Noncentrosymmetric topological Dirac semimetals in three dimensions

Abstract: Topological Dirac semimetals are a class of semimetals that host symmetry-protected Dirac points near the Fermi level, which arise due to a band inversion of the conduction and valence bands. In this work, we study the less explored class of \emph{noncentrosymmetric} topological Dirac semimetals in three dimensions. We identify the noncentrosymmetric crystallographic point groups required to stabilize fourfold degenerate band crossings and derive model Hamiltonians for all distinct types of band inversions allowed by symmetry. Using these model Hamiltonians, which emphasize the physical nature of the allowed couplings, we establish the generic electronic phase diagram noncentrosymmetric Dirac semimetals and show that it generically includes phases with coexistent Weyl point nodes or Weyl line nodes. In particular, for one specific type of band inversion in sixfold symmetric systems we show that Weyl line nodes are always present. Based on first-principles calculations, we predict that BiPd$2$O$_4$ is a noncentrosymmetric Dirac semimetal under 20 Gpa pressure and hosts topological type-II Dirac points on the fourfold rotation axis. Furthermore, we propose that the hexagonal polar alloy LiZnSb${x}$Bi$_{1-x}$ realizes a Dirac semimetal with coexistent Weyl points. Interestingly, the emergence and location of the Weyl points is highly tunable and can be controlled by the alloy concentration $x$. More generally, our results not only establish band-inverted noncentrosymmetric systems as a broad and versatile class of topological semimetals, but also provide a framework for studying the quantum nonlinear Hall effect and nonlinear optical properties in the Dirac semimetals.