Topological classification of Higher-order topological phases with nested band inversion surfaces

Abstract

Higher-order topological phases (HOTPs) hold gapped bulk bands and topological boundary states localized in boundaries with codimension higher than one. In this paper, we provide a unified construction and topological characterization of HOTPs for the full Altland-Zirnbauer tenfold symmetry classes, based on a method known as nested band inversion surfaces (BISs). Specifically, HOTPs built on this method are decomposed into a series of subsystems, and higher-order topological boundary states emerges from the interplay of their first-order topology. Our analysis begins with a general discussion of HOTPs in continuous Hamiltonians for each symmetry class, then moves on to several lattice examples illustrating the topological characterization based on the nested-BIS method. Despite the example minimal models possessing several spatial symmetries, our method does not rely on any spatial symmetry, and can be easily extended into arbitrary orders of topology in dimensions. Furthermore, we extend our discussion to systems with asymmetric boundary states induced by two different mechanisms, namely, crossed BISs that break a ${\mathcal{C}}_4$ rotation symmetry, and non-Clifford operators that break certain chiral-mirror symmetries of the minimal models.

22 pages, 11 figures. Comments are welcome

References in corpus (23)

• Topological Field Theory of Time-Reversal Invariant 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
• Reflection symmetric second-order topological insulators and superconductors
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Observation of topological transitions in interacting quantum circuits
• Higher-Order Weyl Semimetals
• Higher-order Weyl Semimetals
• Topological Phase Transitions in Disordered Electric Quadrupole Insulators
• Chiral-Symmetric Higher-Order Topological Phases of Matter
• Field-Tunable One-Sided Higher-Order Topological Hinge States in Dirac Semimetals
• Reducing electronic transport dimension to topological hinge states by increasing geometry size of Dirac semimetal Josephson junctions
• Edge-Corner Correspondence: Boundary-Obstructed Topological Phases with Chiral Symmetry
• Coulomb instabilities of 3D higher-order topological insulators
• Direct dynamical characterization of higher-order topological insulators with nested band inversion surfaces
• Universal topological quench dynamics: Altland-Zirnbauer tenfold classes
• Topological insulating phases from two-dimensional nodal loop semimetals
• Constructing higher-order topological states in higher dimension
• Characterizing the weak topological properties: Berry phase point of view
• Engineering topological phases with a three-dimensional nodal-loop semimetal
• Topological nature of higher-order hinge states revealed by spin transport

Cited by in corpus (15)

• Activating non-Hermitian skin modes by parity-time symmetry breaking
• Klein-bottle quadrupole insulators and Dirac semimetals
• Unified characterization for higher-order topological phase transitions
• Generalization of Benalcazar-Bernevig-Hughes model to arbitrary dimensions
• Quantum quenches in a pseudo-Hermitian Chern insulator
• Intrinsic-perturbation induced anomalous higher-order boundary states in non-Hermitian systems
• Unveiling Higher-Order Topology via Polarized Topological Charges
• Hierarchical Topological States in Thermal Diffusive Networks
• Topologically compatible non-Hermitian skin effect
• Unconventional hybrid-order topological insulators
• Dynamical characterization of $Z_2$ Floquet topological phases via quantum quenches
• Dynamical characterization of topological phases beyond the minimal models
• Extrinsic higher-order topological corner states in AB-stacked transition-metal dichalcogenides
• Tunable symmetry-protected higher-order topological states with fermionic atoms in bilayer optical lattices
• Multiple topological corner states in the continuum of extended kagome lattice