Topological semimetals predicted from first-principles calculations

We have given a summary on our theoretical predictions of three kinds of topological semimetals (TSMs), namely, Dirac semimetal (DSM), Weyl semimetal (WSM) and node-line semimetal (NLSM). TSMs are new states of quantum matter, which are different from topological insulators. They are characterized by the topological stability of the Fermi surface, whether it encloses band crossing points, i.e. Dirac cone-like energy nodes, or not. They are distinguished from each other by the degeneracy and momentum space distribution of the nodal points. To realize these intriguing topological quantum states is quite challenging and crucial to both fundamental science and future application. Na3Bi and Cd3As2 were theoretically predicted to be DSM in 2012 and 2013 respectively. Their experimental verification in 2014 have ignited intensive studies on TSMs. The subsequent theoretical prediction of a nonmagnetic WSM in the TaAs family stimulated a second wave and many experimental works were released out in 2015. In 2014, a kind of three dimensional crystal of carbon was proposed to be an NLSM due to negligible spin-orbit coupling and coexistence of time-reversal and inversion symmetry. Though the final experimental confirmation of NLSM is still missing, there have been several theoretical proposals, including Cu3PdN from us. In the final part, we have summarized the whole family of TSMs and their relationships.