Abstract
In nodal-line semimetals, the gaps close along loops in k space, which are not at high-symmetry points. Typical mechanisms for the emergence of nodal lines involve mirror symmetry and the π Berry phase. Here we show via ab initio calculations that fcc calcium (Ca), strontium (Sr) and ytterbium (Yb) have topological nodal lines with the π 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 π or 0, depending on the wavevector k, and the π 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).
Highlights
In nodal-line semimetals, the gaps close along loops in k space, which are not at high-symmetry points
In the present study we propose on the basis of ab initio calculation that the alkaline-earth metals Ca, Sr and Yb have topological nodal lines when the spin–orbit interaction (SOI) is neglected
The well-known loafrgteheRassuhrbfaacespAlitgtinagtoims sr,eafloizrmedinwghethneBpi affi3ffitoÂmps ffi3rffiepstlrauccetuornee3-7t.hiTrdo establish the origin of the largpeffiRffi ashpbffiaffi splitting, in Fig. 5h we show the band structure for the 3 Â 3 Ag(111) surface with onethird of the surface Ag atoms depleted (Fig. 1d); surface states exist around 0.6 eV, which is higher than those in Fig. 5g because of depletion of some of the bonds
Summary
In nodal-line semimetals, the gaps close along loops in k space, which are not at high-symmetry points. Ca becomes an NLS under pressure, as shown in the band structure at 7.5 GPa in Fig. 2d; a similar conclusion has been reached in previous works[34,35] without showing the topological origin of the nodal lines.
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