Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

28.4K
Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
28.4K
Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

45.3K
Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
45.3K
Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

3.7K
Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
3.7K
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

8.6K
A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
8.6K
X-ray Crystallography02:18

X-ray Crystallography

24.5K
The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
24.5K
Structures of Solids02:22

Structures of Solids

15.9K
Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
15.9K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Fractional high-Chern insulator in twisted rhombohedral graphene.

Nature·2026
Same authorSame Topic

Stable real-space invariants and topology beyond symmetry indicators.

Nature communications·2026
Same author

Stoichiometric FeTe is a superconductor.

Nature·2026
Same author

Flat band induced quasi-one-dimensional magnon transport in a two-dimensional spin lattice.

Nature communications·2026
Same author

Regarding the existence of abelian fractional topological insulators in twisted MoTe<sub>2</sub> and related systems.

Communications physics·2026
Same author

Moiré enhanced flat band in rhombohedral graphene.

Nature materials·2025

Related Experiment Video

Updated: Oct 17, 2025

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
08:55

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Published on: June 7, 2018

8.7K

Dynamical symmetry indicators for Floquet crystals.

Jiabin Yu1, Rui-Xing Zhang2,3, Zhi-Da Song4

  • 1Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, MD, USA. jiabinyu@umd.edu.

Nature Communications
|October 14, 2021
PubMed
Summary

We developed a general theory for Floquet topology in crystalline systems, introducing dynamical symmetry indicators (DSIs) for efficient classification. This framework reveals numerous anomalous Floquet topological phases and a novel 3+1D topological insulator.

More Related Videos

Hyperspectral Imaging as a Tool to Study Optical Anisotropy in Lanthanide-Based Molecular Single Crystals
07:24

Hyperspectral Imaging as a Tool to Study Optical Anisotropy in Lanthanide-Based Molecular Single Crystals

Published on: April 14, 2020

17.8K
Microfluidic Chips for In Situ Crystal X-ray Diffraction and In Situ Dynamic Light Scattering for Serial Crystallography
11:48

Microfluidic Chips for In Situ Crystal X-ray Diffraction and In Situ Dynamic Light Scattering for Serial Crystallography

Published on: April 24, 2018

14.9K

Related Experiment Videos

Last Updated: Oct 17, 2025

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
08:55

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Published on: June 7, 2018

8.7K
Hyperspectral Imaging as a Tool to Study Optical Anisotropy in Lanthanide-Based Molecular Single Crystals
07:24

Hyperspectral Imaging as a Tool to Study Optical Anisotropy in Lanthanide-Based Molecular Single Crystals

Published on: April 14, 2020

17.8K
Microfluidic Chips for In Situ Crystal X-ray Diffraction and In Situ Dynamic Light Scattering for Serial Crystallography
11:48

Microfluidic Chips for In Situ Crystal X-ray Diffraction and In Situ Dynamic Light Scattering for Serial Crystallography

Published on: April 24, 2018

14.9K

Area of Science:

  • Condensed Matter Physics
  • Topological Matter
  • Quantum Dynamics

Background:

  • Topological phases in Floquet systems are linked to crystalline symmetries.
  • A universal theory for Floquet topology across all crystal symmetry groups is currently lacking.

Purpose of the Study:

  • To propose a general theory for Floquet topology in non-interacting Floquet crystals.
  • To develop computationally efficient methods for classifying these topological phases.

Main Methods:

  • Introduction of quotient winding data for classifying Floquet crystals.
  • Construction of dynamical symmetry indicators (DSIs) for identifying topological phases.
  • Application of the mathematical theory of monoids to compute DSI sets for plane groups.

Main Results:

  • Development of a computationally efficient theory for Floquet topology.
  • Identification of numerous nontrivial classifications, including first-order and higher-order 2+1D anomalous Floquet topological phases.
  • Discovery of a new 3+1D anomalous Floquet second-order topological insulator (AFSOTI) with anomalous chiral hinge modes.

Conclusions:

  • The proposed theory provides a unified framework for understanding Floquet topology in crystalline systems.
  • Dynamical symmetry indicators offer an efficient tool for classifying complex topological phases.
  • The discovery of new topological phases, including the AFSOTI, expands the landscape of topological matter.