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Related Concept Videos

Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

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...
Divergence and Curl of Electric Field01:25

Divergence and Curl of Electric Field

The divergence of a vector is a measure of how much the vector spreads out (diverges) from a point. For example, an electric field vector diverges from the positive charge and converges at the negative charge. The divergence of an electric field is derived using Gauss's law and is equal to the charge density divided by the permittivity of space. Mathematically, it is expressed as
Divergence and Curl of Magnetic Field01:26

Divergence and Curl of Magnetic Field

The magnetic field due to a volume current distribution given by the Biot–Savart Law can be expressed as follows:
Gauss's Law in Dielectrics01:17

Gauss's Law in Dielectrics

Consider a polar dielectric placed in an external field. In such a dielectric, opposite charges on adjacent dipoles neutralize each other, such that the net charge within the dielectric is zero. When a polar dielectric is inserted in between the capacitor plates, an electric field is generated due to the presence of net charges near the edge of the dielectric and the metal plates interface. Since the external electrical field merely aligns the dipoles, the dielectric as a whole is neutral. An...
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
Magnetic Vector Potential01:15

Magnetic Vector Potential

In electrostatics, the electric field can be written as the negative gradient of the potential. In magnetostatics, the zero divergence of the magnetic field ensures that the magnetic field can be expressed as the curl of a vector potential. This potential is known as the magnetic vector potential.
Consider an ideal solenoid with n turns per unit length and radius R. If I is the current through the solenoid, the magnetic field inside the solenoid is expressed as the product of vacuum...

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Related Experiment Video

Updated: Jul 4, 2026

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices
11:24

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices

Published on: July 11, 2025

Graphene with geometrically induced vorticity.

Jiannis K Pachos1, Michael Stone, Kristan Temme

  • 1School of Physics and Astronomy, University of Leeds, Leeds, United Kingdom. j.k.pachos@leeds.ac.uk

Physical Review Letters
|June 4, 2008
PubMed
Summary

Graphene

Area of Science:

  • Condensed matter physics
  • Materials science
  • Quantum mechanics

Background:

  • Graphene's electronic structure at half filling is described by Dirac fermions.
  • Geometrically induced gauge fields can alter hopping matrix elements.

Purpose of the Study:

  • To demonstrate that Kekulé modulation in graphene can lead to a nonreal Higgs field.
  • To explore the implications for fractionally charged vortices and localized zero modes.
  • To investigate low-lying states in fullerene-like molecules.

Main Methods:

  • Explicit demonstration of the correspondence between Kekulé modulation and Higgs field.
  • Application of the index theorem for fullerene-like molecules.

Main Results:

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Synthesis of Graphene Nanofluids with Controllable Flake Size Distributions
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Synthesis of Graphene Nanofluids with Controllable Flake Size Distributions

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Fabrication of Three-Dimensional Graphene-Based Polyhedrons via Origami-Like Self-Folding
14:52

Fabrication of Three-Dimensional Graphene-Based Polyhedrons via Origami-Like Self-Folding

Published on: September 23, 2018

Related Experiment Videos

Last Updated: Jul 4, 2026

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices
11:24

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices

Published on: July 11, 2025

Synthesis of Graphene Nanofluids with Controllable Flake Size Distributions
07:32

Synthesis of Graphene Nanofluids with Controllable Flake Size Distributions

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Fabrication of Three-Dimensional Graphene-Based Polyhedrons via Origami-Like Self-Folding
14:52

Fabrication of Three-Dimensional Graphene-Based Polyhedrons via Origami-Like Self-Folding

Published on: September 23, 2018

  • Kekulé modulation corresponds to a nonreal Higgs field with vorticity.
  • This setting naturally produces fractionally charged vortices with localized zero modes.
  • Six low-lying states in fullerene-like molecules are found to be largely independent of the mass gap.

Conclusions:

  • The study reveals a connection between geometric modulation and topological phenomena in graphene.
  • Fractionally charged vortices and localized zero modes are predicted.
  • The robustness of certain electronic states in fullerene-like molecules is established.