Type-II Symmetry-Protected Topological Dirac Semimetals

The discoveries of Dirac and Weyl semimetal states in real materials led to the realizations of elementary particle analogs in table-top experiments. Recently, a new type of Weyl fermion attracted interest because it strongly violates Lorentz symmetry whose analog does not exist in the Standard Model. While this state has been dubbed the type-II Weyl semimetal and predicted in a number of materials, its Dirac counterpart has remained elusive. In this work, we propose the concept of the type-II Dirac fermion and theoretically identify this new state in MA$_3$ (M=V, Nb, Ta; A=Al, Ga, In) [1]. We show that the VAl$_3$ family features a pair of type-II Dirac nodes and that each Dirac node consists of four type-II Weyl nodes via symmetry breaking. Furthermore, we predict the Landau level spectrum arising from the type-II Dirac fermions in VAl$_3$ that is distinct from that of known Dirac/Weyl semimetals. We also show a topological phase transition from a type-II Dirac to a quadratic Weyl or a topological crystalline insulator via crystalline distortions.\\ $[1]$ T.-R. Chang et al., arXiv:1606.07555