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The discoveries of Dirac and Weyl semimetal states in spin-orbit compoundsled to the realizations of elementary particle analogs in table-topexperiments. In this paper, we propose the concept of a three-dimensionaltype-II Dirac fermion and identify a new topological semimetal state in thelarge family of transition-metal icosagenides, MA3 (M=V, Nb, Ta; A=Al, Ga, In).We show that the VAl3 family features a pair of strongly Lorentz-violatingtype-II Dirac nodes and that each Dirac node consists of four type-II Weylnodes with chiral charge +/-1 via symmetry breaking. Furthermore, we predictthe Landau level spectrum arising from the type-II Dirac fermions in VAl3 thatis distinct from that of known Dirac semimetals. We also show a topologicalphase transition from a type-II Dirac semimetal to a quadratic Weyl semimetalor a topological crystalline insulator via crystalline distortions. The newtype-II Dirac fermions, their novel magneto-transport response, the topologicaltunability and the large number of compounds make VAl3 an exciting platform toexplore the wide-ranging topological phenomena associated withLorentz-violating Dirac fermions in electrical and optical transport,spectroscopic and device-based experiments.

Type-II Topological Dirac Semimetals: Theory and Materials Prediction (VAl3 family)