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.

arXiv comment17 pages, 10 figures

References in corpus (58)

• Topological Insulators
• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Topological Insulators with Inversion Symmetry
• Wannier90: A Tool for Obtaining Maximally-Localised Wannier Functions
• Type-II Weyl Semimetals
• Discovery of a Three-dimensional Topological Dirac Semimetal, Na3Bi
• Topological Crystalline Insulators
• Dirac semimetal and topological phase transitions in A3Bi (A=Na, K, Rb)
• Dirac semimetal in three dimensions
• Experimental discovery of Weyl semimetal TaAs
• Three Dimensional Dirac Semimetal and Quantum Transports in Cd3As2
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials
• An equivalent expression of Z2 Topological Invariant for band insulators using Non-Abelian Berry's connection
• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
• Magnetic Weyl Semimetal Phase in a Kagome Crystal
• Dirac Line Nodes in Inversion Symmetric Crystals
• Topological Nodal Line Semimetal and Dirac Semimetal State in Antiperovskite Cu${}_3$PdN
• Observation of the nonlinear Hall effect under time reversal symmetric conditions
• Topological Node-Line Semimetal in Three Dimensional Graphene Networks
• Topological nodal line semimetals
• Multi-Weyl Topological Semimetals Stabilized by Point Group Symmetry
• Computing topological invariants without inversion symmetry
• Band structure engineering in (Bi1-xSbx)2Te3 ternary topological insulators
• Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals
• Topological Semimetals Predicted from First-principles Calculations
• Experimental Observation of Three-Component 'New Fermions' in Topological Semimetal MoP
• Double Dirac Semimetals in Three Dimensions
• Nodal surface semimetals: Theory and material realization
• Berry Curvature Enhanced Nonlinear Photogalvanic Response of Type-II Weyl Cone
• Node-Surface and Node-Line Fermions From Nonsymmorphic Lattice Symmetries
• Type-II Dirac fermions in the PtSe${}_2$ class of transition metal dichalcogenides
• 3D Dirac semimetals: current materials, design principles and predictions of new materials
• Topological Semimetals from first-principles
• Weyl semimetals from noncentrosymmetric topological insulators
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Unexpected mass acquisition of Dirac fermions at the quantum phase transition of a topological insulator
• Universal phase diagrams for the quantum spin Hall systems
• Predicted Realization of Cubic Dirac Fermion in Quasi-One-Dimensional Transition-Metal MonoChalcogenides
• Topological states from topological crystals
• Exploration and prediction of topological electronic materials based on first-principles calculations
• Emergence of topological semimetals in gap closing in semiconductors without inversion symmetry
• Hybrid Dirac Semimetal in CaAgBi Materials Family
• The Dirac-Weyl semimetal: Coexistence of Dirac and Weyl fermions in polar hexagonal $ABC$ crystals
• Classification of stable Dirac and Weyl semimetals with reflection and rotational symmetry
• Alloy engineering of topological semimetal phase transition in MgTa${}_{2-x}$Nb${}_x$N${}_3$
• Theory of topological quantum phase transitions in 3D noncentrosymmetric systems
• Dirac semimetal phase in the hexagonal LiZnBi
• Heart and diamond Fermi arcs in Pd and Pt oxide topological Dirac semimetals
• MgTa2N3: A new reference Dirac semimetal
• Ideal near-Dirac triple-point semimetal in III-V semiconductor alloys
• Influences of spin-orbit coupling on Fermi surfaces and Dirac cones in ferroelectric-like polar metals
• Multi-type Dirac fermions protected by orthogonal glide symmetries in a noncentrosymmetric system

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• Metamagnetism and anomalous magnetotransport properties in rare-earth-based polar semimetals $R$AuGe ($R=$ Dy, Ho, and Gd)
• Single crystal growths and magnetic properties of hexagonal polar semimetals RAuGe (R = Y, Gd-Tm, and Lu)
• Ideal Spin-Orbit-Free Dirac Semimetal and Diverse Topological Transitions in Pr${}_8$CoGa${}_3$ Family
• Tunable Dual-Type Weyl Points in Dirac-Weyl Semimetal CaAgBi
• Electronic structure and hinge states of strained half-Heusler compounds LiSbZn and LiBiZn