Abstract:

Dirac semimetals have received extensive attention both experimentally and theoretically because of their novel electronic structures and transport properties. Topological Dirac semimetals have symmetry-protected Dirac points near the Fermi level, where the Dirac points are due to the formation of band inversions between the conduction and valence bands in solids. In this review, we introduce centrosymmetric topological Dirac semimetals and a new three-dimensional noncentrosymmetric topological Dirac semimetal. Through the analysis of crystal symmetry and energy band symmetry, one finds that crystals with C$_{\rm 4v}$ or C$_{\rm 6v}$ point groups can realize noncentrosymmetric topological Dirac semimetals. BiPd$_{2}$O$_{4}$ crystal with C$_{\rm 4v}$ point group is theoretically predicted to be noncentrosymmetric Dirac semimetals with topological type Ⅱ Dirac points on the C$_{\rm 4v}$ rotation axis. In addition, SrHgPb crystal and LiZnSb$_{x}$Bi$_{1-x}$ alloys with C$_{\rm 6v}$ point group are predicted to realize topological semimetals in which Dirac and Weyl points coexist, and the appearance and location of Weyl points in LiZnSb$_{x}$Bi$_{1-x}$ alloys can be regulated by the alloy concentration $x$. Compared with centrosymmetric topological Dirac semimetals, noncentrosymmetric topological Dirac semimetals have potential applications in nonlinear optics and nonlinear Hall transport due to the broken inversion symmetry.

Key words: noncentrosymmetric, Dirac semimetal, quantum material, material design