Theoretical Study of Phononic Weyl Nodal Lines and Weyl Points in 2D Hexagonal Lattices

Similar to their electronic counterparts, phonons with nontrivial topological features in their spectra give rise to robust boundary states, which carry transformative potential for applications related to thermal conduction, phonon diodes, waveguides, and even quantum information. In this work, we build tight-binding models to investigate what leads to non-trivial topology in hexagonal monolayers and bilayers. Starting with graphene, we consider models of increasing complexity that host multiple phases with nodal rings and Weyl crossings. We compare our results with those from real materials by performing first-principles density functional theory calculations on IV-V monolayers.