Speaker
Description
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 talk I will show that gyromorphs can host higher-order topological insulating (HOTI) phases protected by average rotational symmetry, and discuss the tools for diagnosing topological phases protected by such symmetry. I will show that symmetry indicators of the effective Hamiltonian, the spectral localizer, and scattering invariants all draw a consistent topological phase diagram.