Topological Gyromorphs

TL;DR

This paper demonstrates that gyromorphs, a new class of disordered systems with average rotational symmetry, can host higher-order topological insulator phases, expanding the understanding of topological matter beyond traditional crystalline structures.

Contribution

It introduces symmetry indicators and diagnostic tools for topological phases in gyromorphs, a disordered system lacking exact rotational symmetry.

Findings

Gyromorphs can host HOTI phases protected by average rotational symmetry.

New symmetry indicators effectively diagnose topological phases in gyromorphs.

Gyromorphs serve as a platform for studying topological phases beyond conventional materials.

Abstract

Gyromorphs are a new class of disordered systems that combine an amorphous-like absence of translational order with quasi-long-range rotational order. Gyromorphs can outperform quasicrystals or hyperuniform arrangements in forming isotropic band gaps, suggesting an avenue to realize robust disordered topological phases. However, gyromorphs lack exact rotational symmetry, which is only realized on average, posing an obstacle for existing real-space invariants to correctly diagnose topological gyromorphs. In this work we show that gyromorphs can host higher-order topological insulating (HOTI) phases protected by average rotational symmetry, and we develop and systematically compare tools for diagnosing topological phases protected by such symmetry. We introduce symmetry indicators of the effective Hamiltonian based on average rotational symmetries which, when combined with the spectral localizer and a scattering invariant, draw a consistent topological phase diagram. Our work unlocks gyromorphs as a novel platform to study topological phases beyond crystals, quasicrystals, and amorphous materials.