Average Symmetry Protected Higher-order Topological Amorphous Insulators

TL;DR

This paper demonstrates the theoretical existence of higher-order topological insulators in two-dimensional amorphous systems, protected by average crystalline symmetry, with unique corner modes and localized bulk states.

Contribution

It introduces the concept of average symmetry protected higher-order topological phases in amorphous materials, expanding topological insulator theory beyond crystalline systems.

Findings

Existence of higher-order topological phases with multiple corner modes in amorphous systems.

Ensemble average symmetry provides protection for topological phases.

Bulk states near zero energy are localized despite vanishing energy gap.

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.