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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Topological protection of photonic mid-gap defect modes
Jiho Noh,Wladimir A. Benalcazar,Sheng Huang,Matthew J. Collins,Kevin P. Chen,Taylor L. Hughes,Mikael C. Rechtsman +6 more
TL;DR: In this article, a topological invariant was proposed to topologically protect the mode frequency at mid-gap and minimize the volume of a photonic defect mode in a femtosecond-laser-written waveguide array.
Journal ArticleDOI
Quantization of fractional corner charge in C n -symmetric higher-order topological crystalline insulators
TL;DR: In this paper, the authors systematically studied charge fractionalization in higher-order topological insulators and showed that charge can be fractionally quantized in units of $e/n.
Journal ArticleDOI
All Magic Angles in Twisted Bilayer Graphene are Topological
Zhida Song,Zhijun Wang,Wujun Shi,Wujun Shi,Gang Li,Chen Fang,Chen Fang,B. Andrei Bernevig,B. Andrei Bernevig,B. Andrei Bernevig +9 more
TL;DR: In this paper, it was shown that the electronic structure of the low-energy bands in bilayer bilayer graphene consists of a series of semimetallic and topological phases, and that the gapped set of bands that exist around all magic angles have a nontrivial topology stabilized by a magnetic symmetry.
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Exploring 4D quantum Hall physics with a 2D topological charge pump.
Michael Lohse,Christian Schweizer,Christian Schweizer,Hannah M. Price,Oded Zilberberg,Immanuel Bloch,Immanuel Bloch +6 more
TL;DR: These findings pave the way to experimentally probing higher-dimensional quantum Hall systems, in which additional strongly correlated topological phases, exotic collective excitations and boundary phenomena such as isolated Weyl fermions are predicted.
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Visualization of Higher-Order Topological Insulating Phases in Two-Dimensional Dielectric Photonic Crystals
Biye Xie,Guangxu Su,Hong-Fei Wang,Hai Su,Xiaopeng Shen,Peng Zhan,Ming-Hui Lu,Zhenlin Wang,Yan-Feng Chen +8 more
TL;DR: It is experimentally demonstrated that second-order topological insulating phases without negative coupling can be realized in two-dimensional dielectric photonic crystals and provide a new mechanism for light manipulating in a hierarchical way.
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.
Journal ArticleDOI
Quantized Hall conductance in a two-dimensional periodic potential
TL;DR: In this article, the Hall conductance of a two-dimensional electron gas has been studied in a uniform magnetic field and a periodic substrate potential, where the Kubo formula is written in a form that makes apparent the quantization when the Fermi energy lies in a gap.
Journal ArticleDOI
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.
Journal ArticleDOI
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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