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Related Concept Videos

Scaling01:26

Scaling

In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...
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The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect. According to this equation,...
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Related Experiment Video

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Fabrication of Gate-tunable Graphene Devices for Scanning Tunneling Microscopy Studies with Coulomb Impurities
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One-parameter scaling at the dirac point in graphene.

J H Bardarson1, J Tworzydło, P W Brouwer

  • 1Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands.

Physical Review Letters
|October 13, 2007
PubMed
Summary

This study numerically calculates graphene conductivity, finding it increases logarithmically with sample size, not reaching a scale-invariant limit, contrary to prior predictions for impurity scattering.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Quantum Mechanics

Background:

  • Graphene's conductivity is crucial for electronic applications.
  • Understanding conductivity scaling with sample size is key to predicting material behavior.
  • Previous theories suggested a fixed point for conductivity scaling in graphene.

Purpose of the Study:

  • To numerically calculate the conductivity of undoped graphene.
  • To investigate the scaling behavior of conductivity with sample size.
  • To determine the scaling function and analyze the scaling flow in the presence of impurity scattering.

Main Methods:

  • Numerical calculation of conductivity (sigma) for graphene sheets of varying size (L).
  • Analysis of one-parameter scaling for random impurity scattering.
  • Determination of the scaling function beta(sigma) = dlnsigma/dlnL.

Main Results:

  • Demonstrated one-parameter scaling for random impurity scattering in graphene.
  • Found no fixed point for the scaling flow (beta > 0) up to and beyond the symplectic metal-insulator transition.
  • Observed that conductivity at the Dirac point increases logarithmically with sample size, without reaching a scale-invariant limit.

Conclusions:

  • The study provides evidence for an alternative scaling flow in graphene conductivity.
  • Results contradict previous predictions of a fixed scaling point.
  • Logarithmic conductivity increase suggests unique size-dependent behavior in graphene without intervalley scattering.