Ubiquitous topological materials protected by hidden partial symmetries

Abstract

Symmetries play a crucial role in protecting the topological phases of insulators, ensuring the robustness of their surface states against perturbations. Traditionally, these symmetries have to be obeyed by the system as a whole, which is a rather strong constraint. In this work, we demonstrate that topological effects can also be realized through a substantially weaker form of symmetry that we coin \emph{partial latent symmetries}. For these, invariance is required only at certain energy scales of an effective Hamiltonian, rather than for the object as a whole. Applying this idea, we construct weak-symmetry versions of the Su-Schrieffer-Heeger and Benalcazar-Bernevig-Hughes models. These weak-symmetry models behave in many aspects just like their conventional brethren---in particular, they host robust edge states---, though the corresponding topological invariants are only \emph{approximately} quantized. We conclude this work by experimentally realizing Hermitian and non-Hermitian versions of such approximate topological insulators and probe their edge states. Overall, given the ubiquity of symmetry in all areas of physics and engineering, we foresee our work to serve as a cornerstone for exploring how conventional, strong symmetry requirements can be replaced by weak-symmetry ones.