Higher-order topology in twisted multilayer systems: a review

Abstract In recent years, there has been a surge of interest in higher-order topological phases (HOTPs) across various disciplines within the field of physics. These unique phases are characterized by their ability to harbor topological protected boundary states at lower-dimensional boundaries, a distinguishing feature that sets them apart from conventional topological phases and is attributed to the higher-order bulk-boundary correspondence. Two-dimensional (2D) twisted systems offer an optimal platform for investigating HOTPs, owing to their strong controllability and experimental feasibility. Here, we provide a comprehensive overview of the latest research advancements on HOTPs in 2D twisted multilayer systems. We will mainly review the HOTPs in electronic, magnonic, acoustic, photonic and mechanical twisted systems, and finally provide a perspective of this topic.