Hyperuniform solids with bond orientiational order

The talk will first discuss how to characterize the hyperuniformity in quasicrystals and other non-periodic self-similar solids. We will then introduce a class of hyperuniform structures with perfect long-range bond orientational order but no long-range periodic or quasiperiodic translational order. Their mathematical construction raises fundamental questions about the nature of hyperuniformity and suggests the possibility of materials with novel physical properties.