Topological nodal line semimetals without drumhead surface states

Topological nodal lines are protected by reflection symmetry or space-time inversion symmetry. The symmetries can quantize Berry phase in a proper basis and the π Berry phase stems from the presence of the protected topological lines. However, it has been shown that the only π Berry phase cannot lead to the presence of the stable drumhead surface states, which connect the bulk nodal lines. The other essential condition for the drumhead surface states is that no atoms should be located at the symmetry centers in the crystal structure. However, in condensed matter systems most of the topological nodal line semimetals fail this requirement and possess the drumhead surface states. In this talk, we show several concrete topological nodal line materials not possessing any drumhead surface states. The examples demonstrate that the bulk-boundary correspondence has very strict conditions for crystalline symmetries.