Body-centered tetragonal C4: A carbon allotrope with real topology and second-order bulk-boundary correspondence

Carbon, being the most common element on Earth, exhibits a diverse range of allotropic phases, hence contributing to its intricate physical characteristics. In recent times, a number of carbon allotropes near the Fermi surfaces have been predicted from first principles with rich topological phases. In this study, we present body-centered tetragonal C₄ (bct C₄), a new form of crystalline sp³ carbon, is a potential candidate for both an obstructed atomic insulator (OAI) and a real Chern insulator (RCI). It is noteworthy that bct C₄ demonstrates an unconventional bulk-boundary correspondence due to its manifestation of hinges boundary states. Our current work reveals that bct C₄ is a viable carbon phase platform for investigating the real topology and second-order bulk-boundary correspondence. It is hoped that our work can serve as a good starting point for future studies on three-dimensional (3D) real Chern insulators.