Network model for magnetic higher-order topological phases

Abstract

We propose a network-model realization of magnetic higher-order topological phases (HOTPs) in the presence of the combined space-time symmetry $C_4\mathcal{T}$ -- the product of a fourfold rotation and time-reversal symmetry. We show that the system possesses two types of HOTPs. The first type, analogous to Floquet topology, generates a total of $8$ corner modes at $0$ or $\pi$ eigenphase, while the second type, hidden behind a weak topological phase, yields a unique phase with $8$ corner modes at $\pm \pi /2$ eigenphase (after gapping out the counterpropagating edge states), arising from the product of particle-hole and phase rotation symmetry. By using a bulk ${\mathbb{Z}}_4$ topological index ($Q$), we found both HOTPs have $Q=2$, whereas $Q=0$ for the trivial and the conventional weak topological phase. Together with a ${\mathbb{Z}}_2$ topological index associated with the reflection matrix, we are able to fully distinguish all phases. Our work motivates further studies on magnetic topological phases and symmetry protected $2\pi /n$ boundary modes, as well as suggests that such phases may find their experimental realization in coupled-ring-resonator networks.

References in corpus (71)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Topological Photonics
• Classification of topological quantum matter with symmetries
• Random-Matrix Theory of Quantum Transport
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological invariants of time-reversal-invariant band structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Quantum Spin Hall Effect
• Quantized Electric Multipole Insulators
• Imaging topological edge states in silicon photonics
• Higher-Order Topological Insulators
• Robust optical delay lines via topological protection
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Prediction and observation of the first antiferromagnetic topological insulator
• Altermagnetism: spin-momentum locked phase protected by non-relativistic symmetries
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Reflection symmetric second-order topological insulators and superconductors
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Higher-Order Topology in Bismuth
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Antiferromagnetic topological insulators
• The space group classification of topological band insulators
• Topological classification of crystalline insulators through band structure combinatorics
• Classical higher-order topological insulators
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Progress and prospects in magnetic topological materials
• Corner states of light in photonic waveguides
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Optical Resonator Analog of a Two-Dimensional Topological Insulator
• Classification of Topological Insulators and Superconductors
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Majorana corner modes in a high-temperature platform
• Magnetic Topological Quantum Chemistry
• Surface State Magnetization and Chiral Edge States on Topological Insulators
• High-Temperature Majorana Corner States
• Higher Order Topological Phases: A General Principle of Construction
• Weak-Pairing Higher Order Topological Superconductors
• Majorana Kramers pairs in higher-order topological insulators
• Higher-order topological insulators protected by inversion and rotoinversion symmetries
• Scattering theory of topological insulators and superconductors
• Minimal model for higher-order topological insulators and phosphorene
• Random Network Models and Quantum Phase Transitions in Two Dimensions
• Spin-split collinear antiferromagnets: a large-scale ab-initio study
• Measurement of a topological edge invariant in a microwave network
• Quantum Hall plateau transitions in disordered superconductors
• Thermal metal in network models of a disordered two-dimensional superconductor
• Higher order symmetry-protected topological states for interacting bosons and fermions
• Models for the integer quantum Hall effect: the network model, the Dirac equation, and a tight-binding Hamiltonian
• Higher-order Topological Mott Insulators
• Realization of Anomalous Floquet Insulators in Strongly-Coupled Nanophotonic Lattices
• Two-dimensional spin-filtered chiral network model for the Z_2 quantum spin-Hall effect
• Higher-order topological phases on fractal lattices
• Phase diagram of disordered higher-order topological insulator: A machine learning study
• Quantum and classical localisation, the spin quantum Hall effect and generalisations
• Point-Contact Conductances at the Quantum Hall Transition
• Observation of pi/2 modes in an acoustic Floquet system
• Higher-order topological band structures
• Phase rotation symmetry and the topology of oriented scattering networks
• `Unhinging' the surfaces of higher-order topological insulators and superconductors
• Subdimensional topologies, indicators and higher order phases
• Edge State, Band Topology, and Time Boundary Effect in the Fine-Grained Categorization of Chern Insulators
• Spin-directed network model for the surface states of weak three-dimensional ${\mathbb{Z}}_2^{}$ topological insulators
• Thermal metal-insulator transition in a helical topological superconductor
• Topological chiral modes in random scattering networks
• Quantum Hall network models as Floquet topological insulators
• Network model for higher-order topological phases
• Pfaffian invariant identifies magnetic obstructed atomic insulators

Cited by in corpus (1)

• Scattering theory of higher order topological phases