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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Boundary edge networks induced by bulk topology
Yan-Qi Wang,Joel E. Moore +1 more
TL;DR: In this paper, the boundary topology of coupled edge states generated from various types of topological insulators is characterized using an effective edge network theory, which can faithfully predict properties such as the energy and fractional charge related to the bound states (edge solitons) in the aforementioned systems, including several aspects that were previously complicated or obscure.
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Time-reversal-invariant C 2 -symmetric higher-order topological superconductors
TL;DR: In this paper, a real-space criterion is proposed to diagnose higher-order topologies for time-reversal-invariant superconductors in two-dimensional space.
Journal ArticleDOI
Type-II quadrupole topological insulators
TL;DR: In this article, a quadrupole topological insulator with zero-energy corner modes and a pair of edge polarizations is presented, which can arise from quench dynamics in non-equilibrium systems.
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Second-Order Photonic Topological Corner States in Square Lattices with Low Symmetry
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Second-order topological phases in C 4v -symmetric photonic crystals beyond the two-dimensional Su-Schrieffer–Heeger model
Yafeng Chen,Zhihao Lan,Jie Zhu +2 more
TL;DR: In this article , second-order photonic topological insulators (SPTIs) with topologically protected corner states were proposed in C 4v -symmetric lattices.
References
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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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