Higher-order topological fermion phase and Weyl phonon phase in Li-intercalated graphene layers

Two-dimensional (2D) higher-order topological fermionic phases coexisting with intriguing topological phonon states have recently become a focal point of condensed matter research. However, the coexistence of the second-order topological phase and valley Weyl phonon features in 2D materials remains unexplored. In this Letter, we present a two-dimensional Li-intercalated graphene material family that serves as an ideal platform for demonstrating the coexistence of topological electron and phonon features. Our study, which utilizes first-principles calculations, investigates the structural, electronic, and topological properties of several Li-intercalated graphene materials. The higher-order topological phases are protected by C6 rotation and inversion symmetries in Li-C6 and Li-C6-Li layers, respectively, as confirmed by their calculated topological invariants (χ6, Z4). Topologically protected corner modes are noticed within the gapped bulk and edge states (in the armchair edge) in the nanoflake geometry of the Li-C6 compound. Notably, the phonon spectra of the Li-C6 and Li-C6-Li materials exhibit Weyl phonon nodes in the Brillouin zone where the phonon bands touch at the valley-high symmetry point. The presence of localized Berry curvature and robust topological phonon edge states further confirms the existence of Weyl phonon nodes in these materials. Our first-principles study predicts potential candidates for hosting the coexisting electronic and phononic features and highlights the technological aspects of Li-intercalated graphene materials.