Green's Function Approach to Interacting Higher-order Topological Insulators

Abstract

The Bloch wave functions have been playing a crucial role in the diagnosis of topological phases in non-interacting systems. However, the Bloch waves are no longer applicable in the presence of finite Coulomb interaction and alternative approaches are needed to identify the topological indices. In this paper, we focus on three-dimensional higher-order topological insulators protected by $C_{4}T$ symmetry and show that the topological index can be computed through eigenstates of inverse Green's function at zero frequency. If there is an additional $S_4$ rotoinversion symmetry, the topological index $P_3$ can be determined by eigenvalues of $S_4$ at high symmetry momenta, similar to the Fu-Kane parity criterion. We verify this method using many-body exact diagonalization in higher-order topological insulators with interaction. We also discuss the realization of this higher-order topological phase in tetragonal lattice structure with $C_{4}T$-preserving magnetic order. Finally, we discuss the boundary conditions necessary for the hinge states to emerge and show that these hinge states exist even when the boundary is smooth and without a sharp hinge.

References in corpus (67)

• Topological Insulators
• Topological insulators and superconductors
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Topological Insulators in Three Dimensions
• Topological Insulators with Inversion Symmetry
• Topological Field Theory of Time-Reversal Invariant Insulators
• Quantized Electric Multipole Insulators
• Higher-Order Topological Insulators
• Topological quantum chemistry
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• The (High Quality) Topological Materials In The World
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Reflection symmetric second-order topological insulators and superconductors
• Catalogue of Topological Electronic Materials
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• An equivalent expression of Z2 Topological Invariant for band insulators using Non-Abelian Berry's connection
• Acoustic higher-order topological insulator on a Kagome lattice
• Higher-Order Topology in Bismuth
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Towards ideal topological materials: Comprehensive database searches using symmetry indicators
• The Quantum-Mechanical Position Operator in Extended Systems
• Topological classification of crystalline insulators through band structure combinatorics
• The effects of interactions on the topological classification of free fermion systems
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• 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
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Symmetry indicators and anomalous surface states of topological crystalline insulators
• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Simplified topological invariants for interacting insulators
• Impurity Bound States and Greens Function Zeroes as Local Signatures of Topology
• 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
• An anomalous higher-order topological insulator
• Symmetry Enforced Chiral Hinge States and Surface Quantum Anomalous Hall Effect in Magnetic Axion Insulator ${\text{Bi}}_{2-x}{\text{Sm}}_x{\text{Se}}_3$
• Many-Body Electric Multipole Operators in Extended Systems
• Many-Body Order Parameters for Multipoles in Solids
• Magnetic second-order topological insulators and semimetals
• Second-order Dirac superconductors and magnetic field induced Majorana hinge modes
• Smooth gauge for topological insulators
• Connecting higher-order topological insulators to lower-dimensional topological insulators
• Many-body topological invariants for fermionic short-range entangled topological phases protected by antiunitary symmetries
• Symmetry representation approach to topological invariants in $C_{2z}T$-symmetric systems
• Topological invariants for interacting topological insulators with inversion symmetry
• Unified understanding of symmetry indicators for all internal symmetry classes
• Hierarchy of higher-order Floquet topological phases in three dimensions
• Strongly Correlated Topological Superconductors and Topological Phase Transitions via Green's Function
• Higher-order topological band structures
• Many-body Chern number without integration
• Hierarchy of higher-order topological superconductors in three dimensions
• Bulk invariants and topological response in insulators and superconductors with nonsymmorphic symmetries
• Splitting the hinge mode of higher-order topological insulators
• 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
• Filling anomaly for general 2D and 3D $C_4$ symmetric lattices
• Pfaffian formalism for higher-order topological insulators
• Coulomb instabilities of 3D higher-order topological insulators
• Many-Body Invariants for Chern and Chiral Hinge Insulators
• Topological insulators and higher-order topological insulators from gauge-invariant 1D lines
• Many-Body Quadrupolar Sum Rule for Higher-Order Topological Insulator

Cited by in corpus (7)

• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Effect of local Coulomb interaction on Majorana corner modes: weak and strong correlation limits
• Disorder-Induced Phase Transitions in Three-Dimensional Chiral Second-Order Topological Insulator
• Fractional second-order topological insulator from a three-dimensional coupled-wires construction
• Zeeman field induced corner states in the Kane-Mele-Hubbard model
• Interaction-Induced Higher-Order Topological Insulator via Floquet Engineering
• Fractional chiral second-order topological insulator from a three-dimensional array of coupled wires