Theory in Materials Science

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Theory in Materials Science

• 5th lecture
• Theory of the electron gas

Associate Professor Koichi Kusakabe
Graduate School of Engineering Science, Osaka
University
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Atomic defects in a carbon nanotube

• A. Hashimoto, K. Suenaga, A. Gloter, K. Urita
  S. Iijima, Nature 430, 870 - 873 (2004).

How does electrons far from the defect know
existence of the defect?
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Inter-electron interaction in a diagram
A Feynman diagram for a perturbation process
A quantum mechanical interaction process is
described by a diagram.
interaction
A propagating wave
At a glance, we notice that the interaction
between electrons is inevitable for the
description of electron systems.
But, the electrons in materials act as free
particles!
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Reasons why we can neglect effects of Coulomb
interaction in the lowest order.

• Screening effects
• Long life times of quasi-particle excitations due
  to the Pauli exclusion principle
• Lets search for the visible explanation on these
  concepts.

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Electron screening
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Interaction in terms of density fluctuation
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A relation between Q and r
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Dielectric function
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A mean field approach
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RPA dielectric function
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Screened potentials
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Polarization function of the electron gas
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The Lindhard function
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The Yukawa screened potential
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The plasma oscillation
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Freezing of long wave-length fluctuation