Topological semi-metals with line nodes and drumhead surface states

Understand

In an ordinary three-dimensional metal the Fermi surface forms a two-dimensional closed sheet separating the filled from the empty states.

• Topological semimetals, on the other hand, 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 wavefunctions.
• 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 semi-metals.
• 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 with a nearly flat dispersion.