<i>d</i> ‐Orbital Corner States in Higher‐Order Orbital Hall Insulators

Abstract Orbital degrees of freedom are essential to understand fundamental features of solid‐state physics and topological quantum states. In spite of the tremendous effort to realize and explore topological systems with orbital degree, only s ‐orbital and p ‐orbital states have been found in higher‐order topological insulators (HOTIs). In this work, the existence of d ‐orbital corner states, being the signature of a strong concentrations in the Berry curvature and orbital angular momentum (OAM), is demonstrated theoretically. It has been identified that strong concentrations of Berry curvature, known as pinch points, generate the orbital Hall insulating phase. To achieve the presence of pinch points, a tight‐binding model with a special d ‐orbital configuration with π and σ bonds, in addition to antibonds of the same type, has been proposed. Interestingly, the tight‐binding model configuration is naturally achieved in a photonic model with a breathing Kagome lattice supporting d ‐orbital bands. The topology of the photonic model is characterized by means of the spectral localizer theory and confirms the existence of d ‐orbital corner states in the orbital Hall insulator phase through the vortices generated in the energy distribution. These results pave the way to consolidate the recent branch known as orbitronic and extend the regime to orbitronic photonics.