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Quadrupole

About: Quadrupole is a research topic. Over the lifetime, 14614 publications have been published within this topic receiving 261495 citations. The topic is also known as: quadrapole & electric quadrupole.


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Journal ArticleDOI
07 Jul 2017-Science
TL;DR: 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.

1,319 citations

Journal ArticleDOI
TL;DR: In this paper, a new classical empirical potential is proposed for water, which uses a polarizable atomic multipole description of electrostatic interactions, and a modified version of Thole's interaction model is used to damp induction at short range.
Abstract: A new classical empirical potential is proposed for water. The model uses a polarizable atomic multipole description of electrostatic interactions. Multipoles through the quadrupole are assigned to each atomic center based on a distributed multipole analysis (DMA) derived from large basis set molecular orbital calculations on the water monomer. Polarization is treated via self-consistent induced atomic dipoles. A modified version of Thole's interaction model is used to damp induction at short range. Repulsion−dispersion (vdW) effects are computed from a buffered 14−7 potential. In a departure from most current water potentials, we find that significant vdW parameters are necessary on hydrogen as well as oxygen. The new potential is fully flexible and has been tested versus a variety of experimental data and quantum calculations for small clusters, liquid water, and ice. Overall, excellent agreement with experimental and high level ab initio results is obtained for numerous properties, including cluster st...

1,315 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that rotational spin echoes provide a convenient means of studying very slow random molecular rotations (τc≲1 sec), which must be described by a proper average Hamiltonian theory.
Abstract: The NMR free induction decay from a spinning sample having inhomogeneous anisotropic interactions (chemical shifts, first order quadrupole couplings) takes the form of a train of rotational spin echoes. The Fourier transform of the echo envelope is a sharp spectrum from which the effects of anisotropy have been removed. The Fourier transform of the echo shape contains information concerning the anisotropies: This information can be extracted by a moment analysis. The effects of localized homonuclear spin–spin interactions are to convert the ’’isotropic’’ spectrum into a characteristic powder pattern. Second order quadrupole coupling produces a similar effect. It is shown in this case that the usual second‐order level shifts cannot be used to calculated this pattern, which must be described by a proper average Hamiltonian theory. Finally it is shown that rotational spin echoes provide a convenient means of studying very slow random molecular rotations (τc≲1 sec).

1,224 citations

Journal ArticleDOI
TL;DR: In this paper, the authors extend the theory of dipole moments in crystalline insulators to higher multipole moments, and describe the topological invariants that protect these moments.
Abstract: We extend the theory of dipole moments in crystalline insulators to higher multipole moments. In this paper, we expand in great detail the theory presented in Ref. 1, and extend it to cover associated topological pumping phenomena, and a novel class of 3D insulator with chiral hinge states. In quantum-mechanical crystalline insulators, higher multipole bulk moments manifest themselves by the presence of boundary-localized moments of lower dimension, in exact correspondence with the electromagnetic theory of classical continuous dielectrics. In the presence of certain symmetries, these moments are quantized, and their boundary signatures are fractionalized. These multipole moments then correspond to new SPT phases. The topological structure of these phases is described by "nested" Wilson loops, which reflect the bulk-boundary correspondence in a way that makes evident a hierarchical classification of the multipole moments. Just as a varying dipole generates charge pumping, a varying quadrupole generates dipole pumping, and a varying octupole generates quadrupole pumping. For non-trivial adiabatic cycles, the transport of these moments is quantized. An analysis of these interconnected phenomena leads to the conclusion that a new kind of Chern-type insulator exists, which has chiral, hinge-localized modes in 3D. We provide the minimal models for the quantized multipole moments, the non-trivial pumping processes and the hinge Chern insulator, and describe the topological invariants that protect them.

1,045 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023382
2022745
2021241
2020259
2019251
2018284