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 $\sim 1.4$ 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.

16 pages, 22 figures

References in corpus (17)

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Cited by in corpus (15)

• Quantum phase transition between hyperuniform density distributions
• Intrinsic vortex pinning in superconducting quasicrystals
• High-Angular-Momentum Topological Superconductivity in the Largest-Angle Twisted Homo-bilayer Systems
• Anomalous suppression of large-scale density fluctuations in classical and quantum spin liquids
• Nematic Superconductivity and Its Critical Vestigial Phases in the Quasi-crystal
• Electronic states of a disordered 2D quasiperiodic tiling: from critical states to Anderson localization
• Properties of the Ammann-Beenker tiling and its square approximants
• Doped Mott insulator on Penrose tiling
• Hyperuniformity in two-dimensional periodic and quasiperiodic point patterns
• Multifractality and Hyperuniformity in Quasicrystalline Bose-Hubbard Models with and without Disorder
• Hyperuniform properties of the square-triangle tilings
• Superconductivity and charge-density-wave in the Holstein model on the Penrose Lattice
• Magnon Confinement on the Two-Dimensional Penrose Lattice: Perpendicular-Space Analysis of the Dynamic Structure Factor
• Critical behavior of the Ising model on square-triangle tilings
• Site-selective correlations in interacting "flat-band" quasicrystals