Second-order topological phases protected by chiral symmetry

Abstract

We study second-order topological insulators and semimetals characterized by chiral symmetry. We investigate topological phase transitions of a model for construction of the two-dimensional second-order topological insulators protected only by chiral symmetry. By the theory of the phase transitions, we propose a second-order topological semimetal and insulators with flat hinge bands in chiral-symmetric three-dimensional systems. The three-dimensional second-order topological phases can be obtained from the stacked two-dimensional second-order topological insulators with chiral symmetry. Moreover, we show that broken chiral symmetry in the three-dimensional second-order topological phase allows a second-order topological insulator with chiral hinge states. We also demonstrate the second-order topological phases by using a lattice model.

arXiv comment9 pages, 5 figures

References in corpus (72)

• Classification of topological insulators and superconductors in three spatial dimensions
• Classification of topological quantum matter with symmetries
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Quantized Electric Multipole Insulators
• Higher-Order Topological Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Topolectrical circuit realization of topological corner modes
• Reflection symmetric second-order topological insulators and superconductors
• Observation of a phononic quadrupole topological insulator
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Higher-Order Topology in Bismuth
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems
• Topolectrical circuits
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Novel Topological Phase with Zero Berry Curvature
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Failure of Nielsen-Ninomiya theorem and fragile topology in two-dimensional systems with space-time inversion symmetry: application to twisted bilayer graphene at magic angle
• Elastic higher-order topological insulator with topologically protected corner states
• Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides XTe${}_2$ (X=Mo,W)
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Majorana corner modes in a high-temperature platform
• Symmetry indicators and anomalous surface states of topological crystalline insulators
• Surface State Magnetization and Chiral Edge States on Topological Insulators
• Band Topology and Linking Structure of Nodal Line Semimetals with Z2 Monopole Charges
• High-Temperature Majorana Corner States
• Higher Order Topological Phases: A General Principle of Construction
• Weak-Pairing Higher Order Topological Superconductors
• Helical Topological Edge States in a Quadrupole Phase
• Majorana Kramers pairs in higher-order topological insulators
• Higher-order topological insulators protected by inversion and rotoinversion symmetries
• Protected boundary states in gapless topological phases
• An anomalous higher-order topological insulator
• Topological Quadrupolar Semimetals
• Minimal model for higher-order topological insulators and phosphorene
• Tunable Majorana corner states in a two-dimensional second-order topological superconductor induced by magnetic fields
• Majorana corner states in a two-dimensional magnetic topological insulator on a high-temperature superconductor
• Unified theory of PT and CP invariant topological metals and nodal superconductors
• Wallpaper Fermions and the Nonsymmorphic Dirac Insulator
• Helical Hinge Majoranas in Iron-Based Superconductors
• Band structure engineering and reconstruction in electric circuit networks
• Lattice models with exactly solvable topological hinge and corner states
• Topological switch between second-order topological insulators and topological crystalline insulators
• Topological insulators in magnetic fields: Quantum Hall effect and edge channels with non-quantized θ-term
• Higher-order Floquet topological phases with corner and bulk bound states
• Coupled-wire construction of static and Floquet second-order topological insulators
• Magnetic second-order topological insulators and semimetals
• Second-order Dirac superconductors and magnetic field induced Majorana hinge modes
• Topological crystalline superconductivity and second-order topological superconductivity in nodal-loop materials
• Connecting higher-order topological insulators to lower-dimensional topological insulators
• Fragile Topology Protected by Inversion Symmetry: Diagnosis, Bulk-Boundary Correspondence, and Wilson Loop
• Proximity-induced Majorana hinge modes in antiferromagnetic topological insulators
• The Axion Insulator as a Pump of Fragile Topology
• Topological superfluid 3He-B in magnetic field and Ising variable
• Edge-of-edge States
• Higher-order topological superconductivity: possible realization in Fermi gases and Sr${}_2$RuO${}_4$
• Fractionalization in a square-lattice model with time-reversal symmetry
• Three-dimensional superconductors with hybrid higher order topology
• Unconventional topological phase transition in two-dimensional systems with space-time inversion symmetry
• Simple model for second-order topological insulators and loop-nodal semimetals in Transition Metal Dichalcogenides XTe${}_2$ (X=Mo,W)
• Strong and weak second-order topological insulators with hexagonal symmetry and ${\mathbb{Z}}_3$ index
• Inversion-symmetry protected chiral hinge states in stacks of doped quantum Hall layers
• Direct prediction of corner state configurations from edge winding numbers in 2D and 3D chiral-symmetric lattice systems
• Topological invariants and corner states for Hamiltonians on a three-dimensional lattice
• Entanglement polarization for the topological quadrupole phase
• Interaction driven surface Chern insulator in nodal line semimetals
• Classification of accidental band crossings and emergent semimetals in two-dimensional noncentrosymmetric systems
• Toeplitz operators on concave corners and topologically protected corner states
• Zero-Energy State Localized near an Arbitrary Edge in Quadrupole Topological Insulators

Cited by in corpus (52)

• Second-order topological non-Hermitian skin effects
• Topological Phase Transitions in Disordered Electric Quadrupole Insulators
• Non-Hermitian second-order skin and topological modes
• Higher-order Topological Anderson Insulators
• Square-root higher-order topological insulator on a decorated honeycomb lattice
• Higher-Order topological insulator in a dodecagonal quasicrystal
• General corner charge formula in two-dimensional C_n-symmetric higher-order topological insulators
• Experimental identification of the second-order non-Hermitian skin effect with physics-graph-informed machine learning
• Higher-order topological insulators and semimetals in generalized Aubry-André-Harper models
• Floquet second-order topological insulators in non-Hermitian systems
• Non-Bloch bands in two-dimensional non-Hermitian systems
• Higher-order topological insulators in hyperbolic lattices
• Helical Liquids in Semiconductors
• Higher-order topology in monolayer graphene
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Topological States in Generalized Electric Quadrupole Insulators
• A Higher-Order Topological Insulator Phase in a Modulated Haldane Model
• Higher-order topological Anderson insulators in quasicrystals
• Bulk-edge and bulk-hinge correspondence in inversion-symmetric insulators
• Anatomy of open-boundary bulk in multiband non-Hermitian systems
• Bulk-boundary correspondence in disordered higher-order topological insulators
• Appearance of hinge states in second-order topological insulators via the cutting procedure
• Theory of inversion-${\mathbb{Z}}_4$ protected topological chiral hinge states and its applications to layered antiferromagnets
• Klein-bottle quadrupole insulators and Dirac semimetals
• Mirror-symmetry-protected dynamical quantum phase transitions in topological crystalline insulators
• Density-driven higher-order topological phase transitions in amorphous solids
• Detecting Bulk Topology of Quadrupolar Phase from Quench Dynamics
• Generalization of Benalcazar-Bernevig-Hughes model to arbitrary dimensions
• Universal Higher-Order Topology from 5D Weyl semimetal: Edge topology, edge Hamiltonian and nested Wilson loop
• Out of equilibrium chiral higher order topological insulator on a $\pi$-flux square lattice
• Wannier Topology and Quadrupole Moments for a generalized Benalcazar-Bernevig-Hughes Model
• Rotoinversion-symmetric bulk-hinge correspondence and its applications to higher-order Weyl semimetals
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- Part I: Chiral number of zero-modes
• General theory for infernal points in non-Hermitian systems
• Unveiling Higher-Order Topology via Polarized Topological Charges
• Fractional second-order topological insulator from a three-dimensional coupled-wires construction
• Hierarchical Topological States in Thermal Diffusive Networks
• Classification of topological invariants related to corner states
• Effects of first- and second-order topological phases on equilibrium crystal shapes
• Higher-order topological superconductor phases in a multilayer system
• An index theorem for quarter-plane Toeplitz operators via extended symbols and gapped Invariants related to corner states
• Anisotropic Penetration Depths of Corner States in a Higher-Order Topological Insulator
• Hermitian and non-Hermitian topology in active matter
• Tunable cornerlike states in topological type-II hyperbolic lattices
• Gapless States Localized along a Staircase Edge in Second-Order Topological Insulators
• Higher order topology in a Creutz ladder
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
• The Quadrupole Moment of Higher-Order Topological Insulator at Finite temperature
• Coupled-wire construction of non-Abelian higher-order topological phases
• Wilson loop invariants and bulk-boundary correspondence in higher-order topological insulators with two anticommuting mirror symmetries
• Boundary Condition Analysis of First and Second Order Topological Insulators
• Hinge modes of three-dimensional Euler insulators