Higher-order topological insulators and superconductors protected by inversion symmetry

Abstract

We study surface states of topological crystalline insulators and superconductors protected by inversion symmetry. These fall into the category of "higher-order" topological insulators and superconductors which possess surface states that propagate along one-dimensional curves (hinges) or are localized at some points (corners) on the surface. We show that the surface states of higher-order topological insulators and superconductors can be thought of as globally irremovable topological defects and provide a complete classification of these inversion-protected phases in any spatial dimension for the ten symmetry classes by means of a layer construction. Furthermore, we discuss possible physical realizations of such states starting with a time-reversal invariant topological insulator (class AII) in three dimensions or a time-reversal invariant topological superconductor (class DIII) in two or three dimensions. The former can be used to build a three-dimensional second-order topological insulator which exhibits one-dimensional chiral or helical modes propagating along opposite edges, whereas the latter enables the construction of three-dimensional third-order or two-dimensional second-order topological superconductors hosting Majorana zero modes localized to two opposite corners. Being protected by inversion, such states are not pinned to a specific pair of edges or corners thus offering the possibility of controlling their location by applying inversion-symmetric perturbations such as magnetic field.

14 pages, 5 figures, 2 tables; published version

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Cited by in corpus (368)

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• Higher-order topological superconductors based on weak topological insulators
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• Pairing Obstructions in Topological Superconductors
• A Higher-Order Topological Insulator Phase in a Modulated Haldane Model
• Axionic Band Topology in Inversion-Symmetric Weyl-Charge-Density Waves
• Tenfold Topology of Crystals: Unified classification of crystalline topological insulators and superconductors
• Systematic generation of the cascade of anomalous dynamical first and higher-order modes in Floquet topological insulators
• Topological electronic structure and spin texture of quasi-one-dimensional higher-order topological insulator Bi4Br4
• Axion coupling in the hybrid Wannier representation
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• High-throughput Investigations of Topological and Nodal Superconductors
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• Majorana corner flat bands in two-dimensional second-order topological superconductors
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• Interaction Enabled Fractonic Higher-Order Topological Phases
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• Topology invisible to eigenvalues in obstructed atomic insulators
• Embedded Topological Insulators
• Superconductors with anomalous Floquet higher-order topology
• Time-reversal-invariant $C_2$-symmetric higher-order topological superconductors
• Generation of higher-order topological insulators using periodic driving
• Second-order topological corner states in zigzag graphene nanoflake with different types of edge magnetic configurations
• Fractional Chiral Hinge Insulator
• Corner- and sublattice-sensitive Majorana zero modes on the kagome lattice
• Topological classification of Higher-order topological phases with nested band inversion surfaces
• Quadrupole spin polarization as signature of second-order topological superconductors
• Controlling a quantum point junction on the surface of an antiferromagnetic topological insulator
• Boundary-obstructed topological phases of a massive Dirac fermion in a magnetic field
• Glide-symmetric magnetic topological crystalline insulators with inversion symmetry
• Klein-bottle quadrupole insulators and Dirac semimetals
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• Sublattice-enriched tunability of bound states in second-order topological insulators and superconductors
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• Boundary Topological Superconductors
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• Generalization of Benalcazar-Bernevig-Hughes model to arbitrary dimensions
• Majorana corner states on the dice lattice
• Floquet second-order topological Anderson insulator hosting corner localized modes
• The General Principle behind Magnetization-induced Second-Order Topological Corner States in the Kane-Mele Model
• Characterization and classification of interacting (2+1)D topological crystalline insulators with orientation-preserving wallpaper groups
• Mirror real Chern insulator in two and three dimensions
• Competition of First-Order and Second-Order Topology on the Honeycomb Lattice
• High-temperature Majorana corner modes in a $d+i{d}^{\prime }$ superconductor heterostructure: Application to twisted bilayer cuprate superconductors
• Topological phases of the dimerized Hofstadter butterfly
• Dynamic bulk-boundary correspondence for anomalous Floquet topology
• Embedded Topological Semimetals
• Higher-order topological semimetals and nodal superconductors with an order-two crystalline symmetry
• Magnetic Flux Periodicity in Second Order Topological Superconductors
• Topological crystalline insulators from stacked graphene layers
• Topological nature of higher-order hinge states revealed by spin transport
• Dirac cones and higher-order topology in quasi-continuous media
• Effects of Disorder On Thouless Pumping In Higher-Order Topological Insulators
• Spin, orbital, Weyl and other glasses in topological superfluids
• Third-order topological insulator induced by disorder
• Transport Induced Dimer State from Topological Corner States
• Topological phonon analysis of the 2D buckled honeycomb lattice: an application to real materials
• Towards a theory of surface orbital magnetization
• Topological Magnetoelectric Response in Ferromagnetic Axion Insulators
• Intertwined Weyl phases emergent from higher-order topology and unconventional Weyl fermions via crystalline symmetry
• Aharonov-Bohm Effect in Three-dimensional Higher-order Topological Insulator
• Multiple higher-order topological phases with even and odd pairs of zero-energy corner modes in a $C_3$ symmetry broken model
• Topological and dynamical features of periodically driven spin ladders
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• Topological insulators and higher-order topological insulators from gauge-invariant 1D lines
• Topological phases of an interacting Majorana Benalcazar-Bernevig-Hughes model
• Network model for higher-order topological phases
• Majorana-induced DC Shapiro steps in topological Josephson junctions
• Observation of the topological Dirac fermions and surface states in superconducting BaSn3
• Time evolution of Majorana corner modes in Floquet second-order topological superconductor
• Topological invariants beyond symmetry indicators: Boundary diagnostics for twofold rotationally symmetric superconductors
• Simulating Floquet topological phases in static systems
• Odd-Parity Spin-Triplet Superconductivity in Centrosymmetric Antiferromagnetic Metals
• Wannier Topology and Quadrupole Moments for a generalized Benalcazar-Bernevig-Hughes Model
• Unconventional Majorana fermions on the surface of topological superconductors protected by rotational symmetry
• Magnetic wallpaper Dirac fermions and topological magnetic Dirac insulators
• Higher-order topological superconductivity in a topological metal 1T${}^{\prime }$-MoTe${}_2$
• Anomalous levitation and annihilation in Floquet topological insulators
• Quasi-One-Dimensional Higher-Order Topological Insulators
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• Green's Function Approach to Interacting Higher-order Topological Insulators
• Protected Gapless Edge States In Trivial Topology
• Non-Hermitian skin effect enforced by nonsymmorphic symmetries
• Effect of local Coulomb interaction on Majorana corner modes: weak and strong correlation limits
• Tunable boson-assisted finite-range interaction and engineering Majorana corner modes in optical lattices
• Majorana corner modes and flat-band Majorana edge modes in superconductor/topological-insulator/superconductor junctions
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- Part I: Chiral number of zero-modes
• Multiorder topological superfluid phase transitions in a two-dimensional optical superlattice
• Classification of time-reversal symmetric topological superconducting phases for conventional pairing symmetries
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• Simulating Higher-Order Topological Insulators in Density Wave Insulators
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• Majorana corner pairs in a two-dimensional $s$-wave cold atomic superfluid
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• Effects of first- and second-order topological phases on equilibrium crystal shapes
• Magnetic impurities along the edge of a quantum spin Hall insulator: Realizing a one-dimensional AIII insulator
• Family of third-order topological insulators from Su-Schrieffer-Heeger stacking
• Majorana corner states in an attractive quantum spin Hall insulator with opposite in-plane Zeeman energy at two sublattice sites
• Model non-Hermitian topological operators without skin effect: A general principle of construction
• An index theorem for quarter-plane Toeplitz operators via extended symbols and gapped Invariants related to corner states
• Corner Modes and Ground-State Degeneracy in Models with Gauge-Like Subsystem Symmetries
• Electric polarization and discrete shift from boundary and corner charge in crystalline Chern insulators
• Exceptional second-order topological insulators
• Scattering theory of higher order topological phases
• Topological characteristics of gap closing points in nonlinear Weyl semimetals
• Higher-order topological superconductors characterized by Fermi level crossings
• Intrinsic (Axion) Statistical Topological Insulator
• Helical Topological Superconducting Pairing at Finite Excitation Energies
• Floquet topological phases with time-reversal and space inversion symmetries and dynamical detection of topological charges
• Mirror-symmetry protected higher-order topological zero-frequency boundary and corner modes in Maxwell lattices
• Realization of a three-dimensional quantum Hall effect in a Zeeman-induced second order topological insulator on a torus
• Hinge Majorana Flat Band in Type-II Dirac Semimetals
• Detecting Topological Superconductivity via Berry Curvature Effects in Spectral Functions
• Topological parafermion corner states in clock-symmetric non-Hermitian second-order topological insulator
• Finite-temperature topological invariant for higher-order topological insulators
• Tunable corner states in topological insulators with long-range hoppings and diverse shapes
• Multiple topological corner states in the continuum of extended kagome lattice
• Boundary topological insulators and superconductors of Altland-Zirnbauer tenfold classes
• Multi-locational Majorana Zero Modes
• Topological defect-mediated corner states and higher-order bulk topology in a two-dimensional crystalline insulator
• Quasiperiodic Quadrupole Insulators
• Surface theory of a second-order topological insulator beyond the Dirac approximation
• Perfectly localized Majorana corner modes in fermionic lattices
• Anomalous gapped boundaries between surface topological orders in higher-order topological insulators and superconductors with inversion symmetry
• Theory of Topological Superconductivity in Doped IV-VI Semiconductors
• Photonic Higher-Order Topological States Induced by Long Range Interactions
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
• Anisotropic transport properties in prismatic topological insulator nanowires
• Network model for magnetic higher-order topological phases
• Zeeman field induced corner states in the Kane-Mele-Hubbard model
• Interaction-Induced Higher-Order Topological Insulator via Floquet Engineering
• Extended Haldane model -- a modern gateway to topological insulators
• Higher-order topological superconductivity in type-II time-reversal-symmetric Weyl semimetals with a hybrid pairing
• Current switching behavior mediated via hinge modes in higher-order topological phases using altermagnets
• Tunable cornerlike states in topological type-II hyperbolic lattices
• Majorana Zero Modes and Topological Nature in Bi2Ta3S6-family Superconductors
• Symmetry-protected gates of Majorana qubits in a high-$T_c$ superconductor platform
• Fragile topological insulators protected by rotation symmetry without spin-orbit coupling
• Gapless States Localized along a Staircase Edge in Second-Order Topological Insulators
• Higher-order topological phases protected by noninvertible and subsystem symmetries
• Higher-order topological insulator in cubic semiconductor quantum wells
• Majorana bound states with chiral magnetic textures
• Higher-order topological quantum paramagnets
• Magnetic-Field Tunable Möbius and Higher-Order Topological Insulators in Three-Dimensional Layered Octagonal Quasicrystals
• Hinge modes of three-dimensional Euler insulators
• Coupled-wire construction of non-Abelian higher-order topological phases
• Topological energy pumping in a quasi-periodically driven four-level system
• Pseudospin-valley-coupled phononic topological insulator with edge and corner states
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases
• Majorana vortex phases in time-reversal invariant higher-order topological insulators and topologically trivial insulators
• Three-nodal surface phonons in solid-state materials: Theory and material realization