Strong and Fragile Topological Dirac Semimetals with Higher-Order Fermi Arcs

Abstract

Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related to the bulk Dirac points, raising the question of whether there exists a topological bulk-boundary correspondence for Dirac semimetals. In this work, we discover that strong and fragile topological Dirac semimetals exhibit 1D higher-order hinge Fermi arcs (HOFAs) as universal, direct consequences of their bulk 3D Dirac points. To predict HOFAs coexisting with topological surface states in solid-state Dirac semimetals, we introduce and layer a spinful model of an $s-d$-hybridized quadrupole insulator (QI). We develop a rigorous nested Jackiw-Rebbi formulation of QIs and HOFA states. Employing $abinitio$ calculations, we demonstrate HOFAs in both the room- ($\alpha$) and intermediate-temperature (${\alpha }^{\prime \prime }$) phases of Cd${}_3$As${}_2$, KMgBi, and rutile-structure (${\beta }^{\prime }$-) PtO${}_2$.

arXiv commentPost Final Version, 12 + 73 pages, 5 + 26 figures. Revtex version updated, minor formatting changes. Sign error corrected in Eq. (D16) and Figs. 8 and 10 replotted with updated parameters, results and conclusions unaffected by this correction. Nested Wilson loop code with example scripts and documentation freely available at https://github.com/kuansenlin/nested_and_spin_resolved_Wilson_loop

References in corpus (55)

• The electronic properties of graphene
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Topological Insulators with Inversion Symmetry
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Topological Crystalline Insulators
• Quantized Electric Multipole Insulators
• Periodic table for topological insulators and superconductors
• Three Dimensional Dirac Semimetal and Quantum Transports in Cd3As2
• Higher-Order Topological Insulators
• Topological quantum chemistry
• On-surface synthesis of graphene nanoribbons with zigzag edge topology
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Reflection symmetric second-order topological insulators and superconductors
• Observation of a phononic quadrupole topological insulator
• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
• Higher-Order Topology in Bismuth
• Dirac Line Nodes in Inversion Symmetric Crystals
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• Topological quantum properties of chiral crystals
• Multiple types of topological fermions in transition metal silicides
• Large Fermi Arcs in Unconventional Weyl Semimetal RhSi
• Transport evidence for Fermi-arc mediated chirality transfer in the Dirac semimetal Cd${}_3$As${}_2$
• Discovery of topological chiral crystals with helicoid arc states
• Fragile Topology and Wannier Obstructions
• New classes of chiral topological nodes with non-contractible surface Fermi arcs in CoSi
• Double Dirac Semimetals in Three Dimensions
• Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides XTe${}_2$ (X=Mo,W)
• Quantitative mappings between symmetry and topology in solids
• Observation of Chiral Fermions with a Large Topological Charge and and Associated Fermi-Arc Surface States in CoSi
• Chiral Topological Semimetal with Multifold Band Crossings and Long Fermi arcs
• Generalized Electromagnetism of Subdimensional Particles: A Spin Liquid Story
• Cd3As2 is Centrosymmetric
• Higher Order Topological Phases: A General Principle of Construction
• Topological Quadrupolar Semimetals
• Are the double Fermi arcs of Dirac semimetals topologically protected?
• Tunable Weyl and Dirac states in the nonsymmorphic compound $\mathbf{CeSbTe}$
• Wallpaper Fermions and the Nonsymmorphic Dirac Insulator
• Rotation Anomaly and Topological Crystalline Insulators
• Topology of Disconnected Elementary Band Representations
• Disconnected Elementary Band Representations, Fragile Topology, and Wilson Loops as Topological Indices: An Example on the Triangular Lattice
• Crystal Field Effect Induced Topological Crystalline Insulators In Monolayer IV-VI Semiconductors
• Edge modes in band topological insulators
• Observation of Dirac-like energy band and ring-torus Fermi surface associated with the nodal line in topological insulator CaAgAs
• Second-order Dirac superconductors and magnetic field induced Majorana hinge modes
• Smooth gauge for topological insulators
• Type-II Dirac semimetals in the YPd${}_2$Sn class
• Three-dimensional Critical Dirac semimetal in KMgBi
• Basal-plane growth of cadmium arsenide by molecular beam epitaxy
• Crystalline topological Dirac semimetal phase in rutile structure ${\beta }^{\prime }$-PtO${}_2$
• Physical properties of KMgBi single crystals

Cited by in corpus (137)

• Progress and prospects in magnetic topological materials
• High-throughput calculations of magnetic topological materials
• Magnetic Topological Quantum Chemistry
• All Topological Bands of All Nonmagnetic Stoichiometric Materials
• Topological Materials Discovery from Crystal Symmetry
• Higher-Order Weyl Semimetals
• Higher-order topological semimetal in acoustic crystals
• Higher-order Weyl Semimetals
• Boundary-obstructed topological phases
• Quadrupole Topological Photonic Crystals
• Chiral-Symmetric Higher-Order Topological Phases of Matter
• Topological Semimetal Nanostructures: From Properties to Topotronics
• Boundary criticality of $PT$-invariant topology and second-order nodal-line semimetals
• Higher-order topological phases in tunable $C_3$-symmetric photonic crystals
• Topological correspondence between magnetic space group representations
• Second-Order Real Nodal-Line Semimetal in Three-Dimensional Graphdiyne
• Higher-order Dirac sonic crystals
• On-chip higher-order topological micromechanical metamaterials
• Higher-order topological phases on fractal lattices
• Hierarchy of higher-order Floquet topological phases in three dimensions
• On the robustness of topological corner modes in photonic crystals
• Acoustic Higher-Order Weyl Semimetal with Bound Hinge States in the Continuum
• Vortex states in an acoustic Weyl crystal with a topological lattice defect
• Higher-Order Topological Dirac Superconductors
• Higher-Order Weyl-Exceptional-Ring Semimetals
• Higher-order topological insulators and semimetals in generalized Aubry-André-Harper models
• Higher-order Dirac Semimetal in a Photonic Crystal
• Spin-Resolved Topology and Partial Axion Angles in Three-Dimensional Insulators
• Quadrupole topological insulators in Ta2M3Te5 (M= Ni, Pd) monolayers
• Field-Tunable One-Sided Higher-Order Topological Hinge States in Dirac Semimetals
• Six-fold Excitations in Electrides
• Non-Hermitian Floquet second order topological insulators in periodically quenched lattices
• Reducing electronic transport dimension to topological hinge states by increasing geometry size of Dirac semimetal Josephson junctions
• Bulk-corner correspondence of time-reversal symmetric insulators: deduplicating real-space invariants
• Filling anomaly for general 2D and 3D $C_4$ symmetric lattices
• Subdimensional topologies, indicators and higher order phases
• Type-II quadrupole topological insulators
• Weyl nodes with higher-order topology in an optically driven nodal-line semimetal
• Experimental observation of non-Abelian earring nodal links in phononic crystals
• Higher-order topology in monolayer graphene
• From triple-point materials to multiband nodal links
• Topological Zero-Dimensional Defect and Flux States in Three-Dimensional Insulators
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Floquet Weyl semimetal phases in light-irradiated higher-order topological Dirac semimetals
• Topological States in Generalized Electric Quadrupole Insulators
• Anomalous Quadrupole Topological Insulators in 2D Nonsymmorphic Sonic Crystals
• Stiefel-Whitney topological charges in a three-dimensional acoustic nodal-line crystal
• Axionic Band Topology in Inversion-Symmetric Weyl-Charge-Density Waves
• Higher-order topological Anderson insulators in quasicrystals
• Symmetry Indicators for Inversion-Symmetric Non-Hermitian Topological Band Structures
• Tunable Fragile Topology in Floquet Systems
• The Global Phase Diagram of disordered Higher-order Weyl Semimetals
• Piezoelectricity and Topological Quantum Phase Transitions in Two-Dimensional Spin-Orbit Coupled Crystals with Time-Reversal Symmetry
• Classification of Dirac points with higher-order Fermi arcs
• Deterministic chaos and fractal entropy scaling in Floquet CFT
• Symmetry-enforced topological band crossings in orthorhombic crystals: Classification and materials discovery
• Non-Abelian tensor Berry connections in multi-band topological systems
• Multiple magnetism controlled topological states in EuAgAs
• Engineering exotic second-order topological semimetals by periodic driving
• Unquantized anomalies in topological semimetals
• Dirty higher-order Dirac semimetal: Quantum criticality and bulk-boundary correspondence
• Topology invisible to eigenvalues in obstructed atomic insulators
• Chiral Dirac-like fermion in spin-orbit-free antiferromagnetic semimetals
• Topological classification of Higher-order topological phases with nested band inversion surfaces
• Engineering second-order topological insulators via coupling two first-order topological insulators
• First principles theory of Dirac semimetal Cd${}_3$As${}_2$ under Zeeman magnetic field
• Wannier Function Methods for Topological Modes in 1D Photonic Crystals
• Quasicrystalline second-order topological semimetals
• Nodal higher-order topological superconductivity from a ${\mathcal{C}}_4$-symmetric Dirac semimetal
• Surface Bogoliubov-Dirac cones and helical Majorana hinge modes in superconducting Dirac semimetals
• Density-driven higher-order topological phase transitions in amorphous solids
• Universal higher-order bulk-boundary correspondence of triple nodal points
• Interacting second-order topological insulators in one-dimensional fermions with correlated hopping
• Topological hinge modes in Dirac semimetals
• Higher-order topological superconductors from Weyl semimetals
• Hinge mode dynamics of periodically driven higher-order Weyl semimetals
• Dynamics of self-dual kagome metamaterials and the emergence of fragile topology
• Tunable Dirac Semimetals with Higher-order Fermi Arcs in Kagome Lattices Pd${}_3$Pb${}_2$X${}_2$ (X = S, Se)
• Embedded Topological Semimetals
• Dephasing enhanced strong Majorana zero modes in 2D and 3D higher-order topological superconductors
• Symmetry indicators in commensurate magnetic flux
• Engineering second-order nodal-line semimetals by breaking $\mathcal{P}\mathcal{T}$ symmetry and periodic driving
• Higher-order topological semimetals and nodal superconductors with an order-two crystalline symmetry
• Higher-order Topological Insulators and Semimetals in Three Dimensions without Crystalline Counterparts
• Topological nature of higher-order hinge states revealed by spin transport
• Effective action approach to the filling anomaly in crystalline topological matter
• Stable Higher-Order Topological Dirac Semimetals with ${\mathbb{Z}}_2$ Monopole Charge in Alternating-twisted Multilayer Graphenes and beyond
• Universal Higher-Order Topology from 5D Weyl semimetal: Edge topology, edge Hamiltonian and nested Wilson loop
• Topological Electromagnetic Effects and Higher Second Chern Numbers in Four-Dimensional Gapped Phases
• Wannier Topology and Quadrupole Moments for a generalized Benalcazar-Bernevig-Hughes Model
• Dipolar Weyl semimetals
• Magnetic field filtering of the hinge supercurrent in unconventional metal NiTe${}_2$-based Josephson junctions
• Dynamical Fragile Topology in Floquet Crystals
• Floquet higher-order topological phases in momentum space
• Rotoinversion-symmetric bulk-hinge correspondence and its applications to higher-order Weyl semimetals
• Majorana corner modes in unconventional monolayers of the 1T-PtSe2 family
• Crystalline-electromagnetic responses of higher order topological semimetals
• Multi higher-order Dirac and nodal line semimetals
• Berry-dipole Semimetals
• Simulating Higher-Order Topological Insulators in Density Wave Insulators
• Observation of the Critical State to Multiple-Type Dirac Semimetal Phases in KMgBi
• Topological Insulators with Hybrid-order Boundary States
• Engineering rich two-dimensional higher-order topological phases by flux and periodic driving
• Discovery of topological metamaterials by symmetry relaxation and smooth topological indicators
• Fractional corner charges in threefold-symmetric two-dimensional materials with fragile topology
• Tunneling in an anisotropic cubic Dirac semi-metal
• Fermionic tensor networks for higher order topological insulators from charge pumping
• Encyclopedia of emergent particles in three-dimensional crystals
• Tailoring higher-order topological phases via orbital hybridization
• Corner states of two-dimensional second-order topological insulators with a chiral symmetry and broken time reversal and charge conjugation
• Family of third-order topological insulators from Su-Schrieffer-Heeger stacking
• Generalization of the Nested Wilson Loop Formalism in Topological Dirac Semimetals with Higher-order Fermi Arcs
• Tunable chiral symmetry breaking in symmetric Weyl materials
• Omnidirectional domain wall modes protected by fragile topological states
• Double Majorana Vortex Flat Bands in the Topological Dirac Superconductor
• Tunneling phase diagrams in anisotropic Multi-Weyl semimetals
• IrRep: symmetry eigenvalues and irreducible representations of ab initio band structures
• Fragmented exceptional points and their bulk and edge realizations in lattice models
• Hinge Majorana Flat Band in Type-II Dirac Semimetals
• Fragile topology in nodal-line semimetal superconductors
• Higher-Order Topological Systems and Their Sub-Symmetry-Protected Topology
• Topological semimetal with coexisting nodal points and nodal lines
• Cubic Dirac Semimetals: General Theory and Application to Rare-Earth Magnets
• Spinless topological chirality from Umklapp scattering in twisted 3D structures
• Correlated second-order Dirac semimetals with Coulomb interactions
• Topological insulators and geometry of vector bundles
• Antichiral edge states and Bogoliubov Fermi surfaces in a two-dimensional proximity-induced superconductor
• Nodal higher-order topological superconductivity from C6-symmetric Dirac semimetals
• Unveiling Topological Hinge States in the Higher-Order Topological Insulator WTe${}_2$ Based on the Fractional Josephson Effect
• Topological Optical Pseudospin Injection Beyond Weyl Semimetals
• Fractional ac Josephson effect as evidence of topological hinge states in a Dirac semimetal NiTe2
• Chiral Anomaly Induced Transverse Planar Transport Phenomena in Three Dimensional Spin-Orbit Coupled Metals
• Group Structure of Wilson Loops in 2D Models with 2- and 4-Band Energy Spectra
• Electronic structure and hinge states of strained half-Heusler compounds LiSbZn and LiBiZn
• Non-Hermitian Higher-Order Dirac Semimetals
• Non-Hermitian Higher-Order Weyl Semimetals
• Uncovering surface states of the Dirac semimetal BaMg2Bi2