Physics Research Conference

Topological materials can host Dirac, Majorana and Weyl fermions as emergent excitations. In this talk, I first present an overview of recent results on topological insulators and related superconductors as Majorana platforms. In these systems the topological fermions are robust in the presence of a gap (Hasan & Kane, Rev. of Mod. Phys. 82, 3045 (2010)). A Weyl semimetal is the rare exception in this scheme which is a topologically robust conductor (semimetal) whose emergent bulk excitations are Weyl fermions. The chiralities associated with the Weyl nodes can be understood as topological charges, leading to split monopoles and anti-monopoles of Berry curvature field in momentum space. Due to this topology it is expected to exhibit Fermi arc states on its surface (Wan et.al., 2011). These arcs 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 nodes on the surface observed recently in experiments. Our theoretical predictions (Huang, Xu et.al., Nature Commun. 2015) and experimental demonstrations (Xu, Belopolski et.al., Science (2015), Nature Physics 2015, Science Adv. 2015) reveal that these arc quasiparticles can only live on the boundary of a 3D crystal which collectively represents the realization of a new state of quantum matter. Strong spin-orbit interaction and crystalline symmetries can also lead to a strong tilt of the Weyl cone which manifestly break Lorentz invariance. We present evidence that the LaAlGe materials family host such a state of matter. Finally, we present results on a topological nodal-line semimetal state in (Pb/Tl)TaSe2  which also superconducts at low temperatures possibly suggesting a new platform to investigate the interplay of superconductivity and topology leading to a new Majorana platform.