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The de Broglie Wavelength02:32

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In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Electromagnetic waves can travel in the vacuum as well as in matter. For example light, which is an electromagnetic wave, can travel through air, water, or glass.
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The existence of combined electric and magnetic fields that propagate through space as electromagnetic (EM) waves is the most significant prediction of Maxwell's equations. As Maxwell's equations hold in free space, the predicted electromagnetic waves do not require a medium for their propagation. An EM wave comprises an electric field, defined as the force per charge on a stationary charge, and a magnetic field, which is the force per charge on a moving charge.
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Updated: Jun 27, 2025

Fabrication of Gate-tunable Graphene Devices for Scanning Tunneling Microscopy Studies with Coulomb Impurities
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Electron wave and quantum optics in graphene.

Himadri Chakraborti1, Cosimo Gorini1, Angelika Knothe2

  • 1Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette, France.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|May 2, 2024
PubMed
Summary
This summary is machine-generated.

Graphene electron optics offers superior control over electron behavior compared to traditional systems. This review explores graphene

Keywords:
electron opticsgraphenemagnetic focusingp-n junctionsquantum hall interferometersnake states

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Nanotechnology

Background:

  • Graphene offers unique electron optical properties surpassing conventional two-dimensional electron gases (2DEGs).
  • Its ultra-high mobilities and electrostatic control enable precise fabrication of p-n interfaces.
  • These interfaces host exotic states like snake states and are crucial for electron interferometers.

Purpose of the Study:

  • To provide a comprehensive review of graphene electron optics.
  • To cover theoretical background, fabrication methods, and simulation techniques.
  • To highlight novel physics and device architectures in graphene-based electron optics.

Main Methods:

  • Review of theoretical frameworks for graphene electron optics.
  • Discussion of fabrication techniques for graphene electron-optical devices.
  • Overview of numerical simulation methods for analyzing electron transport.

Main Results:

  • Graphene enables the creation of gapless p-n interfaces with high precision.
  • The Dirac spectrum and Berry phase in graphene lead to novel phenomena.
  • Ballistic transport experiments reveal unique physics in single and bilayer graphene devices.

Conclusions:

  • Graphene-based electron optics provides a new platform for advanced device architectures.
  • Further exploration of magnetic field effects in graphene nanostructures is crucial.
  • Graphene Mach-Zehnder and Fabry-Perot interferometers represent the state-of-the-art in the field.