Obstructed atomic and real Chern insulating states in bcc C8

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Carbon, an element of fundamental importance in our universe, has a diverse range of allotropic phases, the majority of which exhibit the potential for topological fermions. In this work, by means of first-principle calculations, we report a carbon allotrope with a body-centered cubic form, denoted as bcc C8, which is a candidate for obstructed atomic insulator and real Chern insulator. Interestingly, bcc C8 hosts an unconventional bulk-boundary correspondence because it exhibits boundary states (hinge states) in two dimensions lower than the 3D bulk. Importantly, bcc C8 has already been synthesized in experiments, making it a real carbon phase platform for studying the real topology and hinge states, which can be leveraged to create efficient topological electronic devices.