Type-II Dirac line node in strained Na3N

Dirac line node (DLN) semimetals are a class of topological semimetals that feature band-crossing lines in momentum space. We study the type-I and type-II classification of DLN semimetals by developing a criterion that determines the type using band velocities. Using first-principles calculations, we also predict that ${\mathrm{Na}}₃\mathrm{N}$ under an epitaxial tensile strain realizes a type-II DLN semimetal with vanishing spin-orbit coupling, characterized by the Berry phase, which is ${\mathbb{Z}}₂$ quantized in the presence of inversion and time-reversal symmetries. The surface energy spectrum is calculated to demonstrate the topological phase and the type-II nature is demonstrated by calculating the band velocities. We also develop a tight-binding model and a low-energy effective Hamiltonian that describe the low-energy electronic structure of strained ${\mathrm{Na}}₃\mathrm{N}$. The occurrence of a DLN in ${\mathrm{Na}}₃\mathrm{N}$ under strain is captured in the optical conductivity, which we propose as a means to experimentally confirm the type-II class of DLN semimetals.