Quantized electric multipole insulators
TLDR
This work introduces a paradigm in which “nested” Wilson loops give rise to topological invariants that have been overlooked and opens a venue for the expansion of the classification of topological phases of matter.Abstract:
The Berry phase provides a modern formulation of electric polarization in crystals. We extend this concept to higher electric multipole moments and determine the necessary conditions and minimal models for which the quadrupole and octupole moments are topologically quantized electromagnetic observables. Such systems exhibit gapped boundaries that are themselves lower-dimensional topological phases. Furthermore, they host topologically protected corner states carrying fractional charge, exhibiting fractionalization at the boundary of the boundary. To characterize these insulating phases of matter, we introduce a paradigm in which “nested” Wilson loops give rise to topological invariants that have been overlooked. We propose three realistic experimental implementations of this topological behavior that can be immediately tested. Our work opens a venue for the expansion of the classification of topological phases of matter.read more
Citations
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Robust bulk states
TL;DR: In this paper, topologically robust zero energy bulk states in a disordered tight binding lattice were shown to be robust against any kind of disorder as long as the disordered Hamiltonian is noninvertible.
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Higher-order topological insulator phase in a modified Haldane model
TL;DR: In this article, the strength of the nearest-neighbor and next-nearest neighbor hopping terms is made unequal and the threefold rotational symmetry is broken by introducing a dimerization term in the Hamiltonian.
Posted Content
Acoustic Hierarchical Topological Insulators
TL;DR: In this paper, the hierarchical topological insulator (HOTI) was proposed, where topological Zak phases and quantized quadrupole polarization coexist in a hierarchical manner in a two-dimensional (2D) sonic crystal.
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Chirality polarizations and spectral bulk-boundary correspondence
Akito Daido,Youichi Yanase +1 more
TL;DR: In this paper, the spectral bulk-boundary correspondence in one-dimensional chiral symmetric systems was proved via Wannier functions and a formal proof by considering the adiabatic change of surface chirality charges.
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Ultrahigh-Q Fano resonance using topological corner modes in second-order pseudospin-Hall photonic systems
Kang-Hyok O,Kwang-Hyon Kim +1 more
TL;DR: In this article, a topological edge waveguide coupled to the cavity supporting the corner states was used to obtain ultrahigh-Q Fano resonances in photonic crystal structures supporting topologically protected corner states by coherent coupling.
References
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Maximally localized generalized Wannier functions for composite energy bands
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