Ca3P2 and other topological semimetals with line nodes and drumhead surface states

As opposed to ordinary metals, whose Fermi surfaces are two dimensional, topological (semi)metals can exhibit protected one-dimensional Fermi lines or zero-dimensional Fermi points, which arise due to an intricate interplay between symmetry and topology of the electronic wave functions. Here, we study how reflection symmetry, time-reversal symmetry, SU(2) spin-rotation symmetry, and inversion symmetry lead to the topological protection of line nodes in three-dimensional semimetals. We obtain the crystalline invariants that guarantee the stability of the line nodes in the bulk and show that a quantized Berry phase leads to the appearance of protected surfaces states, which take the shape of a drumhead. By deriving a relation between the crystalline invariants and the Berry phase, we establish a direct connection between the stability of the line nodes and the drumhead surface states. Furthermore, we show that the dispersion minimum of the drumhead state leads to a Van Hove singularity in the surface density of states, which can serve as an experimental fingerprint of the topological surface state. As a representative example of a topological semimetal, we consider Ca₃P₂ , which has a line of Dirac nodes near the Fermi energy. The topological properties of Ca₃P₂ are discussed in terms of a low-energy effective theory and a tight-binding model, derived from ab initio DFT calculations. Our microscopic model for Ca₃P₂ shows that the drumhead surface states have a rather weak dispersion, which implies that correlation effects are enhanced at the surface of Ca₃P₂ .