Condensed Matter Seminars

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, and inversion symmetry leads to the topological protection of line nodes in three-dimensional semi-metals. We derive the Z- and Z2-type invariants that guarantee the stability of the line nodes and lead to the appearance of protected surfaces states. As a representative example of a topological semimetal with line nodes, we consider Ca3P2 and discuss the topological properties of its Fermi line in terms of a tight-binding model, derived from ab initio DFT calculations. We show that due to a bulk-boundary correspondence, Ca3P2 displays nearly dispersionless surface states, which take the shape of a drumhead. These topological surface states give rise to the charge polarization.