Discovery of Weyl fermion and topological nodal-line fermions as emergent excitations in topological materials
Topological materials can host Dirac, Majorana and Weyl fermions as quasiparticle modes on their boundaries or bulk. First, I briefly mention the basic theoretical concepts defining insulators and superconductors where topological surface state modes are robust only in the presence of a gap (Rev. of Mod. Phys. 82, 3045 (2010)). In these systems topological protection is lost once the gap is closed turning the system into a trivial metal. A Weyl semimetal is the rare exception in this scheme which is a topologically robust conductor (semimetal) whose low energy emergent bulk excitations are Weyl fermions. In a Weyl semimetal, the chiralities associated with the Weyl nodes can be understood as topological charges, leading to split monopoles and anti-monopoles of Berry curvature in momentum space. This gives a measure of the topological strength of the system. Due to this topology a Weyl semimetal is expected to exhibit 2D Fermi arc quasiparticles on its surface (Wan et.al., 2011). These arcs (``fractional'' Fermi surfaces) are discontinuous or disjoint segments of a two dimensional Fermi contour with non-trivial spin textures, which are terminated onto the projections of the Weyl fermion nodes on the surface observed recently in experiments. Our theoretical predictions (Nature Commun. 2015) and experimental demonstrations (Xu et.al., Science 349, 613 (2015), Nature Physics 2015, Science Advances 2015) reveal that these Fermi arc quasiparticles can only live on the boundary of a 3D crystal which collectively represents the realization of a new state of quantum matter beyond our earlier work on spin-textured Fermi arcs in topological materials (Xu et.al., Science 347, 294 (2015)). We provide a comparison. Very recently, we theoretically and experimentally discovered a related state of matter, a topological nodal-line semimetal state in (Pb/Tl)TaSe2 (which also superconduct at low temperatures) where the Fermi surface is a protected nodal-line loop in three dimensional momentum space (Bian et,al., Nature Commun. 7:10556 (2016)) possibly suggesting a new platform to investigate the interplay of superconductivity and non-trivial topology.