Topological materials can host Dirac, Majorana and Weyl fermions as emergent excitations. In this talk, we will first briefly overview our recent results on topological insulators and helical superconductors based on topological insulators and consider new frontiers. It is possible to start with a topological insulator and close the gap in such a way that the low-lying bulk excitations emerge as Weyl fermions whereas the surface features non-closed Fermi surfaces resulting in the realization of a new state of topological matter via a topological phase transition. Strong spin-orbit interaction and crystalline symmetries can lead to a strong tilt of the Weyl cone which break Lorentz invariance. We present theoretical and experimental evidence that the LaAlGe materials family host such a state of topological matter. Finally, we present results on a topological nodal-line phase in (Pb/Tl)TaSe2 which also superconducts at low temperatures providing opportunities to investigate the interplay of superconductivity, symmetry and topology leading to a new type of Majorana platform.
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