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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Orbital corner states on breathing kagome lattices
TL;DR: In this article, the existence of a different class of orbital corner states is demonstrated on the (zero-dimensional) finite-size triangular structure, and the orbital configurations of the corner states are also explored and rich orbital orders are identified.
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Higher-Order Topology of Three-Dimensional Strong Stiefel-Whitney Insulators
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Floquet higher-order Weyl and nexus semimetals
TL;DR: In this article, the authors report the general design and characterization of two exotic, anomalous nonequilibrium topological phases, namely, higher-order Weyl semimetals and Floquet higher order nexus semometals, where the concerned topological singularities in the three-dimensional Brillouin zone border anomalous two-dimensional higher order Floquet phases.
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Zoology of non-Hermitian spectra and their graph topology
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TL;DR: The graph configuration of complex spectra are characterized by the algebraic structures of their corresponding energy dispersions, drawing new intimate links between combinatorial graph theory, algebraic geometry and non-Hermitian band topology as mentioned in this paper .
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Universal higher-order topology from a five-dimensional Weyl semimetal: Edge topology, edge Hamiltonian, and a nested Wilson loop
Koji Hashimoto,Yoshinori Matsuo +1 more
TL;DR: In this article, it was shown that the 5D Weyl semimetals, upon dimensional reduction, lead to universal higher-order topology, and that the topological structure is identical to that of a Wilson loop of a Dirac monopole.
References
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New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance
TL;DR: In this article, the Hall voltage of a two-dimensional electron gas, realized with a silicon metal-oxide-semiconductor field effect transistor, was measured and it was shown that the Hall resistance at particular, experimentally well-defined surface carrier concentrations has fixed values which depend only on the fine-structure constant and speed of light, and is insensitive to the geometry of the device.
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Maximally localized generalized Wannier functions for composite energy bands
Nicola Marzari,David Vanderbilt +1 more
TL;DR: In this paper, a method for determining the optimally localized set of generalized Wannier functions associated with a set of Bloch bands in a crystalline solid is presented, which is suitable for use in connection with conventional electronic-structure codes.
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Theory of polarization of crystalline solids
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