent magnetic susceptibility of electrons on this tiling, which also has six characteristic dependences. We show the existence of a non-local spin susceptibility, which decays with the square of the distance between sites and is the quasiperiodic version of Ruderman-Kittel oscillations. These results are obtained for a tight-binding Hamiltonian with pure hopping.Finally, we investigate the formation of local magnetic moments when electron-electron interactions are included.