Average Symmetry Protected Higher-order Topological Amorphous Insulators

Abstract

While topological phases have been extensively studied in amorphous systems in recent years, it remains unclear whether the random nature of amorphous materials can give rise to higher-order topological phases that have no crystalline counterparts. Here we theoretically demonstrate the existence of higher-order topological insulators in two-dimensional amorphous systems that can host more than six corner modes, such as eight or twelve corner modes. Although individual sample configuration lacks crystalline symmetry, we find that an ensemble of all configurations exhibits an average crystalline symmetry that provides protection for the new topological phases. To characterize the topological phases, we construct two topological invariants. Even though the bulk energy gap in the topological phase vanishes in the thermodynamic limit, we show that the bulk states near zero energy are localized, as supported by the level-spacing statistics and inverse participation ratio. Our findings open an avenue for exploring average symmetry protected higher-order topological phases in amorphous systems without crystalline counterparts.

17 pages, 7 figures

References in corpus (13)

• Classification of topological insulators and superconductors in three spatial dimensions
• Localization of interacting fermions at high temperature
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Reflection symmetric second-order topological insulators and superconductors
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Surface State Magnetization and Chiral Edge States on Topological Insulators
• Toward Realistic Amorphous Topological Insulators
• Robust Edge States in Amorphous Gyromagnetic Photonic Lattices
• Effective Model for Fractional Topological Corner Modes in Quasicrystals
• Topological states in quasicrystals
• Structural and electronic properties of realistic two-dimensional amorphous topological insulators
• Density-driven higher-order topological phase transitions in amorphous solids
• Role of the edges in a quasicrystalline Haldane model

Cited by in corpus (12)

• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Structural disorder-induced topological phase transitions in quasicrystals
• Higher-order Topological Insulators and Semimetals in Three Dimensions without Crystalline Counterparts
• Topological diffusive metal in amorphous transition metal monosilicides
• Higher-order topology in twisted multilayer systems: a review
• Hong-Ou-Mandel Interference in a temporal-average-inversion-symmetric chain
• Tunable corner states in topological insulators with long-range hoppings and diverse shapes
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• Three-Dimensional Quantum Hall Effect in Topological Amorphous Metals
• The Quadrupole Moment of Higher-Order Topological Insulator at Finite temperature
• Tunable cornerlike states in topological type-II hyperbolic lattices
• Non-self-averaging topological Anderson insulator