Topological semi-metals with line nodes and drumhead surface states

摘要

In an ordinary three-dimensional metal the Fermi surface forms atwo-dimensional closed sheet separating the filled from the empty states.Topological semimetals, on the other hand, can exhibit protectedone-dimensional Fermi lines or zero-dimensional Fermi points, which arise dueto an intricate interplay between symmetry and topology of the electronicwavefunctions. Here, we study how reflection symmetry, time-reversal symmetry,SU(2) spin-rotation symmetry, and inversion symmetry lead to the topologicalprotection of line nodes in three-dimensional semi-metals. We obtain thecrystalline invariants that guarantee the stability of the line nodes in thebulk and show that a quantized Berry phase leads to the appearance of protectedsurfaces states with a nearly flat dispersion. By deriving a relation betweenthe crystalline invariants and the Berry phase, we establish a directconnection between the stability of the line nodes and the topological surfacestates. As a representative example of a topological semimetal with line nodes,we consider Ca$_3$P$_2$ and discuss the topological properties of its Fermiline in terms of a low-energy effective theory and a tight-binding model,derived from ab initio DFT calculations. Due to the bulk-boundarycorrespondence, Ca$_3$P$_2$ displays nearly dispersionless surface states,which take the shape of a drumhead. These surface states could potentially giverise to novel topological response phenomena and provide an avenue for exoticcorrelation physics at the surface.