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

The discoveries of Dirac and Weyl semimetal states in spin-orbit compounds led to the realizations of elementary particle analogs in table-top experiments. In this paper, we propose the concept of a three-dimensional type-II Dirac fermion and identify a new topological semimetal state in the large 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-violating type-II Dirac nodes and that each Dirac node consists of four type-II Weyl nodes with chiral charge +/-1 via symmetry breaking. Furthermore, we predict the Landau level spectrum arising from the type-II Dirac fermions in VAl3 that is distinct from that of known Dirac semimetals. We also show a topological phase transition from a type-II Dirac semimetal to a quadratic Weyl semimetal or a topological crystalline insulator via crystalline distortions. The new type-II Dirac fermions, their novel magneto-transport response, the topological tunability and the large number of compounds make VAl3 an exciting platform to explore the wide-ranging topological phenomena associated with Lorentz-violating Dirac fermions in electrical and optical transport, spectroscopic and device-based experiments.