Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices

Abstract

A second-order topological insulator in $d$ dimensions is an insulator which has no $d-1$ dimensional topological boundary states but has $d-2$ dimensional topological boundary states. It is an extended notion of the conventional topological insulator. Higher-order topological insulators have been investigated in square and cubic lattices. In this paper, we generalize them to breathing Kagome and pyrochlore lattices. First, we construct a second-order topological insulator on the breathing Kagome lattice. Three topological boundary states emerge at the corner of the triangle, realizing a 1/3 fractional charge at each corner. Second, we construct a third-order topological insulator on the breathing pyrochlore lattice. Four topological boundary states emerge at the corners of the tetrahedron with a 1/4 fractional charge at each corner. These higher-order topological insulators are characterized by the quantized polarization, which constitutes the bulk topological index. Finally, we study a second-order topological semimetal by stacking the breathing Kagome lattice.

arXiv comment5 pages, 7 figures, version accepted for publication in Phys. Rev. Lett

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• Disorder-induced delocalization and reentrance in a Chern-Hopf insulator
• Zeeman field induced corner states in the Kane-Mele-Hubbard model
• Theta electromagnetism in quantum spin ice: Microscopic analysis of improper symmetries
• Interaction-Induced Higher-Order Topological Insulator via Floquet Engineering
• Extended Haldane model -- a modern gateway to topological insulators
• Intrinsic higher-order topological states in 2D honeycomb Z_2 quantum spin Hall insulators
• Nonlinearity-induced corner states in a kagome lattice
• Modeling of a twisted-Kagome HoAgGe spin ice using Reduced-Configuration-Space Search and Density Functional Theory
• Current switching behavior mediated via hinge modes in higher-order topological phases using altermagnets
• Magnetic doping-induced second-order and first-order topological phase transition inthe photonic alloy
• Wilson Loop and Topological Properties in 3D Woodpile Photonic Crystal
• Higher-Order Topology in Monolayer FeSe
• Gapless States Localized along a Staircase Edge in Second-Order Topological Insulators
• When Wannier centers jump: Critical points between atomic insulating phases
• Nanoimprinted topological laser in the visible
• Analytic description of spin waves in dipolar/octupolar pyrochlore magnets
• Topological energy pumping in a quasi-periodically driven four-level system
• Topologically protected strong coupling and entanglement between distant quantum emitters
• Higher-order topological phases protected by noninvertible and subsystem symmetries
• Emergent One-Dimensional Helical Channel in Higher-Order Topological Insulators with Step Edges
• Higher-order topological phase induced by hybrid magneto-electric resonances
• Quantized edge magnetizations and their symmetry protection in one-dimensional quantum spin systems
• Topological Photonics on a Small Scale
• Three-nodal surface phonons in solid-state materials: Theory and material realization
• Electronic structure and hinge states of strained half-Heusler compounds LiSbZn and LiBiZn
• Floquet first- and higher-order topological superconductors: A review
• Higher-order topological insulator in cubic semiconductor quantum wells
• An all-dielectric photonic crystal with unconventional higher-order topology
• Topologically protected long-range coherent energy transfer
• Proposal for realizing and probing topological crystalline insulators in optical lattices
• Direct visualization of topological transitions and higher-order topological states in photonic metasurfaces
• Pseudospin-valley-coupled phononic topological insulator with edge and corner states
• Graphyne as a second-order and real Chern topological insulator in two dimensions
• Floquet second-order topological insulator in strained graphene
• Layer-number parity induced topological phase transition