Hyperuniform electron distributions controlled by electron interactions in quasicrystals

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 similar to 1.4 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.

Automated summary

We investigate the influence of electron-electron interactions on the charge distributions in the metallic state of quasicrystals. By introducing an extended Hubbard model on the Penrose lattice and numerically solving it within the Hartree-Fock approximation, we find that the Coulomb interaction between lattice sites, due to the different local geometries, leads to a nontrivial redistribution of charge. The resulting charge distribution patterns exhibit hyperuniformity, which can distinguish various inhomogeneous but ordered distributions. We also reveal that the intersite interaction significantly affects the hyperuniformity on the electron-rich side.