Hyperuniform electron distributions controlled by electron interactions in quasicrystal

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 ∼ 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.

Doped Mott insulator on Penrose tiling

“…As Fig. 4(b) shows, this suppression of the spread is captured by the HFA, too 30,31 . In contrast, for U 6, the spread of n i increases with U in the RDMFT results [Fig.…”

“…In this case, various electronic phases have been studied, based on the Heisenberg-type or Hubbard-type models. These include metallic [25][26][27][28][29][30][31] , magnetic [32][33][34][35][36][37][38][39][40][41][42][43][44][45] , superconducting [46][47][48][49][50][51][52][53][54] and excitonic insulating 55 phases, where relations between the local site geometry and the electron density or order parameters have been clarified. While these ordered states are basically captured by a static mean-field approach, the Mott insulating state, involving a singular electron self-energy, cannot be described by it: We need to take account of dynamical correlation effects in a nonperturbative way.…”