Two-dimensional macroporous carbon: An ideal nodal-line semimetal with combined electronic and phononic topology

Ideal nodal-line semimetals (NLSMs) exhibit clean nodal lines strictly localized at the Fermi energy, devoid of trivial state interference. The stringent criteria for such states make them exceptionally rare, especially those concurrently displaying nontrivial topological properties in both electronic and phononic bands. Here, we propose an ideal NLSM material, termed BODG, characterized by perfect band crossings and precisely located at the Fermi energy. It features type-II nodal lines and quadratic Weyl cones within its optical phonon branches. As a two-dimensional macroporous carbon allotrope composed of octagonal and dodecagonal rings, BODG’s nodal line remains robust against tensile strain, which is protected by mirror-reflection symmetry.