Hyperuniform electron distributions controlled by electron interactions in quasicrystal

TL;DR

This study investigates how electron-electron interactions in quasicrystals influence charge distributions, revealing that intersite Coulomb interactions induce hyperuniformity, a unique form of ordered inhomogeneity, in the metallic state.

Contribution

It introduces a large-scale numerical analysis of an extended Hubbard model on the Penrose lattice, demonstrating the impact of electron interactions on hyperuniform charge distributions in quasicrystals.

Findings

Electron interactions induce hyperuniform charge distributions.

Intersite Coulomb interactions significantly alter hyperuniformity.

Charge patterns are not multifractal but hyperuniform.

Abstract

We study how the electron-electron interactions influence the charge distributions in the metallic state of quasicrystals. As a simple theoretical model, we introduce an extended Hubbard model on the Penrose lattice, and numerically solve the model (up to $\sim1.4$ million sites) within the Hartree-Fock approximation. Because each site on the quasiperiodic lattice has a different local geometry, the Coulomb interaction, in particular the intersite one, works in a site-dependent way, leading to a nontrivial redistribution of the charge. The resultant charge distribution patterns are not multifractal but characterized by hyperuniformity, which offers a measure to distinguish various inhomogeneous but ordered distributions. We clarify how the electron interactions alter the order metric of the hyperuniformity, revealing that the intersite interaction considerably affects the hyperuniformity in particular on the electron-rich side.