Topological Dirac Nodal Lines and Surface Charges in fcc Alkaline Earth Metals

In nodal-line semimetals, the gaps close along loops in ${\bf k}$ space, which are not at high-symmetry points. Typical mechanisms for the emergence of nodal lines involve mirror symmetry and the $\pi$ Berry phase. Here, we show via ab initio calculations that fcc calcium (Ca), strontium (Sr) and ytterbium (Yb) have topological nodal lines with the $\pi$ Berry phase near the Fermi level, when spin-orbit interaction is neglected. In particular, Ca becomes a nodal-line semimetal at high pressure. Owing to nodal lines, the Zak phase becomes either $\pi$ or 0 depending on the wavavector ${\bf k}$, and the $\pi$ Zak phase leads to surface polarization charge. Carriers eventually screen it, leaving behind large surface dipoles. In materials with nodal lines, both the large surface polarization charge and the emergent drumhead surface states enhance Rashba splitting when heavy adatoms are present, as we have shown to occur in Bi/Sr(111) and in Bi/Ag(111).