Classification of stable three-dimensional Dirac semimetals with nontrivial topology

Abstract

A three-dimensional (3D) Dirac semimetal is the 3D analog of graphene whose bulk band shows a linear dispersion relation in the 3D momentum space. Since each Dirac point with four-fold degeneracy carries a zero Chern number, a Dirac semimetal can be stable only in the presence of certain crystalline symmetries. In this work, we propose a general framework to classify stable 3D Dirac semimetals. Based on symmetry analysis, we show that various types of stable 3D Dirac semimetals exist in systems having the time-reversal, inversion, and uniaxial rotational symmetries. There are two distinct classes of stable 3D Dirac semimetals. In the first class, a pair of 3D Dirac points locate on the rotation axis, away from its center. Moreover, the 3D Dirac semimetals in this class have nontrivial topological properties characterized by 2D topological invariants, such as the $Z_2$ invariant or the mirror Chern number. These 2D topological indices give rise to stable 2D surface Dirac cones, which can be deformed to Fermi arcs when the surface states couple to the bulk states on the Fermi level. On the other hand, the second class of Dirac SM phases possess a 3D Dirac point at a time-reversal invariant momentum (TRIM) on the rotation axis and do not have surface states in general.

27 pages, 3 figures, 2 tables

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• Filling-enforced Dirac loops and their evolutions under various perturbations
• Electron-phonon superconductivity in C-doped topological nodal-line semimetal Zr${}_5$Pt${}_3$: A muon spin rotation and relaxation ($\mu$SR) study
• Two-dimensional Peierls instability via zone boundary Dirac line nodes in layered perovskite oxides
• Electronic and magnetic properties of the topological semimetal SmMg${}_2$Bi${}_2$
• Existence of Dirac cones in Brillouin zone of diperiodic atomic crystals according to group theory
• Non-local signatures of the chiral magnetic effect in Dirac semimetal Bi${}_{0.97}$Sb${}_{0.03}$
• Renormalized quasiparticles, topological monopoles and superconducting line nodes in heavy fermion CeTX${}_3$ compounds
• Dual topological superconducting states in the layered titanium-based oxypnictide superconductor BaTi${}_2$Sb${}_2$O
• Tuning Dirac nodes with correlated d-electrons in BaCo_{1-x}Ni_{x}S_{2}
• Symmetry-protected Spinful Magnetic Weyl Nodal Loops and Multi-Weyl Nodes in $5d^n$ Cubic Double Perovskites $(n=1,2)$
• Identification of strongly interacting organic semimetals
• Transverse Chiral Magnetic Photocurrent Induced by Linearly Polarized Light in Mirror-Symmetric Weyl Semimetals
• Evidence of 3D Dirac conical bands in TlBiSSe by optical and magneto-optical spectroscopy
• Novel Family of Topological Semimetals with Butterfly-like Nodal Lines
• Large Fermi-arc and robust Weyl semimetal phase in Ag${}_2$S
• Semi-Quantized Spin Pumping and Spin-Orbit Torques in Topological Dirac Semimetals
• Spin-orbital magnetic response of relativistic fermions with band hybridization
• Surface states in Dirac metals and topological crystalline insulators
• Non-Abelian properties of electron wave packets in Dirac semimetals A${}_3$Bi (A=Na,K,Rb)
• A new length scale, and modified Einstein-Cartan-Dirac equations for a point mass
• Classification of Weyl points and nodal lines based on magnetic point groups for spin-$\frac{1}{2}$ quasiparticles
• Nonsymmorphic Dirac semimetal and carrier dynamics in doped spin-orbit-coupled Mott insulator Sr${}_2$IrO${}_4$
• Weyl nodes and magnetostructural instability in antiperovskite Mn${}_3$ZnC
• Dual topological nodal line and nonsymmorphic Dirac semimetal in three dimensions
• Larkin-Ovchinnikov state of superconducting Weyl metals: Fundamental differences between pairings restricted and extended in the $\text{k}$-space
• Topological antiferromagnetic spintronics: Part of a collection of reviews on antiferromagnetic spintronics
• Mirror anomaly and anomalous Hall effect in type-I Dirac semimetals
• Dirac energy spectrum and inverted band gap in metamorphic InAsSb/InSb superlattices
• Cubic Dirac and quadruple Weyl points in screw-symmetric materials
• Helical currents in metallic Rashba strips
• Pressure Effect on Band Inversion in AECd2As2
• Topological Dirac Semimetal Phase in Bismuth Based Anode Materials for Sodium-Ion Batteries
• Hydrodynamics of topological Dirac semi-metals with chiral and ${\mathbb{Z}}_2$ anomalies
• Evidence for Half-Quantized Chiral Edge Current in a C = 1/2 Parity Anomaly State
• Electronic properties of the Dirac and Weyl systems with first- and higher-order dispersion in non-Fermi-liquid picture
• Symmetry-enforced planar nodal chain phonons in non-symmorphic materials
• Nodal lines and mapping to mirror Chern numbers in Ca${}_2$As family
• Towards the theory of types III and IV non-Hermitian Weyl fermions
• Type-II Topological Dirac Semimetals: Theory and Materials Prediction (VAl3 family)
• Soft Modes and Nonanalyticities in a Clean Dirac Metal
• Positive longitudinal spin magnetoconductivity in ${\mathbb{Z}}_2$ topological Dirac semimetals
• Multi-type Dirac fermions protected by orthogonal glide symmetries in a noncentrosymmetric system
• Monopole versus spherical harmonic superconductors: Topological repulsion, coexistence and stability
• Topological gapless points in superconductors: From the viewpoint of symmetry
• Effect of incommensurate potential on nodal-link semimetals
• Orbit topology analysed from $\pi$ phase shift of magnetic quantum oscillations in three-dimensional Dirac semimetal
• Electrically tunable Kondo effect as a direct measurement of the chiral anomaly in disorder Weyl semimetals
• 3D Topological Plasmons in Weyl Semimetals
• Topological Fermi-arc surface resonances in bcc iron
• Nodeless time-reversal symmetry breaking in the centrosymmetric superconductor Sc${}_5$Co${}_4$Si${}_{10}$ probed by muon-spin spectroscopy
• Crystal-symmetry-protected gapless vortex-line phases in superconducting Dirac semimetals
• Topological Critical Materials of Ternary Compounds
• Tunneling in an anisotropic cubic Dirac semi-metal
• Fate of Weyl semimetals in the presence of incommensurate potentials
• Unconventional topological phase transition from semimetal to insulator in SnBi2Te4: Role of anomalous thermal expansion
• Triply degenerate nodal lines in topological and non-topological metals
• Electron Currents from Gradual Heating in Tilted Dirac Cone Materials
• Magnetotransport of Weyl semimetals with ${\mathbb{Z}}_2$ topological charge and chiral anomaly
• Characterization of Lifshitz transitions in topological nodal line semimetals
• Linear Magnetoresistance and Type-I Superconductivity in $\beta$-IrSn${}_4$
• Merging of momentum-space monopoles by controlling magnetic field: From cubic-Dirac to triple-Weyl fermion systems
• Evidence for three-dimensional Dirac semimetal state in strongly correlated organic quasi-two-dimensional material
• Observation of Fermi Arc Surface States in a Topological Metal: A New Type of 2D Electron Gas beyond Z2 Topological Insulators
• Absence of metallicity and bias-dependent resistivity in low-carrier-density EuCd2As2
• Ultrafast Spectroscopy of Dirac Semimetal Cd3As2 under Pressure
• On Anderson Localization and Chiral Anomaly in Disordered Time-Reversal Invariant Weyl Semimetals: Nonperturbative and Berry Phase Effects
• Generalization of the Nested Wilson Loop Formalism in Topological Dirac Semimetals with Higher-order Fermi Arcs
• Long-range spin transport on the surface of topological Dirac semimetal
• Robustness of the semimetal state of Na3Bi and Cd3As2 against Coulomb interaction
• Emergence of Topological Superconductivity in Doped Topological Dirac Semimetals under Symmetry-Lowering Lattice Distortions
• Probing mirror anomaly and classes of Dirac semimetals with circular dichroism
• Encyclopedia of emergent particles in three-dimensional crystals
• Topological phases in $\alpha$-Li${}_3$N-type crystal structure of light-element compounds
• Low-lying Electronic Structure of Rare-Earth Based Topological Nodal Line Semimetal Candidate DySbTe
• Laser induced surface magnetization in Floquet-Weyl semimetals
• $Z_2$ Dirac points with topologically protected multihelicoid surface states
• Model non-Hermitian topological operators without skin effect: A general principle of construction
• Ideal Spin-Orbit-Free Dirac Semimetal and Diverse Topological Transitions in Pr${}_8$CoGa${}_3$ Family
• Topological Enhancement of Nonlinear Transports in Unconventional Point-Node Semimetals
• Parallel and anti-parallel helical surface states for topological semimetals
• Prediction of topological superconductivity in 1$T$-TiTe${}_2$ under pressure
• Tunneling phase diagrams in anisotropic Multi-Weyl semimetals
• Pressure-induced reconstructive phase transition in Cd${}_3$As${}_2$
• Tunable chiral symmetry breaking in symmetric Weyl materials
• Characteristic singular behaviors of nodal line materials emerging in orbital magnetic susceptibility and Hall conductivity
• Stable halogen 2D Materials: the case of iodine and astatine
• Inverse Faraday effect in massive Dirac electrons
• Correlated Fractional Dirac Materials
• Representation Theory for Massless Quasiparticles in Bogoliubov-de Gennes Systems
• Interplay of magnetism and band topology in Eu${}_{1-x}$Ca${}_x$Mg${}_2$Bi${}_2$ (x=0, 0.5) from first principles study
• Morse theory study on the evolution of nodal lines in $\mathcal{P}\mathcal{T}$-symmetric nodal-line semimetals
• Distinct quasiparticle interference patterns for surface impurity scattering on various Weyl semimetals
• Signature of nodal topology in nonlinear quantum transport across junctions in Weyl and multi-Weyl semimetals
• Topological nonsymmorphic insulator versus Dirac semimetal in KZnBi
• Collective excitations and screening in two-dimensional tilted nodal-line semimetals
• Phase diagram and critical behavior of Hubbard model on the square-hexagon-octagon lattice
• Pressuring the low-temperature orthorhombic phase with a non-trivial topological state of Ru2Sn3 to room temperature
• Emergence of topological phases from the extension of two-dimensional lattice with nonsymmorphic symmetries
• Fate of superconductivity in disordered Dirac and semi-Dirac semimetals
• Higher-Order Topological Systems and Their Sub-Symmetry-Protected Topology
• Three-Dimensional Topological Semimetal/Insulator States in α-Type Organic Conductors with Interlayer Spin-Orbit Interaction
• A topological Hund nodal line antiferromagnet
• Fermi surface and light quasi particles in hourglass nodal chain metal \b{eta}-ReO2
• Superconducting topological Dirac semimetals: $P6/m$-Si${}_6$ and $P6/m$-NaSi${}_6$
• Unremovable linked nodal structures protected by crystalline symmetries in stacked bilayer graphene with Kekulé texture
• Emergent topological states via digital (001) oxide superlattices
• Spin susceptibilities in magnetic type-I and type-II Weyl semimetals
• Correlated interaction effects in three-dimensional semi-Dirac semimetal
• Antiferromagnetism and spin density waves in 3D Dirac semimetals
• Dirac state switching in transition metal diarsenides
• Non-trivial topological valence bands of common diamond and zinc-blende semiconductors
• Selective branching, quenching, and converting of topological modes
• Constraints on proximity-induced ferromagnetism in a Dirac semimetal (Cd${}_3$As${}_2$)/ferromagnetic semiconductor (Ga${}_{1-x}$Mn${}_x$Sb) heterostructure
• Anomalous Linear and Quadratic Nodeless Surface Dirac Cones in Three-Dimensional Dirac Semimetals
• Nodal lines and boundary modes in topological Dirac semimetals with magnetism
• Topological Aspects of Antiferromagnets
• Candidate entanglement invariants for two Dirac spinors
• Tuning nodal line semimetals in trilayered systems
• Realization of Hopf-link structure in phonon spectra: Symmetry guidance and High-throughput investigation
• Existence of nodal-arc and its evolution into Weyl-nodes in the presence of spin-orbit coupling in TaAs & TaP
• Cubic Dirac Semimetals: General Theory and Application to Rare-Earth Magnets
• Symmetry-enforced three-dimensional Dirac phononic crystals
• Magneto-thermoelectricty of anisotropic two-dimensional materials
• Electronic Structure of a Nodal Line Semimetal Candidate TbSbTe
• Floquet-Weyl semimetals generated by an optically resonant interband-transition
• Anisotropic marginal Fermi liquid for Coulomb interacting generalized Weyl fermions
• Global phase diagram of Coulomb-interacting anisotropic Weyl semimetals with disorder
• Topological Optical Pseudospin Injection Beyond Weyl Semimetals
• Electronic band structure of a nodal line semimetal candidate ErSbTe
• Longitudinal magnetoconductivity and magnetodielectric effect in bilayer graphene
• Possible Topological Superconductivity in a Topological Crystalline Insulator (Pb${}_{1-x}$Sn${}_x$)${}_{1-y}$In${}_y$Te
• Topological Fermi-arc-like surface states in Kramers nodal line metals
• Majorana Flat Bands in the Vortex Line of Superconducting Weyl Semimetals
• Low degree Lorentz invariant polynomials as potential entanglement invariants for multiple Dirac spinors
• Intrinsic spin Nernst effect in topological Dirac and magnetic Weyl semimetals
• Axionic quantum criticality of generalized Weyl semimetals
• Exact solutions of Kondo problems in higher-order fermions
• Signature of topological crystalline insulating behavior in new B2X2Zn (X=Ir, Rh, Co) compound from first-principles Computation
• Quantized Spin Hall Effect in Three-Dimensional Nodal-Ring Semimetal: Geometric Scaling and Symmetry-Engineered Spin Response
• Correlated Dirac semimetal states in nonsymmorphic MIrO${}_3$ (M=Sr, Ba and Ca)
• Anomalous transport in Kane fermions
• Chiral Anomaly Induced Transverse Planar Transport Phenomena in Three Dimensional Spin-Orbit Coupled Metals
• Tunable SSH model in ferromagnetic systems
• Non-adiabatic corrections to chiral charge pumping in topological nodal semimetals
• Tunable spin-charge conversion in class-I topological Dirac semimetals
• Discovery of ideal Weyl points with helicoid surface states
• Three-nodal surface phonons in solid-state materials: Theory and material realization
• Elemental topological Dirac semimetal α-Sn with high quantum mobility
• A Raman Probe of Phonons and Electron-phonon Interactions in NbIrTe4