Composite Dirac Semimetal

In this work, we investigate the possibility to construct a new topological state, which may be regarded as a combination of a WTI and a Dirac semimetal, hence it may be termed as a composite Dirac semimetal (CDSM). We start with an effective model, which can be derived from a tight-binding model defined on a stacked honeycomb lattice. By analyzing the possible band ordering at the high symmetry points on the rotation axis, we show that a CDSM state can be realized, for which one pair of low-energy bands cross at the Fermi level to form two symmetry-protected Dirac points, whereas another pair of bands have inverted band ordering along the high symmetry path . The hallmark of this state is that on the side surfaces, a pair of Fermi arcs connecting the projected Dirac points coexist with a pair of helical Fermi loops traversing the surface Brillouin zone (BZ). Without breaking any symmetry, the CDSM may undergo a topological phase transition to an insulating state via a band inversion scenario, accompanied by two pairs of helical surface Fermi loops. Finally, by using first-principles calculations, we show that the discussed physics can be realized in a realistic material system.