Unified characterization for higher-order topological phase transitions

Abstract

Higher-order topological phase transitions (HOTPTs) are associated with closing either the bulk energy gap (type-I) or boundary energy gap (type-II) without changing symmetry, and conventionally the both transitions are captured in real space and characterized separately. Here we propose a momentum-space topological characterization of the HOTPTs, which unifies the both types of topological transitions and enables a precise detection by quench dynamics. Our unified characterization is based on a novel correspondence between the mass domain walls on real-space boundaries and the higher-order band-inversion surfaces (BIS) which are characteristic interfaces in the momentum subspace. The topological transitions occur when momentum-space topological nodes, dubbed higher-order topological charges, cross the higher-order BISs after proper projection. Particularly, the bulk (boundary) gap closes when all (part of) topological charges cross the BISs, characterizing the type-I (type-II) HOTPTs. These distinct dynamical behaviours of higher-order topological charges can be feasibly measured from quench dynamics driven with control in experiments. Our work opens an avenue to characterize and detect the two types of HOTPTs within a unified framework, and shall advance the research in both theory and experiment.

8+15 pages, 3+7 figures; Discussions are updated. References are updated

References in corpus (28)

• 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
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Classical higher-order topological insulators
• Novel Topological Phase with Zero Berry Curvature
• Tools for quantum simulation with ultracold atoms in optical lattices
• Surface State Magnetization and Chiral Edge States on Topological Insulators
• Photonic Floquet topological insulators in a fractal lattice
• Topological Phase Transitions in Disordered Electric Quadrupole Insulators
• Hybrid-order topological insulators in a phononic crystal
• Chiral-Symmetric Higher-Order Topological Phases of Matter
• 3D hinge transport in acoustic higher-order topological insulators
• Edge-Corner Correspondence: Boundary-Obstructed Topological Phases with Chiral Symmetry
• Realization of Surface-Obstructed Topological Insulators
• Two-particle Berry phase mechanism for Dirac and Majorana Kramers pairs of corner modes
• Direct dynamical characterization of higher-order topological insulators with nested band inversion surfaces
• Higher-order topological phases emerging from the Su-Schrieffer-Heeger stacking
• Interaction Enabled Fractonic Higher-Order Topological Phases
• Topological classification of Higher-order topological phases with nested band inversion surfaces
• Universal topological quench dynamics: Altland-Zirnbauer tenfold classes
• Emergent topology under slow non-adiabatic quantum dynamics
• Engineering topological phases with a three-dimensional nodal-loop semimetal
• Dynamically characterizing topological phases by high-order topological charges
• Orbital shift-induced boundary obstructed topological materials with a large energy gap
• Generating many Majorana corner modes and multiple phase transitions in Floquet second-order topological superconductors
• Higher-order topological phase of interacting photon pairs
• Wannier band transitions in disordered $\pi$-flux ladders

Cited by in corpus (13)

• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Generalization of Benalcazar-Bernevig-Hughes model to arbitrary dimensions
• Generating many Majorana corner modes and multiple phase transitions in Floquet second-order topological superconductors
• Unveiling Higher-Order Topology via Polarized Topological Charges
• Direct demonstration of bulk-boundary correspondence in higher-order topological superconductors with chiral symmetry
• 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
• Multiple topological corner states in the continuum of extended kagome lattice
• Boundary topological insulators and superconductors of Altland-Zirnbauer tenfold classes
• Proposal for realizing and probing topological crystalline insulators in optical lattices
• Breakdown of the symmetry constraint in a Floquet topological insulator