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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Journal ArticleDOI
Optimization and robustness of the topological corner state in second-order topological photonic crystals
Xin Xie,Jianchen Dang,Sai Yan,Weixuan Zhang,Huiming Hao,Shan Xiao,Shushu Shi,Zhanchun Zuo,Haiqiao Ni,Zhichuan Niu,Xiangdong Zhang,Can Wang,Xiulai Xu +12 more
TL;DR: In this paper, the robustness of the topological corner state in the second-order topological photonic crystal with the 0D corner state was investigated both in theory and in experiment.
Journal ArticleDOI
Experimental demonstration of a reconfigurable acoustic second-order topological insulator using condensed soda cans array
Zichong Yue,Danwei Liao,Zhiwang Zhang,Wei Xiong,Ying Cheng,Ying Cheng,Xiaojun Liu,Xiaojun Liu +7 more
TL;DR: In this paper, a reconfigurable condensed acoustic second-order topological insulator in free space was demonstrated by using subwavelength soda cans whose side length was significantly reduced to 1.89 times of the corresponding wavelength.
Journal ArticleDOI
Quantum metric and correlated states in two-dimensional systems
TL;DR: In this article, the general connection between quantum metric and the properties of correlated states that break a continuous symmetry is discussed, and the specific case when the correlated state is a superfluid and show how the quantum metric is related to its superfluid stiffness.
Posted Content
Nanoscale topological corner states in nonlinear optics
TL;DR: In this article, the concept of topological corner states was brought to the nanoscale for enhancing nonlinear optical processes, and topologically nontrivial hybrid metasurfaces with C6-symmetric honeycomb lattices supporting both edge and corner states were designed.
Dissertation
Simulation and bulk detection of topological phases of matter
TL;DR: In this paper, the authors illustrati prima alcuni concetti teorici: i protocolli di quantum walk atti a simulare fasi topologiche della materia condensata in una e due dimensioni, and i metodi di misura per osservare sperimentalmente queste fasi, con un' enfasi particolare sulle misure di bulk.
References
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Journal ArticleDOI
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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