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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Fractional chiral hinge insulator
Anna Hackenbroich,Ana Hudomal,Ana Hudomal,Norbert Schuch,B. Andrei Bernevig,Nicolas Regnault,Nicolas Regnault +6 more
TL;DR: In this paper, a wave function describing an interacting three-dimensional fractional chiral hinge insulator (FCHI) constructed by Gutzwiller projection of two noninteracting second-order topological insulators was proposed.
Posted Content
Non-Hermitian physics without gain or loss: the skin effect of reflected waves.
TL;DR: In this paper, the authors introduce an alternative avenue to the realm of non-Hermitian physics, which involves neither gain nor loss, and show that for any strong topological insulator in a Wigner-Dyson class, the reflected waves are characterized by a reflection matrix exhibiting the non-hermitian skin effect.
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Higher-order topological phases in tunable $C_3$-symmetric photonic crystals
TL;DR: In this paper, the authors demonstrate that multiple higher-order topological transitions can be triggered via the continuous change of the geometry in kagome photonic crystals composed of three dielectric rods.
Journal ArticleDOI
Generalized Lieb-Schultz-Mattis theorem on bosonic symmetry protected topological phases
TL;DR: In this paper, a family of generalized Lieb-Schultz-Mattis (LSM) theorems for symmetry protected topological (SPT) phases on boson/spin models in any dimensions is presented.
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Aspects of Topological Superconductivity in 2D Systems: Noncollinear Magnetism, Skyrmions, and Higher-order Topology
TL;DR: In this article, a review of topological superconductivity in the absence of spin-orbit interaction in two-dimensional systems with long-range noncollinear spin ordering or magnetic skyrmions is presented.
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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Quantized Hall conductance in a two-dimensional periodic potential
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Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the 'Parity Anomaly'
TL;DR: A two-dimensional condensed-matter lattice model is presented which exhibits a nonzero quantization of the Hall conductance in the absence of an external magnetic field, and exhibits the so-called "parity anomaly" of (2+1)-dimensional field theories.
Journal ArticleDOI
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
TL;DR: It is shown that physically $\ensuremath{\Delta}P can be interpreted as a displacement of the center of charge of the Wannier functions.
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